Simulation method and system for double-mode frequency tuning of double-slit caisson oscillating water column

Abstract

The application relates to the technical field of wave energy simulation, and discloses a double-slit caisson oscillating water column double-mode frequency tuning simulation method and system. The method comprises the following steps: establishing a two-degree-of-freedom dynamic equation group by taking a slit transmission coefficient as a parameter according to water column displacements of a front cavity and a rear cavity to obtain coupling stiffness; substituting the coupling stiffness into an eigenvalue equation to decompose two-cavity oscillation modes to obtain a modal transformation matrix and a modal amplitude ratio; performing convolution integral operation on the modal amplitude ratio and a target sea area wave power spectrum to obtain a first-order modal weight and a second-order modal weight; performing double-layer nested iteration on the slit transmission coefficient and the rear cavity volume by taking a preset target first-order modal weight as an outer layer convergence target and a preset target natural frequency as an inner layer convergence constraint to obtain an optimal slit width and an optimal rear cavity volume. The application solves the problem that in the prior art, the contribution proportion of each order modal energy is unobservable and un-designable, and the wave spectrum matching is mismatched.

Description

Technical Field

[0001] This application relates to the field of wave energy simulation technology, and in particular to a simulation method and system for dual-mode frequency tuning of oscillating water column in a double-slit caisson. Background Technology

[0002] Oscillating Water Column (OWC) wave energy conversion devices are devices that convert wave energy into electrical energy. Their basic principle is that waves excite a water column within a chamber to oscillate back and forth, driving airflow at the top of the chamber to oscillate back and forth through an air turbine generator. Integrating OWC devices into breakwater caisson structures is one of the main engineering forms for nearshore wave energy utilization. Double-slit caisson breakwaters divide the interior of the caisson into two coupled water spaces—a front cavity and a rear cavity—by setting two vertical slits on the front wall of the caisson. Studies have confirmed that this structure possesses two inherent oscillation modes: a first-order mode corresponding to low-frequency oscillations of the water columns in phase between the front and rear cavities, and a second-order mode corresponding to high-frequency oscillations of the water columns in opposite phases between the front and rear cavities. This dual-mode resonance characteristic gives the structure superior energy capture potential compared to single-cavity OWCs under broadband wave excitation.

[0003] Existing OWC dual-modal simulation studies of double-slit caissons are represented by the modal superposition method proposed by Iino et al. This approach involves offline identification of the natural frequencies and damping coefficients of the two modes through free attenuation flume experiments, followed by time-domain simulation using the identified parameters as fixed inputs to verify the agreement between the simulation results and the experimental time histories. This approach suffers from two fundamental shortcomings: First, the natural frequency parameters are fixed inputs after offline experimental identification, lacking an explicit parameterized mapping between structural parameters such as slot width and chamber volume and the modal natural frequencies. The simulation framework cannot serve as a design tool to output structural parameters. Second, existing research uses the correct position of the two resonant frequencies as the sole tuning objective, without defining or calculating the energy contribution ratio of each mode under the actual wave power spectrum excitation in the target sea area. This results in an uncontrollable situation where, even if the two resonant frequency positions are correctly set, the energy contribution of each mode under specific sea area wave spectrum conditions remains uncontrollable, completely ignoring the essential difference between correct frequency and reasonable energy distribution. Summary of the Invention

[0004] This application provides a simulation method and system for dual-mode frequency tuning of oscillating water column in a double-slit caisson. It solves the problems of lack of explicit mapping between gap geometry parameters and dual-mode frequencies in the existing double-slit caisson OWC simulation framework, and the inability to compensate for the real-time drift of the natural frequency linkage during the adjustment process. It also solves the problem of unobservable and undesignable energy contribution ratios of each mode in the prior art, which leads to spectral mismatch.

[0005] In a first aspect, this application provides a simulation method for dual-mode frequency tuning of oscillating water column in a double-slit caisson, the simulation method comprising: Step S1: Based on the displacement of the water column in the front cavity and the displacement of the water column in the rear cavity, establish a two-degree-of-freedom dynamic equation system with the slit transmission coefficient as the parameter to obtain the coupling stiffness. Step S2: Substitute the coupling stiffness into the eigenvalue equation to decompose the two-cavity oscillation modes and obtain the mode transformation matrix and mode amplitude ratio; Step S3: Substitute the modal amplitude ratio and the wave power spectrum of the target sea area into the modal frequency response function, and obtain the first-order modal weights and second-order modal weights by convolution integral operation of the wave power spectrum and the square of the modal frequency response function. Step S4: Using the preset target first-order modal weight as the outer convergence target and the preset target natural frequency as the inner convergence constraint, perform a double-layer nested iterative solution for the slit transmission coefficient and the back cavity volume. The outer layer adjusts the slit transmission coefficient to make the first-order modal weight converge to the target first-order modal weight, and the inner layer adjusts the back cavity volume to compensate for the natural frequency drift caused by the change in the slit transmission coefficient, thereby obtaining the optimal slit width and the optimal back cavity volume.

[0006] Secondly, this application provides a dual-mode frequency tuning simulation system for a double-slit caisson oscillating water column, the dual-mode frequency tuning simulation system comprising: The analysis module is used to establish a two-degree-of-freedom dynamic equation system based on the displacement of the water column in the front cavity and the displacement of the water column in the rear cavity, with the slit transmission coefficient as a parameter, and to obtain the coupling stiffness. The decomposition module is used to substitute the coupling stiffness into the eigenvalue equation to decompose the two-cavity oscillation modes and obtain the mode transformation matrix and mode amplitude ratio. The calculation module is used to substitute the modal amplitude ratio and the wave power spectrum of the target sea area into the modal frequency response function, and obtain the first-order modal weight and the second-order modal weight by performing a convolution integral operation on the wave power spectrum and the square of the modal frequency response function. The solution module is used to perform a double-layer nested iterative solution on the slit transmission coefficient and the back cavity volume, with a preset target first-order modal weight as the outer convergence target and a preset target natural frequency as the inner convergence constraint. The outer layer adjusts the slit transmission coefficient to make the first-order modal weight converge to the target first-order modal weight, and the inner layer adjusts the back cavity volume to compensate for the natural frequency drift caused by the change in the slit transmission coefficient, so as to obtain the optimal slit width and the optimal back cavity volume.

[0007] Thirdly, a dual-mode frequency tuning simulation device for a double-slit caisson oscillating water column is provided, comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor calls the instructions in the memory to cause the dual-mode frequency tuning simulation device for the double-slit caisson oscillating water column to execute the above-described dual-mode frequency tuning simulation method for the double-slit caisson oscillating water column.

[0008] Fourthly, a computer-readable storage medium is provided, wherein instructions are stored therein, which, when executed on a computer, cause the computer to perform the above-described simulation method for dual-mode frequency tuning of a double-slit caisson oscillating water column.

[0009] In the technical solution provided in this application, a two-degree-of-freedom dynamic equation system is established using the gap transmission coefficient as a parameter to obtain the coupling stiffness. The gap width and gap draft, two directly measurable geometric quantities, are explicitly embedded into the dynamic model through the transmission coefficient conversion relationship. This makes the coupling stiffness no longer a fixed input constant after offline experimental identification, but a parameterized quantity that continuously varies with the gap geometric parameters, fundamentally opening up the calculation channel between structural geometric design parameters and dual-mode dynamic characteristics. Based on this, the coupling stiffness is substituted into the eigenvalue equation to decompose the two-cavity oscillation modes, obtaining the mode transformation matrix and mode amplitude ratio. The mode transformation matrix transforms the mutually coupled front and rear cavity displacements in the physical coordinate system into two independent oscillation equations in the modal coordinate system, achieving complete decoupling of the first-order in-phase mode and the second-order out-of-phase mode in mathematical structure. This creates the preconditions for subsequent independent tuning operations on individual modes. This decoupling operation has never been used as a design method in the existing double-slit caisson OWC simulation framework. Furthermore, by substituting the modal amplitude ratio and the wave power spectrum of the target sea area into the modal frequency response function, the first-order modal weights and second-order modal weights are obtained through the convolution integral operation of the wave power spectrum and the square of the modal frequency response function. This convolution integral operation quantitatively couples the frequency distribution of actual sea area wave energy with the frequency selective response of each mode within the same integral framework, making the energy contribution ratio of each mode under real wave excitation a calculable and measurable numerical quantity for the first time. This makes up for the fundamental defect of existing technologies that only take the resonance peak frequency position as the tuning target and ignore the rationality of modal energy distribution.

[0010] The double-layer nested iterative solution uses a preset target first-order modal weight as the outer convergence objective and a preset target natural frequency as the inner convergence constraint to jointly solve for the gap transmission coefficient and the rear cavity volume. The outer iteration utilizes the monotonically reversible mapping relationship between the gap transmission coefficient and the first-order modal weight, searching for the gap transmission coefficient that satisfies the target value of the modal weight within the allowable range of the structure using a bisection method. The inner iteration addresses the natural frequency drift that inevitably occurs during the adjustment of the gap transmission coefficient by adjusting the gas volume in the rear cavity to change the aeroelastic stiffness of the rear cavity to compensate for the drift in real time, and uses the Newton-Raphson iteration method to quickly converge to the rear cavity volume that satisfies the target natural frequency. The two iterations are executed alternately and mutually correct each other, ultimately satisfying both the modal weight target and the natural frequency constraint, and outputting the optimal gap width and optimal rear cavity volume. This upgrades the simulation output from the verification frequency response curve in the existing technology to a combination of structural parameters directly oriented towards engineering implementation, realizing a complete computational closed loop from spectral analysis to structural design parameters. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a schematic diagram of an embodiment of the simulation method for dual-mode frequency tuning of oscillating water column in a double-slit caisson in this application. Figure 2 This is a schematic diagram of the double-nested iterative convergence process in an embodiment of this application, wherein, Figure 2 (a) is a schematic diagram of the curves showing the convergence of the first-order modal weights to the target first-order modal weights with the number of iterations in the outer iteration. Figure 2 (b) is a schematic diagram of the curve of the first-order natural angular frequency converging to the target natural frequency with the number of iterations in the inner iteration. Detailed Implementation

[0013] This application provides a simulation method and system for dual-mode frequency tuning of a double-slit caisson oscillating water column. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0014] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the simulation method for dual-mode frequency tuning of oscillating water column in a double-slit caisson in this application includes: Step S1: Based on the displacement of the water column in the front cavity and the displacement of the water column in the rear cavity, establish a two-degree-of-freedom dynamic equation system with the slit transmission coefficient as the parameter to obtain the coupling stiffness. Specifically, the slot transmission coefficient is a dimensionless parameter describing the degree of water flow between the front and rear cavities through the two slot walls of the double-slotted caisson. Its value is determined by dividing the slot width by the sum of the products of the slot width, the slot shape correction coefficient, and the slot draft. The shape correction coefficient for rectangular cross-section slots is taken as 0.42, and this value is determined by the analytical solution of the potential flow around the slot rather than empirical estimation. The coupling stiffness is an equivalent stiffness parameter characterizing the intensity of fluid pressure transmission between the front and rear cavities. Its value is proportional to the quotient of the square of the slot transmission coefficient and the square of the difference between the two slot transmission coefficients, multiplied by the seawater density, gravitational acceleration, and the effective permeable area of ​​the slot. This relationship directly embeds the slot geometric parameters into the dynamic equation, making the slot width an adjustable physical quantity for subsequent double-layer nested iterations. The damping term adopts a velocity square proportional nonlinear form instead of a nonlinear damping ratio form because the fluid resistance at the slots of the double-slotted caisson is dominated by orifice resistance, and its dissipated power is proportional to the square of the velocity. A linear damping form would cause the attenuation time history to deviate from the measured data.

[0015] Step S2: Substitute the coupling stiffness into the eigenvalue equation to decompose the two-cavity oscillation modes and obtain the mode transformation matrix and mode amplitude ratio; Specifically, the modal amplitude ratio is a parameter describing the ratio between the amplitude of the rear chamber water column and the amplitude of the front chamber water column under a certain oscillation mode. The first-order modal amplitude ratio is positive, corresponding to the low-frequency mode of in-phase oscillation of the sea-side and land-side water columns; the second-order modal amplitude ratio is negative, corresponding to the high-frequency mode of out-of-phase oscillation of the sea-side and land-side water columns. The modal transformation matrix is ​​composed of the first-order and second-order modal amplitude ratios arranged in column vector form. Its function is to transform the two generalized coordinates of the front chamber water column displacement and the rear chamber water column displacement, which are coupled in physical space, into independent first-order and second-order modal coordinates in the modal coordinate system, thereby decoupling the equations of the two oscillation modes and allowing them to be solved independently.

[0016] Step S3: Substitute the modal amplitude ratio and the wave power spectrum of the target sea area into the modal frequency response function, and obtain the first-order modal weights and second-order modal weights by convolution integral operation of the wave power spectrum and the square of the modal frequency response function. Specifically, the modal weighting coefficient is a self-created physical quantity in this invention, defined as the ratio of the contribution of a certain mode to the root mean square of the total gas volume flow rate in the chamber to the sum of the contributions of all modes under the excitation of the wave power spectrum in the target sea area. The sum of the weights of the first and second modes is always one. The wave power spectrum in the target sea area adopts the JONSWAP spectrum, with the peak frequency and peak rise factor as inputs. The numerical integration interval is taken as half to three times the peak frequency, and the integration step size is 0.01 radians per second. The step size is set based on ensuring that the frequency resolution is sufficient to accurately capture the spectral area of ​​the two resonance peaks within this interval, while controlling the computational load. The physical meaning of the convolution integral operation is to multiply and integrate the amplitude-frequency characteristic of the modal frequency response function with the actual wave energy distribution to obtain the energy contribution of the mode under the actual sea state excitation, rather than simply examining whether the resonance peak frequency position is correct.

[0017] Step S4: Using the preset target first-order mode weight as the outer convergence target and the preset target natural frequency as the inner convergence constraint, perform a double-layer nested iterative solution for the slit transmission coefficient and the back cavity volume. The outer layer adjusts the slit transmission coefficient to make the first-order mode weight converge to the target first-order mode weight, and the inner layer adjusts the back cavity volume to compensate for the natural frequency drift caused by the change in the slit transmission coefficient, thus obtaining the optimal slit width and the optimal back cavity volume.

[0018] It should be noted that the target natural frequencies are the design values ​​of the first-order and second-order natural angular frequencies pre-set according to the peak frequency of the wave power spectrum of the target sea area. These are used to match the first-order and second-order natural oscillation frequencies of the double-slit caisson structure with the frequency range where wave energy is concentrated in the target sea area. The target first-order mode weight is the design value of the proportion of first-order mode energy contribution pre-set according to the engineering design requirements for broadband wave energy capture in the target sea area. This is used to retain the ability of the second-order mode to supplement the capture of high-frequency wave energy while the first-order mode dominates the capture of low-frequency energy, so as to avoid weakening the broadband adaptability of the structure by pursuing an excessively high proportion of the first-order mode.

[0019] The outer layer iteration uses a preset target first-order mode weight as the convergence objective. It searches for the slit transmission coefficient within the structurally permissible range of the slit transmission coefficient using a bisection method, ensuring that the first-order mode weight equals the target value. The outer layer convergence threshold is set at a weight absolute error of less than 0.005, corresponding to a power contribution ratio error of less than half a percentage point, meeting the engineering design accuracy requirements. The inner layer iteration uses a preset target natural frequency as the convergence constraint. To address the natural frequency drift caused by each adjustment of the slit transmission coefficient in the outer layer, the drift is compensated by adjusting the gas volume in the rear cavity to change its aeroelastic stiffness. The Newton-Raphson iteration method is used for the solution. The inner layer convergence threshold is set at a natural frequency relative error of less than 0.002, corresponding to a resonance period error of less than 0.2%. At this accuracy, the influence of the resonance peak position shift on the spectral convolution integral result is negligible. The two-layer iteration is executed alternately. After the outer layer completes the gap transmission coefficient update, the inner layer volume compensation calculation is immediately triggered. After the inner layer converges, the corrected natural frequency is fed back to the outer layer modal weight calculation. This cycle continues until the outer layer weight error and the inner layer frequency error simultaneously meet their respective convergence thresholds. Finally, the optimal gap width and the optimal back cavity volume are output.

[0020] In one specific embodiment, step S1 includes: Based on the cross-sectional area of ​​the water surface in the anterior cavity, the equivalent length of the water column in the anterior cavity, and the density of seawater, the inertial and elastic terms of the water column in the anterior cavity are calculated to obtain the equivalent mass and equivalent stiffness of the anterior cavity. Based on the cross-sectional area of ​​the water surface in the rear cavity, the equivalent length of the water column in the rear cavity, and the density of seawater, the inertial and elastic terms of the water column in the rear cavity are calculated to obtain the equivalent mass and equivalent stiffness of the rear cavity. The transmission coefficient of the gap is obtained by converting the gap width and the gap draft into the transmission coefficient; based on the gap transmission coefficient, seawater density, gravitational acceleration and the effective water permeable area of ​​the gap, the fluid coupling effect of the front and rear cavities is parametrically expressed to obtain the coupling stiffness. The equivalent mass and stiffness of the front cavity, the equivalent mass and stiffness of the rear cavity, and the coupling stiffness are assembled into a matrix in the form of nonlinear damping proportional to the square of the velocity, resulting in a two-degree-of-freedom dynamic equation system.

[0021] Specifically, the equivalent mass of the front cavity is determined by the product of the cross-sectional area of ​​the water surface in the front cavity, the equivalent length of the water column in the front cavity, and the density of the seawater. The equivalent stiffness of the front cavity is determined by the product of the cross-sectional area of ​​the water surface in the front cavity, the density of the seawater, and the acceleration due to gravity. Both are derived from the potential flow dynamics of the oscillating water column. The equivalent length of the water column in the front cavity is taken as the vertical distance from the still water surface of the front cavity to the bottom of the gap. The calculation methods for the equivalent mass and equivalent stiffness of the rear cavity are the same as those for the front cavity, substituting the corresponding geometric parameters of the rear cavity. The gap transmission coefficient is determined by dividing the gap width by the sum of the products of the gap width, the gap shape correction coefficient, and the gap draft. The shape correction coefficient for the rectangular cross-section gap is taken as 0.42. This value is given by the analytical solution of the potential flow around the gap, reflecting the correction of the gap cross-sectional shape to the water permeability. The coupling stiffness is determined by multiplying the square of the gap transmission coefficient by the quotient of the square of the gap transmission coefficient minus one by the product of the seawater density, gravitational acceleration, and the effective permeable area of ​​the gap. The effective permeable area of ​​the gap is the sum of the actual cross-sectional areas of the water flowing through the openings of the two gap walls.

[0022] The two-degree-of-freedom dynamic equations are composed of the simultaneous equations of motion for the front and rear cavities. Each equation contains four parts: inertial, damping, elastic, and coupling terms. The damping term adopts a nonlinear form proportional to the square of the velocity, meaning the damping force is proportional to the product of the absolute value of the water column velocity and the velocity itself, rather than a linear damping form proportional to the velocity itself. This choice is based on the fact that the fluid resistance at the gaps in the double-slit caisson is generated by the flow around the orifice. The orifice resistance coefficient multiplied by the dynamic head determines the magnitude of dissipation. The dynamic head itself is proportional to the square of the velocity. If linear damping were used, the damping in the low-speed range would be overestimated and the damping in the high-speed range underestimated, leading to discrepancies between the free decay time history and the measured values. The coupling term coefficients are taken as the coupling stiffness, and the sign is determined by the relative displacement direction of the front and rear cavities. In the front cavity equation, the coupling term is the coupling stiffness multiplied by the front cavity displacement minus the rear cavity displacement; in the rear cavity equation, the coupling term is the coupling stiffness multiplied by the rear cavity displacement minus the front cavity displacement. The two equations are then combined and expressed in matrix form to obtain the two-degree-of-freedom dynamic equations.

[0023] The matrix form of the two-degree-of-freedom dynamic equations is as follows:

[0024] The meanings of each parameter are as follows: The equivalent mass of the front cavity is determined by the product of the cross-sectional area of ​​the water surface in the front cavity, the equivalent length of the water column in the front cavity, and the density of the seawater. The equivalent mass of the rear cavity is determined by the product of the cross-sectional area of ​​the water surface in the rear cavity, the equivalent length of the water column in the rear cavity, and the density of the seawater. This represents the displacement of the water column in the anterior cavity. The velocity of the water column in the anterior chamber is... This refers to the acceleration of the water column in the anterior chamber; For the displacement of the water column in the posterior cavity, The velocity of the water column in the rear chamber. This refers to the acceleration of the water column in the rear cavity; The nonlinear damping coefficient of the front cavity is... The nonlinear damping coefficient of the rear cavity is... This represents the nonlinear damping term that represents the square-proportional velocity. The equivalent stiffness of the front cavity is determined by the product of the cross-sectional area of ​​the water surface in the front cavity, the density of seawater, and the acceleration due to gravity. The equivalent stiffness of the rear cavity is determined by the product of the cross-sectional area of ​​the water surface in the rear cavity, the density of seawater, and the acceleration due to gravity. The coupling stiffness is determined by the following formula:

[0025] in The density of seawater, It is the acceleration due to gravity. For the effective water permeable area of ​​the gap, The slit transmission coefficient is determined by the following formula:

[0026] in The width of the gap. For the depth of water flow in the gap, The gap shape correction factor is taken as the rectangular cross-section gap. =0.42.

[0027] In one specific embodiment, step S2 includes: The coupling stiffness is assembled with the equivalent mass, equivalent stiffness, equivalent mass, and equivalent stiffness of the front cavity, the rear cavity, and the rear cavity into a mass matrix and a stiffness matrix, and the undamped generalized eigenvalue problem is solved to obtain the first-order natural angular frequency and the second-order natural angular frequency. Based on the first-order natural angular frequency, the amplitude relationship between the rear cavity and the front cavity under the first-order mode is calculated to obtain the first-order mode amplitude ratio; based on the second-order natural angular frequency, the amplitude relationship between the rear cavity and the front cavity under the second-order mode is calculated to obtain the second-order mode amplitude ratio. Arrange the first-order mode amplitude ratio and the second-order mode amplitude ratio in column vector form to obtain the mode transformation matrix; Based on the modal transformation matrix, coordinate transformation is performed on the two-degree-of-freedom dynamic equations to convert the displacements of the water column in the front and rear chambers into first-order and second-order modal coordinates, respectively, resulting in two decoupled modal oscillation equations and their corresponding modal damping ratios.

[0028] Specifically, the mass matrix is ​​a diagonal matrix composed of the equivalent masses of the front cavity and the rear cavity, and the stiffness matrix is ​​a symmetric matrix composed of the sum of the equivalent stiffness of the front cavity and the coupling stiffness, and the sum of the equivalent stiffness of the rear cavity and the coupling stiffness placed in diagonal positions, with the negative values ​​of the coupling stiffness placed in off-diagonal positions. The undamped generalized eigenvalue problem is solved by subtracting the product of the square of the natural angular frequency and the mass matrix from the stiffness matrix until the determinant is zero. Expanding this gives a quadratic equation about the square of the natural angular frequency. The square roots of the two positive real roots are the first-order and second-order natural angular frequencies, respectively. A smaller first-order natural angular frequency corresponds to a low-frequency in-phase mode, and a larger second-order natural angular frequency corresponds to a high-frequency out-of-phase mode. The first-order mode amplitude ratio is determined by subtracting the product of the square of the first-order natural angular frequency and the equivalent mass of the front cavity from the sum of the equivalent stiffness of the front cavity and the coupling stiffness, and then dividing by the coupling stiffness. This ratio is positive, which physically means that the amplitude of the rear cavity is in the same direction as the amplitude of the front cavity in the first-order mode and the ratio is greater than zero. The second-order mode amplitude ratio is determined by substituting the second-order natural angular frequency into the same formula. This ratio is negative, which physically means that the amplitude of the rear cavity is in the opposite direction to the amplitude of the front cavity in the second-order mode.

[0029] The modal transformation matrix is ​​a second-order square matrix with the first-order modal shape column vector as the first column and the second-order modal shape column vector as the second column. Each column of mode shape vectors is expressed in the form of the front cavity component being normalized to one and the back cavity component being the amplitude ratio of the corresponding mode. The physical coordinate column vector is expressed as the product of the modal transformation matrix and the modal coordinate column vector. After substituting it into the two-degree-of-freedom dynamic equations, both ends are multiplied by the transpose of the modal transformation matrix on the left. Utilizing the orthogonality of the mass matrix and stiffness matrix with respect to the mode shape, the off-diagonal terms are eliminated to zero. The equations are decoupled into two independent single-degree-of-freedom modal oscillation equations. The generalized mass of each equation is determined by multiplying the corresponding mode shape transpose by the mass matrix and then by the mode shape. The generalized stiffness is determined by multiplying the corresponding mode shape transpose by the stiffness matrix and then by the mode shape. The modal damping ratio is determined by dividing the linearized equivalent of the nonlinear damping coefficient in the original equation system at the current amplitude level by the product of twice the generalized mass and the corresponding natural angular frequency. The linearization equivalence adopts the energy equivalence principle, that is, the energy dissipated by the equivalent linear damping in one oscillation period is equal to the actual energy dissipated by the nonlinear damping.

[0030] In one specific embodiment, step S3 includes: Based on the first-order modal coordinates and modal damping ratio, the first-order modal steady-state harmonic response is solved to obtain the first-order modal frequency response function; based on the second-order modal coordinates and modal damping ratio, the second-order modal steady-state harmonic response is solved to obtain the second-order modal frequency response function. By substituting the modal amplitude ratio with the cross-sectional area of ​​the water surface in the front chamber and the cross-sectional area of ​​the water surface in the rear chamber into the superposition relationship of gas volume flow rate, the contribution coefficient of each mode to the total gas volume flow rate of the chamber is calculated, and the amplitude amplification coefficient of the first mode and the amplitude amplification coefficient of the second mode are obtained. Substituting the first-order mode amplitude amplification factor into the first-order mode frequency response function and the second-order mode amplitude amplification factor into the second-order mode frequency response function, respectively, convolution integral operations are performed on the target sea area wave power spectrum and the square of the first-order mode frequency response function, and the target sea area wave power spectrum and the square of the second-order mode frequency response function in the range of half to three times the peak frequency, to obtain the integral value of the first-order mode power spectrum and the integral value of the second-order mode power spectrum; Divide the integral value of the first-order mode power spectrum by the sum of the integral values ​​of the first-order mode power spectrum and the second-order mode power spectrum, and normalize the energy contribution ratio of each mode to obtain the first-order mode weight and the second-order mode weight.

[0031] Specifically, the first-order modal frequency response function is determined by three parameters: the first-order modal generalized mass, the first-order natural angular frequency, and the first-order modal damping ratio. Its amplitude-frequency characteristic is expressed as the complex modulus of the imaginary term of the product of the square of the first-order natural angular frequency, the square of the first-order natural angular frequency and the square of the excitation angular frequency, plus twice the first-order modal damping ratio, the first-order natural angular frequency, and the excitation angular frequency. This expression is the standard analytical form of the steady-state response of a single-degree-of-freedom resonant system. The second-order modal frequency response function is determined by substituting the second-order natural angular frequency and the second-order modal damping ratio into the same form. The modal amplitude amplification factor describes the actual contribution weight of each modal oscillation to the total gas volume flow rate of the chamber. The first-order modal amplitude amplification factor is determined by multiplying the cross-sectional area of ​​the water surface in the front chamber and the cross-sectional area of ​​the water surface in the rear chamber by the ratio of the first-order modal amplitude. Its physical meaning is the total sum of the gas volume flow rates in the front and rear chambers driven by the unit modal coordinate amplitude of the first-order mode. The second-order modal amplitude amplification factor is determined by substituting the second-order modal amplitude ratio into the same relationship. Since the second-order modal amplitude ratio is negative, the gas flow rates in the front and rear chambers partially cancel each other out. The absolute value of the second-order modal amplitude amplification factor is usually less than that of the first-order modal amplitude amplification factor.

[0032] The convolution integration interval is set to half to three times the peak frequency. This interval is based on the fact that the energy concentration range of the JONSWAP spectrum covers approximately one octave band on both sides of the peak frequency. Setting it to half to three times the peak frequency can completely encompass the effective energy segment near the resonance peaks of both modes. The integration step size is 0.01 radians per second. This step size generates no less than one hundred integration nodes within the above interval, which is sufficient to accurately capture the spectral area of ​​the resonance peaks without introducing significant numerical integration errors. The integral value of the first-order modal power spectrum is obtained by integrating the product of the target sea area wave power spectrum and the square of the first-order modal amplitude amplification factor multiplied by the square of the amplitude of the first-order modal frequency response function within the above interval. The integral value of the second-order modal power spectrum is obtained by integrating the corresponding quantity of the second-order mode in the same way. The first-order mode weight is defined as the integral value of the first-order mode power spectrum divided by the sum of the integral values ​​of the first-order and second-order mode power spectra. The second-order mode weight is one minus the first-order mode weight, and the sum of the two is always one. This normalization process makes the mode weight directly reflect the contribution ratio of each mode to the root mean square of the total output gas volume flow rate under the actual wave excitation in the target sea area, rather than just reflecting whether the resonant peak frequency position matches the wave spectrum.

[0033] In one specific embodiment, step S4 involves using a preset target first-order mode weight as the outer convergence target and a preset target natural frequency as the inner convergence constraint to perform a double-layer nested iterative solution for the slit transmission coefficient and the back cavity volume, including: Based on the minimum allowable value for structural construction of the gap width and the maximum constraint value for the overall width of the breakwater, the upper and lower bounds of the search interval for the gap transmission coefficient are determined, thus obtaining the search interval for the gap transmission coefficient. The midpoint between the upper and lower bounds of the gap transmission coefficient search interval is taken and substituted into the coupling stiffness calculation relationship to update the coupling stiffness under the current gap transmission coefficient, thus obtaining the current coupling stiffness. Substitute the current coupling stiffness into the mass matrix and stiffness matrix, and resolve for the current first-order natural angular frequency and the current second-order natural angular frequency to obtain the current natural frequency set. Substitute the current natural frequency group into the first-order modal frequency response function and the second-order modal frequency response function to calculate the current first-order modal weight. Then compare the difference between the current first-order modal weight and the target first-order modal weight with the outer convergence threshold. When the absolute value of the difference exceeds the outer convergence threshold, update the upper or lower bound of the search interval according to the sign of the difference and return to iterate again by taking the median. When the absolute value of the difference does not exceed the outer convergence threshold, determine the current gap transmission coefficient as the converged gap transmission coefficient and obtain the optimal gap width.

[0034] Specifically, the lower bound of the search interval for the gap transmission coefficient is determined by substituting the minimum gap width allowed by structural construction into the gap transmission coefficient conversion relationship. The minimum gap width is taken as 0.3 meters. This value is determined by the minimum requirement for gap forming accuracy in the breakwater construction process. Below this value, the influence of the roughness of the gap inner wall on the transmission coefficient cannot be ignored. The upper bound of the search interval is determined by substituting the maximum gap width under the overall width constraint of the breakwater into the same conversion relationship. The maximum gap width is taken as 2.0 meters. Exceeding this value, the structural strength of the partition wall between the front and rear cavities does not meet the wave load requirements. In each iteration of the bisection method, the arithmetic mean of the current upper and lower bounds of the search interval is taken as the current gap transmission coefficient. This value is then substituted into the coupling stiffness calculation relationship, that is, the quotient of the square of the gap transmission coefficient and the square of the difference between the two gap transmission coefficients is multiplied by the product of seawater density, gravitational acceleration, and the effective permeable area of ​​the gap to obtain the current coupling stiffness. After the current coupling stiffness is updated, it is substituted into the off-diagonal elements and diagonal element correction terms of the stiffness matrix, and the undamped generalized eigenvalue problem is solved again to obtain the current first-order natural angular frequency and the current second-order natural angular frequency. The two together constitute the current natural frequency group.

[0035] Substitute the current natural frequency group into the first-order modal frequency response function and the second-order modal frequency response function respectively, and calculate the current first-order modal weight using convolution integral operation. The outer layer convergence threshold is set to the absolute value of the difference between the current first-order modal weight and the target first-order modal weight being less than 0.005. This value corresponds to a modal energy contribution ratio error of less than half a percentage point. Under this precision, the change in the spectral convolution integral result has an impact on the total output power that is below the allowable range of engineering design error. When the absolute value of the difference exceeds the outer layer convergence threshold, if the current first-order modal weight is greater than the target first-order modal weight, it indicates that the current slit transmission coefficient is too large, the coupling between the front and rear cavities is too strong, and the proportion of the first-order mode is too high. In this case, the upper bound of the search interval is updated to the current slit transmission coefficient, and the median value is returned. If the current first-order modal weight is less than the target first-order modal weight, the lower bound of the search interval is updated to the current slit transmission coefficient, and the median value is returned. When the absolute value of the difference does not exceed the outer layer convergence threshold, the current gap transmission coefficient is the converged gap transmission coefficient. Substituting it into the inverse calculation relationship between gap width and gap transmission coefficient, that is, gap width equals 0.42 multiplied by gap draft depth, then multiplied by gap transmission coefficient, divided by one minus gap transmission coefficient, to obtain the optimal gap width.

[0036] Figure 2 This is a schematic diagram of the double-nested iterative convergence process in an embodiment of this application. It shows the convergence trajectory of the two iterative variables in a double-nested iterative solution process where the preset target first-order mode weights are the outer convergence target and the preset target natural frequency is the inner convergence constraint. Figure 2(a) shows the curve of the first-order mode weight gradually converging from the initial value of 0.820 to the target value of 0.60 during the outer bisection method iteration process. The gray dashed line is the target weight of 0.60, and the gray shaded band is the outer convergence threshold band. When the absolute value of the difference between the first-order mode weight and the target value does not exceed 0.005, the outer iteration is determined to be converged. Figure 2 (b) shows the convergence curve of the first-order natural angular frequency gradually compensated and corrected from the initial drift value of 0.5980 rad / s to the target value of 0.628 rad / s during the inner Newton iteration process. The gray shaded band is the inner convergence threshold band (±0.2%). When the relative error of the natural frequency does not exceed 0.002, the inner iteration is determined to be converged. The two iterations are executed alternately until the weight error and frequency error simultaneously meet their respective convergence thresholds. Finally, the optimal gap width and the optimal back cavity volume are output.

[0037] In one specific embodiment, the natural frequency-linked drift caused by the change in the transmission coefficient of the gap after adjusting the inner layer cavity volume in step S4 includes: Based on the convergent gap transmission coefficient and the current natural frequency group, the natural frequency linkage drift between the target natural frequency and the current natural frequency group is calculated to obtain the first-order natural frequency drift and the second-order natural frequency drift. Based on the adiabatic index of the gas in the rear chamber, the standard atmospheric pressure, and the cross-sectional area of ​​the water surface in the rear chamber, the inverse proportional relationship between the elastic stiffness of the gas in the rear chamber and the volume of the rear chamber is parametrically expressed, and the expression for the aeroelastic stiffness of the rear chamber is obtained. The aeroelastic stiffness expression of the rear cavity is superimposed onto the equivalent stiffness of the rear cavity, and the modified stiffness matrix is ​​substituted back into the eigenvalue equation to solve for the volume-corrected natural frequency. Based on the first-order natural frequency drift, the square of the difference between the volume-corrected natural frequency and the target natural frequency is used as the convergence criterion. The back cavity volume is corrected by Newton iteration. When the convergence criterion does not exceed the inner layer convergence threshold, the current back cavity volume is output as the frequency compensation volume, thus obtaining the optimal back cavity volume.

[0038] Specifically, the natural frequency drift is determined by the difference between the target natural frequency and the corresponding natural angular frequency in the current natural frequency group. The first-order natural frequency drift is the target first-order natural angular frequency minus the current first-order natural angular frequency, and the second-order natural frequency drift is the target second-order natural angular frequency minus the current second-order natural angular frequency. Both drifts are expressed in radians per second. The physical source of the aeroelastic stiffness of the rear chamber lies in the restoring force generated when the gas in the rear chamber is compressed or expanded. Based on the adiabatic compression process, the gas elastic stiffness is proportional to the product of the gas adiabatic index, standard atmospheric pressure, and the square of the cross-sectional area of ​​the water surface in the rear chamber, and inversely proportional to the static volume of the gas in the rear chamber. The adiabatic index is taken as 1.4, and the standard atmospheric pressure is taken as 101325 Pa. Both of these parameters are well-known thermodynamic constants of air. The expression for the aeroelastic stiffness of the rear cavity uses the rear cavity volume as the sole variable; a smaller volume results in a larger aeroelastic stiffness. This stiffness, when superimposed on the equivalent stiffness of the rear cavity, increases the overall equivalent stiffness, thus shifting the second-order natural angular frequency towards higher frequencies. The first-order natural angular frequency, due to the unchanged mass matrix, experiences a smaller but non-zero indirect influence. By superimposing the aeroelastic stiffness of the rear cavity onto the diagonal elements of the stiffness matrix and resolving the undamped generalized eigenvalue problem, the volume-corrected natural frequencies are obtained.

[0039] After Newton's iteration correction, the cavity volume is used as the iteration variable. The iteration format is: the current cavity volume minus the difference between the square of the corrected first-order natural angular frequency and the square of the target first-order natural angular frequency, divided by the partial derivative of the square of the first-order natural angular frequency with respect to the cavity volume. The partial derivative is analytically obtained by subtracting the derivative of the cavity aeroelastic stiffness with respect to the cavity volume and then inputting the sensitivity relationship of the eigenvalues ​​to the elements of the stiffness matrix, without the need for numerical difference approximation. The initial value of the iteration is the cavity volume corresponding to the point where the cavity aeroelastic stiffness is equal to the cavity hydrodynamic equivalent stiffness, i.e., the product of the adiabatic index, standard atmospheric pressure, and the square of the cavity water surface cross-sectional area divided by the cavity equivalent stiffness. This initial value makes the aerodynamic stiffness comparable to the hydrodynamic stiffness, ensuring that Newton's iteration starts from a reasonable range. The inner-layer convergence threshold is set to a value where the square of the difference between the volume-corrected first-order natural angular frequency and the target first-order natural angular frequency is less than 1 x 10^-6 radians per square second, corresponding to a natural frequency relative error of less than 0.2%. At this precision, the influence of the resonance period deviation on the spectral convolution integral result is negligible. When the convergence criterion does not exceed the inner-layer convergence threshold, the current back cavity volume is the frequency-compensated volume, and the output is the optimal back cavity volume.

[0040] In one specific embodiment, after obtaining the optimal slit width and the optimal rear cavity volume in step S4, the method further includes: Based on the optimal gap width and optimal rear cavity volume, the updated coupling stiffness and rear cavity aeroelastic stiffness are re-substituted, and the first-order modal weights, first-order natural angular frequencies and second-order natural angular frequencies are simultaneously verified to obtain the weight verification values ​​and frequency verification values. The absolute value of the difference between the weight verification value and the target first-order modal weight is compared with the outer convergence threshold, and the relative error between the frequency verification value and the target intrinsic frequency is compared with the inner convergence threshold. When the absolute value of the weight difference and the relative error of the frequency do not exceed their respective convergence thresholds, the double-layer nested iteration is determined to be converged, and the simultaneous convergence determination result is obtained. Based on the simultaneous convergence determination results, the optimal gap width, optimal back cavity volume, first-order mode amplitude amplification factor, and second-order mode amplitude amplification factor are substituted into the root mean square calculation of the total gas volume flow rate to solve for the optimal aerodynamic damping coefficient, thus obtaining the optimal aerodynamic damping coefficient. The optimal gap width, optimal rear cavity volume, and optimal aerodynamic damping coefficient were substituted into the two-degree-of-freedom dynamic equations for time-domain simulation verification, resulting in the optimal combination of structural parameters for spectral matching.

[0041] Specifically, the simultaneous verification calculation substitutes the optimal gap width into the gap transmission coefficient conversion relationship to obtain the corresponding gap transmission coefficient, and then substitutes it into the coupling stiffness calculation relationship to obtain the updated coupling stiffness. The optimal rear cavity volume is substituted into the rear cavity aeroelastic stiffness expression to obtain the updated rear cavity aeroelastic stiffness. Both update the off-diagonal elements of the stiffness matrix and the diagonal elements of the rear cavity, respectively. The undamped generalized eigenvalue problem is solved again to obtain the frequency verification values, namely the verified first-order natural angular frequency and second-order natural angular frequency. At the same time, the updated coupling stiffness is substituted into the modal amplitude ratio calculation relationship and then subjected to convolution integral operation to obtain the weight verification value. The comparison threshold for the absolute value of the weight difference is 0.005, which is the same as the outer convergence threshold. The comparison threshold for the relative frequency error is 0.002, which is the same as the inner convergence threshold. Both conditions must be met simultaneously to determine the convergence of the nested double-layer iteration. If either condition is not met, the current optimal gap width and optimal back cavity volume are returned to the outer iteration and re-executed until the combined convergence judgment results confirm that both errors are within the threshold.

[0042] The optimal aerodynamic damping coefficient is determined by the root mean square of the total gas volume flow rate. The root mean square of the total gas volume flow rate is obtained by taking the square root of the sum of the square of the first-order mode amplitude amplification factor multiplied by the integral value of the first-order mode power spectrum and the square of the second-order mode amplitude amplification factor multiplied by the integral value of the second-order mode power spectrum. The optimal aerodynamic damping coefficient is equal to the square of the first-order target natural angular frequency multiplied by the product of the first-order mode generalized mass and the first-order mode weight, plus the square of the second-order target natural angular frequency multiplied by the product of the second-order mode generalized mass and the second-order mode weight, and then divided by twice the square of the root mean square of the total gas volume flow rate. This calculation is based on the extreme condition that the derivative of the output power of each mode with respect to the aerodynamic damping coefficient is zero. Time-domain simulation verification substitutes the optimal gap width, optimal rear cavity volume, and optimal aerodynamic damping coefficient into the two-degree-of-freedom dynamic equations. The irregular wavefront time history generated by the JONSWAP spectrum is used as the excitation input. The time-domain integration duration is set to 1800 seconds, the time step to 0.05 seconds, and the Runge-Kutta fourth-order method is employed. The integration duration is set based on the fact that it is more than 180 times the period of the corresponding spectral peak, which is sufficient to ensure that the statistical mean converges to a steady state. The steady-state total output power output from the simulation, together with the optimal gap width, optimal rear cavity volume, and optimal aerodynamic damping coefficient, constitutes the optimal combination of structural parameters for spectral matching.

[0043] The above describes the simulation method for dual-mode frequency tuning of oscillating water column in a double-slit caisson according to the embodiments of this application. The following describes the simulation system for dual-mode frequency tuning of oscillating water column in a double-slit caisson according to the embodiments of this application. One embodiment of the simulation system for dual-mode frequency tuning of oscillating water column in a double-slit caisson according to the embodiments of this application includes: The analysis module is used to establish a two-degree-of-freedom dynamic equation system based on the displacement of the water column in the front cavity and the displacement of the water column in the rear cavity, with the slit transmission coefficient as a parameter, and to obtain the coupling stiffness. The decomposition module is used to substitute the coupling stiffness into the eigenvalue equation to decompose the two-cavity oscillation modes and obtain the mode transformation matrix and mode amplitude ratio. The calculation module is used to substitute the modal amplitude ratio and the wave power spectrum of the target sea area into the modal frequency response function, and obtain the first-order modal weight and the second-order modal weight by performing a convolution integral operation on the wave power spectrum and the square of the modal frequency response function. The solution module is used to perform a double-layer nested iterative solution on the slit transmission coefficient and the back cavity volume, with a preset target first-order modal weight as the outer convergence target and a preset target natural frequency as the inner convergence constraint. The outer layer adjusts the slit transmission coefficient to make the first-order modal weight converge to the target first-order modal weight, and the inner layer adjusts the back cavity volume to compensate for the natural frequency drift caused by the change in the slit transmission coefficient, so as to obtain the optimal slit width and the optimal back cavity volume.

[0044] This invention also provides a dual-mode frequency tuning simulation device for a double-slit caisson oscillating water column, which can be a server. The device includes a processor, memory, display screen, input device, network interface, and database connected via a system bus. The processor provides computational and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database stores the data corresponding to this embodiment. The network interface communicates with external terminals via a network connection. The computer program is executed by the processor to implement the above-described method.

[0045] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when the instructions are executed on a computer, cause the computer to perform the steps of the simulation method for dual-mode frequency tuning of oscillating water column in a double-slit caisson.

[0046] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0047] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a double-slit caisson oscillating water column dual-mode frequency tuning simulation device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0048] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A simulation method for dual-mode frequency tuning of oscillating water column in a double-slit caisson, characterized in that, The method includes: Step S1: Based on the displacement of the water column in the front cavity and the displacement of the water column in the rear cavity, establish a two-degree-of-freedom dynamic equation system using the slit transmission coefficient as a parameter to obtain the coupling stiffness. This includes: calculating the inertial and elastic terms of the water column in the front cavity based on the cross-sectional area of ​​the water surface in the front cavity, the equivalent length of the water column in the front cavity, and the seawater density to obtain the equivalent mass and equivalent stiffness of the front cavity; calculating the inertial and elastic terms of the water column in the rear cavity based on the cross-sectional area of ​​the water surface in the rear cavity, the equivalent length of the water column in the rear cavity, and the seawater density to obtain the equivalent mass and equivalent stiffness of the rear cavity. Stiffness; the transmission coefficient of the gap is obtained by converting the gap width and the gap draft; based on the gap transmission coefficient, seawater density, gravitational acceleration and effective water-permeable area of ​​the gap, the fluid coupling effect of the front and rear cavities is parameterized to obtain the coupling stiffness; the equivalent mass of the front cavity, the equivalent stiffness of the front cavity, the equivalent mass of the rear cavity, the equivalent stiffness of the rear cavity and the coupling stiffness are assembled into a matrix in the form of velocity square ratio nonlinear damping to obtain the two-degree-of-freedom dynamic equations; Step S2: Substitute the coupling stiffness into the eigenvalue equation to decompose the two-cavity oscillation modes and obtain the mode transformation matrix and mode amplitude ratio; Step S3: Substitute the modal amplitude ratio and the wave power spectrum of the target sea area into the modal frequency response function. Obtain the first-order modal weight and the second-order modal weight by convolution integration of the wave power spectrum and the square of the modal frequency response function. This includes: solving the first-order modal steady-state harmonic response based on the first-order modal coordinates and the modal damping ratio to obtain the first-order modal frequency response function; solving the second-order modal steady-state harmonic response based on the second-order modal coordinates and the modal damping ratio to obtain the second-order modal frequency response function; substituting the modal amplitude ratio, the cross-sectional area of ​​the water surface in the front chamber, and the cross-sectional area of ​​the water surface in the rear chamber into the gas volume flow rate superposition relationship, calculating the contribution coefficient of each mode to the total gas volume flow rate of the chamber, and obtaining the first-order modal amplitude amplification factor and the second-order modal amplitude amplification factor. The amplitude amplification factor of the first-order mode is used; the amplitude amplification factor of the second-order mode is substituted into the frequency response function of the first-order mode, and the amplitude amplification factor of the second-order mode is substituted into the frequency response function of the second-order mode. Convolution integral operations are performed on the wave power spectrum of the target sea area and the square of the frequency response function of the first-order mode, and the wave power spectrum of the target sea area and the square of the frequency response function of the second-order mode, respectively, in the range of half to three times the peak frequency, to obtain the integral value of the first-order mode power spectrum and the integral value of the second-order mode power spectrum; the integral value of the first-order mode power spectrum is divided by the sum of the integral values ​​of the first-order mode power spectrum and the second-order mode power spectrum, and the energy contribution ratio of each mode is normalized to obtain the weight of the first-order mode and the weight of the second-order mode. Step S4: Using a preset target first-order modal weight as the outer convergence target and a preset target natural frequency as the inner convergence constraint, perform a double-layer nested iterative solution for the slit transmission coefficient and the back cavity volume. The outer layer adjusts the slit transmission coefficient to converge the first-order modal weight to the target first-order modal weight, while the inner layer adjusts the back cavity volume to compensate for the natural frequency drift caused by the change in the slit transmission coefficient, thus obtaining the optimal slit width and the optimal back cavity volume. Based on the converged slit transmission coefficient and the current natural frequency group, the natural frequency drift between the target natural frequency and the current natural frequency group is calculated to obtain the first-order natural frequency drift and the second-order natural frequency drift. Based on the adiabatic index of the gas in the rear cavity, standard atmospheric pressure, and the cross-sectional area of ​​the water surface in the rear cavity, the inverse relationship between the elastic stiffness of the gas in the rear cavity and the volume of the rear cavity is parameterized to obtain the expression for the aeroelastic stiffness of the rear cavity. The expression for the aeroelastic stiffness of the rear cavity is superimposed on the equivalent stiffness of the rear cavity, and the corrected stiffness matrix is ​​substituted back into the eigenvalue equation for solution to obtain the natural frequency after volume correction. Based on the first-order natural frequency drift, the volume of the rear cavity is corrected by Newton iteration using the square of the difference between the natural frequency after volume correction and the target natural frequency as the convergence criterion. When the convergence criterion does not exceed the inner convergence threshold, the current volume of the rear cavity is output as the frequency-compensated volume to obtain the optimal volume of the rear cavity.

2. The simulation method for dual-mode frequency tuning of oscillating water column in a double-slit caisson according to claim 1, characterized in that, Step S2 includes: The coupling stiffness is assembled with the equivalent mass, equivalent stiffness, equivalent mass, and equivalent stiffness of the front cavity, the rear cavity, and the rear cavity into a mass matrix and a stiffness matrix, and the undamped generalized eigenvalue problem is solved to obtain the first-order natural angular frequency and the second-order natural angular frequency. Based on the first-order natural angular frequency, the amplitude relationship between the rear cavity and the front cavity in the first-order mode is calculated to obtain the first-order mode amplitude ratio; based on the second-order natural angular frequency, the amplitude relationship between the rear cavity and the front cavity in the second-order mode is calculated to obtain the second-order mode amplitude ratio. The first-order mode amplitude ratio and the second-order mode amplitude ratio are arranged in column vector form to obtain the mode transformation matrix; Based on the modal transformation matrix, the coordinate transformation of the two-degree-of-freedom dynamic equations is performed to convert the displacement of the water column in the front cavity and the displacement of the water column in the rear cavity into first-order modal coordinates and second-order modal coordinates, resulting in two decoupled modal oscillation equations and corresponding modal damping ratios.

3. The simulation method for dual-mode frequency tuning of oscillating water column in a double-slit caisson according to claim 2, characterized in that, In step S4, the slit transmission coefficient and the back cavity volume are solved using a double-layer nested iterative method, with the preset target first-order mode weights as the outer convergence target and the preset target natural frequency as the inner convergence constraint. This includes: Based on the minimum allowable value for structural construction of the gap width and the maximum constraint value for the overall width of the breakwater, the upper and lower bounds of the search interval for the gap transmission coefficient are determined, thus obtaining the search interval for the gap transmission coefficient. The midpoint between the upper and lower bounds of the gap transmission coefficient search interval is taken and substituted into the coupling stiffness calculation relationship to update the coupling stiffness under the current gap transmission coefficient, thus obtaining the current coupling stiffness. Substitute the current coupling stiffness into the mass matrix and stiffness matrix, and re-solve for the current first-order natural angular frequency and the current second-order natural angular frequency to obtain the current natural frequency group. Substitute the current natural frequency group into the first-order modal frequency response function and the second-order modal frequency response function to calculate the current first-order modal weight. Compare the difference between the current first-order modal weight and the target first-order modal weight with the outer convergence threshold. When the absolute value of the difference exceeds the outer convergence threshold, update the upper or lower bound of the search interval according to the sign of the difference and return to iterate again by taking the median. When the absolute value of the difference does not exceed the outer convergence threshold, determine the current gap transmission coefficient as the converged gap transmission coefficient and obtain the optimal gap width.

4. The simulation method for dual-mode frequency tuning of oscillating water column in a double-slit caisson according to claim 3, characterized in that, After obtaining the optimal slit width and optimal rear cavity volume in step S4, the method further includes: Based on the optimal gap width and the optimal rear cavity volume, the updated coupling stiffness and rear cavity aeroelastic stiffness are re-substituted, and the first-order modal weight, the first-order natural angular frequency and the second-order natural angular frequency are simultaneously verified to obtain the weight verification value and the frequency verification value. The absolute value of the difference between the weight verification value and the target first-order mode weight is compared with the outer convergence threshold, and the relative error between the frequency verification value and the target intrinsic frequency is compared with the inner convergence threshold. When the absolute value of the weight difference and the relative error of the frequency do not exceed their respective convergence thresholds, the double-layer nested iterative convergence is determined, and the simultaneous convergence determination result is obtained. Based on the simultaneous convergence determination result, the optimal gap width, the optimal rear cavity volume, the first-order mode amplitude amplification factor, and the second-order mode amplitude amplification factor are substituted into the root mean square of the total gas volume flow rate to calculate the optimal aerodynamic damping coefficient, and the optimal aerodynamic damping coefficient is obtained. The optimal gap width, the optimal rear cavity volume, and the optimal aerodynamic damping coefficient are substituted into the two-degree-of-freedom dynamic equations for time-domain simulation verification, resulting in the optimal combination of structural parameters for spectral matching.

5. A dual-mode frequency tuning simulation system for a double-slit caisson oscillating water column, characterized in that, For implementing the dual-mode frequency tuning simulation method for oscillating water column in a double-slit caisson as described in any one of claims 1-4, the dual-mode frequency tuning simulation system for oscillating water column in a double-slit caisson comprises: The analysis module is used to establish a two-degree-of-freedom dynamic equation system based on the displacement of the water column in the anterior and posterior chambers, using the slit transmission coefficient as a parameter, to obtain the coupling stiffness. This includes: calculating the inertial and elastic terms of the water column in the anterior chamber based on the cross-sectional area of ​​the water surface, the equivalent length of the water column in the anterior chamber, and the seawater density, to obtain the equivalent mass and equivalent stiffness of the anterior chamber; and calculating the inertial and elastic terms of the water column in the posterior chamber based on the cross-sectional area of ​​the water surface, the equivalent length of the water column in the posterior chamber, and the seawater density, to obtain the equivalent mass and equivalent stiffness of the posterior chamber. Effective stiffness; the transmission coefficient of the gap is obtained by converting the gap width and the gap draft; based on the gap transmission coefficient, seawater density, gravitational acceleration and effective permeable area of ​​the gap, the fluid coupling effect of the front and rear cavities is parametrically expressed to obtain the coupling stiffness; the equivalent mass of the front cavity, the equivalent stiffness of the front cavity, the equivalent mass of the rear cavity, the equivalent stiffness of the rear cavity and the coupling stiffness are assembled into a matrix in the form of velocity square ratio nonlinear damping to obtain the two-degree-of-freedom dynamic equations; The decomposition module is used to substitute the coupling stiffness into the eigenvalue equation to decompose the two-cavity oscillation modes and obtain the mode transformation matrix and mode amplitude ratio; The computation module is used to substitute the modal amplitude ratio and the wave power spectrum of the target sea area into the modal frequency response function, and obtain the first-order modal weight and the second-order modal weight by convolution integral operation of the wave power spectrum and the square of the modal frequency response function. This includes: solving the first-order modal steady-state harmonic response based on the first-order modal coordinates and the modal damping ratio to obtain the first-order modal frequency response function; solving the second-order modal steady-state harmonic response based on the second-order modal coordinates and the modal damping ratio to obtain the second-order modal frequency response function; and substituting the modal amplitude ratio, the cross-sectional area of ​​the water surface in the front cavity, and the cross-sectional area of ​​the water surface in the rear cavity into the gas volume flow rate superposition relationship to calculate the contribution coefficient of each mode to the total gas volume flow rate of the chamber, thereby obtaining the first-order modal amplitude amplification factor and the second-order modal weight. Modal amplitude amplification factor; Substituting the first-order modal amplitude amplification factor into the first-order modal frequency response function, and substituting the second-order modal amplitude amplification factor into the second-order modal frequency response function, respectively, convolution integral operations are performed on the target sea area wave power spectrum and the square of the first-order modal frequency response function, and the target sea area wave power spectrum and the square of the second-order modal frequency response function, within the range of half to three times the peak frequency, to obtain the first-order modal power spectrum integral value and the second-order modal power spectrum integral value; Dividing the first-order modal power spectrum integral value by the sum of the first-order modal power spectrum integral value and the second-order modal power spectrum integral value, the energy contribution ratio of each mode is normalized to obtain the first-order modal weight and the second-order modal weight; The solution module is used to perform a double-layer nested iterative solution on the slit transmission coefficient and the back cavity volume, with a preset target first-order modal weight as the outer convergence target and a preset target natural frequency as the inner convergence constraint. The outer layer adjusts the slit transmission coefficient to converge the first-order modal weight to the target first-order modal weight, while the inner layer adjusts the back cavity volume to compensate for the natural frequency drift caused by the change in the slit transmission coefficient, thus obtaining the optimal slit width and the optimal back cavity volume. Based on the converged slit transmission coefficient and the current natural frequency group, the natural frequency drift between the target natural frequency and the current natural frequency group is calculated to obtain the first-order natural frequency drift and the second-order natural frequency. The drift amount; based on the adiabatic index of the gas in the rear cavity, standard atmospheric pressure, and the cross-sectional area of ​​the water surface in the rear cavity, the inverse proportional relationship between the elastic stiffness of the gas in the rear cavity and the volume of the rear cavity is parameterized to obtain the expression for the aeroelastic stiffness of the rear cavity; the expression for the aeroelastic stiffness of the rear cavity is superimposed on the equivalent stiffness of the rear cavity, and the corrected stiffness matrix is ​​substituted back into the eigenvalue equation for solution to obtain the natural frequency after volume correction; based on the drift amount of the first-order natural frequency, the volume of the rear cavity is corrected by Newton iteration using the square of the difference between the natural frequency after volume correction and the target natural frequency as the convergence criterion; when the convergence criterion does not exceed the inner convergence threshold, the current volume of the rear cavity is output as the frequency-compensated volume to obtain the optimal volume of the rear cavity.

6. A dual-mode frequency tuning simulation device for a double-slit caisson oscillating water column, characterized in that, It includes a memory and a processor, the memory storing a computer program that can run on the processor, and the processor executing the computer program to implement the dual-mode frequency tuning simulation method for oscillating water column of a double-slit caisson as described in any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it causes the processor to execute the dual-mode frequency tuning simulation method for the oscillating water column of the double-slit caisson as described in any one of claims 1 to 4.

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