Method, device and equipment for solving motion response of circular porous elastic structure suitable for thin-film floating photovoltaic platform

Abstract

The application discloses a kind of circular openwork elastic structure motion response solving method, device and equipment suitable for thin film floating photovoltaic platform, the method comprises: determining the coupling equation of openwork effect, elastic deformation and fluid motion in fluid domain of circular openwork elastic structure;Determine the outer region velocity potential and the inner region velocity potential of circular openwork elastic structure;In the case where vertical coordinate is zero, the vertical displacement equation of circular openwork elastic structure is constructed;The modal eigenvalue of outer region velocity potential is obtained by outer region velocity potential, the modal eigenvalue of inner region velocity potential is obtained by inner region velocity potential and coupling equation, as the modal eigenvalue in vertical displacement equation;And the modal amplitude in vertical displacement equation is solved;Thus, the vertical displacement of circular openwork elastic structure can be quantitatively output, to provide data support for the vibration control of thin film floating photovoltaic platform.

Description

Technical Field

[0001] This application relates to the field of thin-film floating photovoltaic platform technology, and in particular to a method, apparatus and equipment for solving the motion response of a circular permeable elastic structure suitable for thin-film floating photovoltaic platforms. Background Technology

[0002] Driven by both the global clean energy transition and the development of marine space resources, thin-film floating photovoltaic (PV) platforms have become a core development direction in the offshore photovoltaic field due to their advantages of lightweight design, high flexibility and adaptability, and multi-scenario deployment in near-shore and deep-sea areas. By integrating flexible thin-film PV modules onto floating carriers, they can effectively utilize idle marine resources in near-shore areas and around islands and reefs, while avoiding the land occupation problems of traditional terrestrial PV, thus possessing extremely high industrialization value. However, the marine service environment of thin-film floating PV platforms presents significant contradictions, directly restricting their reliability and power generation efficiency: on the one hand, the thin-film floating PV platform itself is highly flexible but has weak resistance to mechanical vibration and wave impact, which may lead to structural strength failing to meet operating requirements under dangerous sea conditions; on the other hand, waves in the marine environment can easily cause water accumulation on the surface of the thin-film floating PV platform, and long-term water accumulation may cause crystal formation on the surface of the flexible thin-film PV modules, corroding the electrodes, shortening the lifespan of the modules, and exacerbating the loss of power generation efficiency.

[0003] Currently, circular permeable elastic structures, as core structures that balance wave energy dissipation and elastic buffering, can theoretically address the aforementioned pain points of thin-film floating photovoltaic platforms through the synergistic effect of "wave reduction through permeability and water penetration" and "energy absorption through elastic deformation." Their permeability weakens wave energy and reduces wave impact; elastic deformation buffers wave impact loads and controls the vibration amplitude of the thin-film floating photovoltaic platform. The combination of these two characteristics can precisely match the core requirements of flexible thin-film photovoltaic modules for "low vibration and no water accumulation." However, current research on circular permeable elastic structures struggles to quantitatively output vertical displacement, thus hindering the provision of data support for vibration control of thin-film floating photovoltaic platforms. Summary of the Invention

[0004] This application provides a method, apparatus, and device for solving the motion response of a circular permeable elastic structure suitable for thin-film floating photovoltaic platforms. It can quantitatively output the vertical displacement of the circular permeable elastic structure, providing data support for the vibration control of thin-film floating photovoltaic platforms.

[0005] In a first aspect, embodiments of this application provide a method for solving the motion response of a circular permeable elastic structure suitable for a thin-film floating photovoltaic platform, including:

[0006] The kinematic and dynamic equations of the circular permeable elastic structure in the frequency domain are determined, and the coupling equations of the permeability effect, elastic deformation and fluid motion in the fluid domain of the circular permeable elastic structure are determined based on the kinematic and dynamic equations.

[0007] Determine the free edge conditions of the circular perforated elastic structure;

[0008] Based on the Laplace equation of scattering potential in the fluid domain, the bottom condition, the free liquid surface boundary condition, the object surface boundary condition satisfying the circular open elastic structure, and the far-field radiation condition, the velocity potential of the outer region and the velocity potential of the inner region of the circular open elastic structure are determined.

[0009] Based on the velocity potential of the inner region and the kinematic equations, and with the vertical coordinates being zero, the vertical displacement equations of the circular permeable elastic structure are constructed.

[0010] The outer region dispersion relation of the circular permeable elastic structure is constructed based on the outer region velocity potential and the free liquid surface boundary conditions. The modal eigenvalues ​​of the outer region velocity potential are solved based on the outer region dispersion relation. The inner region dispersion relation of the circular permeable elastic structure is determined based on the inner region velocity potential and the coupling equation. The modal eigenvalues ​​of the inner region velocity potential are determined based on the inner region dispersion relation and used as the modal eigenvalues ​​in the vertical displacement equation.

[0011] At the boundary between the outer and inner regions of the circular permeable elastic structure, a relational equation between the velocity potential of the outer region and the velocity potential of the inner region is constructed based on the velocity potential and the continuity condition of the radial derivative of the velocity potential. This equation serves as the target relational equation. A set of linear equations containing the target modal amplitude is determined based on the target relational equation through inner product operations, and this set serves as the first set of linear equations. The target modal amplitude includes the modal amplitude of the velocity potential of the outer region and the modal amplitude of the velocity potential of the inner region.

[0012] Based on the vertical displacement equation and the free edge condition of the circular open elastic structure, the deformation equation of the free edge condition is determined, and a linear equation set containing the target mode amplitude is determined based on the deformation equation of the free edge condition through inner product operation, as the second linear equation set.

[0013] Based on the first set of linear equations, the second set of linear equations, the modal eigenvalues ​​of the velocity potential in the outer region and the modal eigenvalues ​​of the velocity potential in the inner region, the target modal amplitude is solved, and the modal amplitude of the velocity potential in the inner region in the solved target modal amplitude is used as the modal amplitude of the vertical displacement equation.

[0014] Secondly, embodiments of this application provide an electronic device, characterized in that it includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the method provided in embodiments of this application.

[0015] Thirdly, embodiments of this application provide a computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the method provided in embodiments of this application.

[0016] The technical solution provided in this application determines the coupling equations of the permeability effect, elastic deformation, and fluid motion of a circular permeable elastic structure through the kinematic and dynamic equations in the frequency domain. This allows for a deep integration of the permeability effect, elastic deformation, and fluid motion of the circular permeable elastic structure. The outer and inner velocity potentials of the circular permeable elastic structure are determined using the Laplace equation, bottom conditions, free surface boundary conditions, object surface boundary conditions, and far-field radiation conditions in the fluid domain. The vertical displacement equation of the circular permeable elastic structure is constructed using the inner velocity potential and kinematic equations with zero vertical coordinates. The modal eigenvalues ​​of the outer velocity potential are solved using the dispersion relation obtained from the outer velocity potential and free surface boundary conditions. Similarly, the modal eigenvalues ​​of the inner velocity potential are solved using the dispersion relation obtained from the inner velocity potential and coupling equations, serving as the modal eigenvalues ​​in the vertical displacement equation. Furthermore, the solution is applied to the circular permeable elastic structure... The first linear equation set is constructed using the target relationship equation at the boundary between the outer and inner regions and inner product operations. The second linear equation set is determined based on the vertical displacement equation and the free edge conditions of the circular permeable elastic structure using inner product operations. The modal amplitude of the vertical displacement equation is obtained using the first and second linear equation sets, the modal eigenvalues ​​of the velocity potential in the outer and inner regions, and the modal eigenvalues ​​of the velocity potential in the inner region. In other words, the vertical displacement equation is obtained by integrating the coupling equations of the permeability effect, elastic deformation, and fluid motion of the circular permeable elastic structure. Solving the modal eigenvalues ​​and modal amplitudes in the vertical displacement equation quantifies the correlation mechanism between pore parameters and wave energy dissipation, achieving synergistic optimization of the water permeability and structural stability of the thin-film floating photovoltaic platform. This fundamentally alleviates vibration damage to flexible thin-film photovoltaic modules and reduces the risk of salt spray corrosion. The vertical displacement of the circular permeable elastic structure is quantitatively output using the above method, providing data support for the vibration control of the thin-film floating photovoltaic platform. Attached Figure Description

[0017] Figure 1 A flowchart illustrating a method for solving the motion response of a circular permeable elastic structure suitable for thin-film floating photovoltaic platforms, provided for the implementation of this application;

[0018] Figure 2A schematic diagram showing the division of the velocity potential in the inner and outer regions;

[0019] Figure 3 In order to be in time, and the incident wave azimuth angle In this case, A schematic diagram of the vertical displacement at that time;

[0020] Figure 4 In order to be in time, and the incident wave azimuth angle In this case, A schematic diagram of the vertical displacement at that time;

[0021] Figure 5 In order to be in time, and the incident wave azimuth angle In this case, A schematic diagram of the vertical displacement at that time;

[0022] Figure 6 A structural block diagram of a motion response solving device for a circular permeable elastic structure suitable for a thin-film floating photovoltaic platform, provided for the implementation of this application;

[0023] Figure 7 This is a schematic diagram of an electronic device structure provided in an embodiment of this application. Detailed Implementation

[0024] The present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] Figure 1 This is a flowchart of a motion response solution method for a circular permeable elastic structure suitable for a thin-film floating photovoltaic platform, provided by an embodiment of this application. The method can be executed by a motion response solution device for the circular permeable elastic structure. The device can be implemented by software and / or hardware and can be configured in an electronic device such as a computer. The circular permeable elastic structure is suitable for a thin-film floating photovoltaic platform.

[0026] like Figure 1 As shown, the technical solutions provided in this application include:

[0027] S110: Determine the kinematic and dynamic equations of the circular permeable elastic structure in the frequency domain, and determine the coupling equation between the circular permeable elastic structure and the fluid motion in the fluid domain based on the kinematic and dynamic equations.

[0028] In this embodiment, the circular permeable elastic structure can be a three-dimensional circular permeable elastic structure. This three-dimensional circular permeable elastic structure has a thin film as its basic form, with a thickness much smaller than the planar feature size, satisfying the core assumptions of thin-plate theory. The vibration analysis of the circular permeable elastic structure is based on Kirchhoff's thin-plate theory. Combining the coupling effect between the permeable medium and the fluid, the vibration differential equation, i.e., the dynamic equation, is derived. From a physical mechanism perspective, as a thin, uniform structure, the bending deformation of the circular permeable elastic structure is dominated by the fourth-order Laplace operator. Simultaneously, its own inertial force and the force exerted by the fluid on the structure must be considered. The specific dynamic equation is as follows:

[0029] (1);

[0030] in, The bending stiffness of a circular, open elastic structure. The thickness is that of a circular, open, elastic structure. The density of a circular, open, elastic structure. For the density of the fluid, The vertical displacement of the circular, open elastic structure in the time domain; This represents the vertical displacement of the circular openwork structure in the frequency domain. The total velocity potential of the flow field in the time domain; The total velocity potential of the flow field in the frequency domain; Indicates taking the real part; For time; Let be the angular frequency of the incident wave; where, The hydrostatic restoring force of a circular permeable elastic structure in the time domain.

[0031] The above formula (1) can be converted into a frequency domain equation as follows:

[0032] (2);

[0033] in, It is the acceleration due to gravity; It is the structural force of a circular, open elastic structure in the frequency domain. For inertial forces in the frequency domain, For dynamic pressure in the frequency domain, This refers to the static water restoring force in the frequency domain.

[0034] Normalizing the above formula (2) yields:

[0035] (3);

[0036] in, The normalized bending stiffness is determined by the actual bending stiffness of the circular open elastic structure, water density, and water depth, and directly affects the ability of the circular open elastic structure to resist deformation. The normalized surface mass reflects the ratio of the unit area mass of the circular permeable elastic structure to the water density, which determines the inertial response characteristics of the circular permeable elastic structure. The ratio of the square of the angular frequency to the gravitational acceleration is related to the angular frequency of the incident wave and the gravitational acceleration, reflecting the frequency characteristics of the external excitation.

[0037] In this embodiment, the flow rate of the fluid in the medium is directly proportional to the pressure gradient, the permeability of the medium, and the cross-sectional area, and inversely proportional to the fluid viscosity and the seepage length. Using a micro-element of the circular permeable elastic structure, the velocity difference of the fluid along the normal vector of the micro-element is inversely proportional to the pressure gradient. Therefore, the kinematic equation of the circular permeable elastic structure is:

[0038] (4);

[0039] Transformed into the frequency domain equation:

[0040] (5);

[0041] in, Pore ​​parameters, calculated from the permeability, fluid dynamic viscosity coefficient, and thickness of the circular permeable elastic structure, are used to describe the damping effect of the circular permeable elastic structure on the fluid. As the porosity increases... As the fluid rises, the pressure loss through the circular perforated elastic structure increases, thereby suppressing the vibration of the circular perforated elastic structure. The viscosity coefficient is the fluid dynamics coefficient. The permeability of a circular, permeable elastic structure (dependent only on the material itself); ; The vertical coordinates are for a circular, open, elastic structure.

[0042] Among them, the following can be obtained from the dynamic equation (3) and kinematic equation (5) of the circular open elastic structure in the frequency domain:

[0043] (6);

[0044] The function of the above formula (6) is to transform the vibration behavior of the circular permeable elastic structure into a solvable mathematical relationship, reflecting the balance of the structural force, inertial force and fluid motion of the circular permeable elastic structure. In principle, it realizes the three-dimensional coupling of the permeability effect, elastic deformation and fluid motion of the circular permeable elastic structure. That is, the above formula (6) is the coupling equation of the permeability effect, elastic deformation and fluid motion of the circular permeable elastic structure. In effect, the influence of different parameters (such as pore parameters and bending stiffness) on vibration can be quantitatively analyzed through this equation, providing a theoretical basis for subsequent parameter optimization.

[0045] S120: Determine the free edge conditions of the circular open elastic structure.

[0046] In this embodiment, the free edge condition of the circular permeable elastic structure applies to the boundary (circumference of the horizontal projection domain, at the radial coordinate) of the circular permeable elastic structure, requiring zero bending moment and zero shear force. From an operational perspective, this condition aligns with the practical engineering application of circular permeable elastic structures. In thin-film floating photovoltaic platforms, the permeable elastic circular structure typically lacks fixed support, and its edges are not subject to additional constraints, making it unable to withstand bending moment and shear force. Its principle is based on the edge stress balance of thin plates in structural mechanics, describing the mechanical state of the edge through normal and tangential differential operators. Specifically, in… At this point, the bending moment and shear force are 0, meaning the free edge condition is:

[0047] (7);

[0048] in, The coordinates of the circular perforated elastic structure are circumferential. The radial coordinates of the circular perforated elastic structure; The radius of the circular permeable elastic structure; and These are the bending moment and shear force at the edge of the circular permeable elastic structure, respectively. The Poisson's ratio of the circular permeable elastic structure; Let the normal derivative of the edge be , These parameters, which are the derivatives of the edge azimuth angle, work together to ensure that the mechanical state of the edge is consistent with the actual state, thus avoiding deviations in the calculation of structural displacement caused by excessive constraints.

[0049] S130: Based on the Laplace equation of scattering potential in the fluid domain, the bottom condition, the free liquid surface boundary condition, the object surface boundary condition satisfying the circular open elastic structure, and the radiation condition, determine the velocity potential of the outer region and the velocity potential of the inner region of the circular open elastic structure.

[0050] In this embodiment, velocity potential is the core physical quantity describing the irrotational motion of the fluid. Based on the axisymmetric characteristics of the circular permeable elastic structure, a cylindrical coordinate system is used to separate variables, and the velocity potentials of the inner and outer regions of the circular permeable elastic structure are expanded separately to achieve a regional description of the fluid motion, laying the foundation for subsequent coupled solutions. Specifically, the circular permeable elastic structure can divide the flow field into an inner and outer region; the inner region of the circular permeable elastic structure is equivalent to the entire flow domain projected onto the water bottom; the outer region of the circular permeable elastic structure refers to the region outside the inner region of the structure. Therefore, the velocity potentials of the inner and outer regions can be referenced... Figure 2 .

[0051] In this embodiment, optionally, determining the outer and inner velocity potentials of the circular permeable elastic structure based on the Laplace equation of the scattering potential in the fluid domain, the bottom conditions, the free surface boundary conditions, the object surface boundary conditions satisfying the circular permeable elastic structure, and the far-field radiation conditions includes: determining the outer scattering potential of the circular permeable elastic structure constructed using the Hankel function and the inner scattering potential of the circular permeable elastic structure constructed using the Bessel function based on the Laplace equation, the bottom conditions, the free surface boundary conditions, the object surface boundary conditions, and the far-field radiation conditions; constructing the outer velocity potential based on the incident wave potential, the outer scattering potential, and the condition satisfying the outer scattering potential when the radial coordinate of the circular permeable elastic structure tends to 0; and constructing the inner velocity potential based on the inner scattering potential and the bounded condition of the center of the circular permeable elastic structure.

[0052] In this embodiment, the boundary conditions in the fluid domain include bottom boundary conditions, free surface boundary conditions, structure-fluid interface conditions (i.e., object surface boundary conditions), and far-field radiation conditions. The bottom boundary conditions act on the lower boundary in the water depth direction. The principle is that there is no vertical fluid penetration at the bottom surface, therefore the vertical fluid velocity is zero. The free surface boundary conditions act on the still water surface outside the circular permeable elastic structure. The principle is to combine the kinematics and dynamics of the free surface in fluid dynamics, simplifying it by eliminating the wave surface elevation. Its function is to describe the water wave propagation law covering the outer region, effectively ensuring that the water wave motion in the outer region conforms to the basic characteristics of gravity waves. The structure-fluid interface conditions act on the still water surface inside the circular permeable elastic structure, and are divided into two categories: kinematic continuity and dynamic continuity. Kinematic continuity... The principle of the first condition is that there is no relative slip between the structure and the fluid, and the vertical velocity of the fluid must match the velocity of the structure. Simultaneously, a velocity correction term due to pore parameters is added. The principle of the dynamic continuity condition is that the pressure at the interface between the structure and the fluid is continuous, and the velocity potential must be correlated with the displacement and elastic deformation of the structure. The combined effect of these two conditions is to achieve strong coupling between the fluid and the structure, effectively establishing a quantitative correlation between their motions. The far-field radiation condition acts on the horizontal far field. The principle is that scattered waves propagate into the far field without energy reflection, ensuring the uniqueness of the solution and preventing non-physical wave reflection phenomena in the far field. Therefore, the complete equation for the scattering potential in the fluid domain is obtained:

[0053] (8);

[0054] In formula (8), the first equation is the Laplace equation for the scattering potential, the second equation is the bottom boundary condition, the third equation is the free surface boundary condition, the fourth equation is the surface boundary condition satisfied by the circular porous elastic structure, and the fifth equation is the far-field radiation condition. It is the scattering potential; The vertical coordinates of the circular permeable elastic structure; ω is the angular frequency of the incident wave; Let A be a point in the flow field; Let it be the set of midpoints of the flow field; λ is the wavelength.

[0055] In this embodiment, the Laplace equation in formula (8) is solved, and under steady-state conditions, the spatial variables are separated, and the underwater boundary conditions are applied to obtain the outer region scattering potential of the circular permeable elastic structure as follows:

[0056] (9);

[0057] in, The scattering potential of the outer region; Let be the order of the circumferential mode; for Hankel function of the first kind; It is a hyperbolic cosine function; for Hankel function of the second kind; These are the expansion coefficients for external and internal propagation, respectively;

[0058] In formula (9), the scattering potential of the outer region is expressed in the form of a Hankel function. The scattering potential of the outer region describes the outward propagation of waves caused by the deformation of a circular, open elastic structure. The first type of Hankel function describes the outward propagation property, which is consistent with the actual situation of the scattering potential of the outer region. However, the second type of Hankel function describes the inward propagation property, which is inconsistent with reality. Therefore, it is necessary to use a different function in formula (9). Specifically, to facilitate the application of long-range radiation conditions, and considering that the outer region of the circular permeable elastic structure is an open water area, the velocity potential is formed by the superposition of the incident wave potential and the scattered potential. This serves to describe the initial excitation of the incident wave and the scattering response of the circular permeable elastic structure to the wave, respectively. The expansion of the incident wave potential is based on the decomposition of a plane wave in cylindrical coordinates. The principle is that a plane incident wave can be transformed into radially distributed wave components through a Bessel function to accommodate the axisymmetry of the circular permeable elastic structure. This expansion accurately characterizes the spatial distribution of the incident wave in the outer region of the circular permeable elastic structure, providing a benchmark for scattered wave analysis. The expansion of the scattering potential must satisfy the far-field radiation condition. The principle is that the Hankel function has damped oscillation characteristics in the far field, which conforms to the physical laws of outward propagation of scattered waves. Therefore, a first-order Hankel function is used to describe the radial distribution, while introducing multiple wave numbers to encompass both propagating and damped waves. This expansion comprehensively describes the scattering effect of the circular permeable elastic structure on the incident wave, effectively capturing the propagation characteristics of far-field scattered waves and the attenuation characteristics of near-field damped waves.

[0059] Wherein, the velocity potential of the outer region is:

[0060] (10);

[0061] in, The velocity potential of the outer region; Let be the order of the circumferential mode; The order of the radial modes; , which represents the eigenvalue of the 0th order radial mode of the velocity potential in the outer region; The coordinates of the circular perforated elastic structure are circumferential. The radial coordinates of the circular perforated elastic structure; The azimuth angle of the incident wave; The vertical coordinates of the circular permeable elastic structure; Water depth; The first of the velocity potentials in the outer region First mode amplitude; for Hankel function of the first kind; The velocity potential of the outer region eigenvalues ​​of the first radial mode; It is a hyperbolic cosine function; When the eigenvalue is And the radial coordinate is time The first-order Bessel function of the order.

[0062] In this embodiment, the Laplace equation is also solved for the inner region of the circular open elastic structure, but it is written in the form of a Bessel function series:

[0063] (11);

[0064] in, and These are the corresponding expansion coefficients; The first radial mode eigenvalue of the velocity potential in the inner region; The first of the velocity potentials in the inner region Eigenvalues ​​of the first radial mode; for The second-order Bessel function of the second kind; When the modal eigenvalue is And the radial coordinate is time The second-order Bessel function of the order; in the above formula (11) The velocity potential of the inner region of the circular open elastic structure is obtained:

[0065] (12);

[0066] in, The velocity potential of the inner region; The first of the velocity potentials in the inner region First mode amplitude; When the modal eigenvalue is And the radial coordinate is time The first-order Bessel function.

[0067] Specifically, the inner region of the circular permeable elastic structure is constrained by the structure itself. Fluid motion is strongly coupled with the elastic deformation of the structure. The velocity potential expansion of the inner region must satisfy the physical requirement that the center of the circular permeable elastic structure has no singularities. The principle is based on the Bessel function... Whether the value at a given point conforms to the actual state of fluid motion at the center of a circular permeable elastic structure is considered. Therefore, a first-order Bessel function of the first kind is used to describe the radial distribution, while a second-order Bessel function of the second kind diverges at the center of the circular permeable elastic structure. The characteristic value of the radial mode of the velocity potential in the inner region of the circular permeable elastic structure is given. The expansion in the above formula (12) is to correlate the fluid motion with the elastic deformation of the circular permeable elastic structure. In effect, the influence of the pore parameters on the flow field inside the circular structure can be directly reflected through the velocity potential in the inner region, providing fluid excitation data for the subsequent calculation of the vertical displacement of the circular permeable elastic structure.

[0068] S140: Based on the velocity potential of the inner region and the kinematic equations, and with the vertical coordinates being zero, construct the vertical displacement equations of the circular permeable elastic structure.

[0069] In this embodiment, based on the kinematic equation of the circular permeable elastic structure in the frequency domain, i.e., the above formula (5), and the velocity potential of the inner region, i.e., the above formula (12), in... Under the given conditions, the vertical displacement equation of the circular open elastic structure in the frequency domain is obtained, which is the expression for the vertical displacement:

[0070] (13);

[0071] in, This represents the vertical displacement in the frequency domain; It is the hyperbolic tangent function.

[0072] S150: Construct the outer region dispersion relation of the circular permeable elastic structure based on the outer region velocity potential and the free liquid surface boundary conditions; solve the modal eigenvalues ​​of the outer region velocity potential based on the outer region dispersion relation; determine the inner region dispersion relation of the circular permeable elastic structure based on the inner region velocity potential and the coupling equation; determine the modal eigenvalues ​​of the inner region velocity potential based on the inner region dispersion relation, and use them as modal eigenvalues ​​in the vertical displacement equation.

[0073] In this embodiment, the modal eigenvalues ​​of the velocity potential in the outer region are the wavenumbers of the outer region of the circular permeable elastic structure; the modal eigenvalues ​​of the velocity potential in the inner region are the wavenumbers of the inner region of the circular permeable elastic structure. The wavenumber is the core parameter determining the spatial distribution of the velocity potential, obtained by solving the corresponding dispersion relation. This step determines the propagation and attenuation characteristics of each wave component in the velocity potential expansion. The principle is that the dispersion relation describes the quantitative correlation between wavenumber and frequency, and structural parameters (such as porosity and stiffness). Effectively, it provides an accurate wavenumber basis for the velocity potential expansion, ensuring the correctness of the fluid motion description.

[0074] In this context, the outer region of the circular permeable elastic structure is an open water area without the constraint of the circular permeable elastic structure. The dispersion relation only needs to consider the propagation law of gravity waves. The specific solution process is to substitute the velocity potential of the outer region into the boundary conditions of the free liquid surface to obtain the dispersion relation of the outer region of the circular permeable elastic structure. That is, to substitute formula (10) into the third equation in formula (8) to obtain the dispersion relation of the outer region:

[0075] (14);

[0076] in, It is the ratio of the square of the angular frequency to the acceleration due to gravity; The characteristic value of the radial mode of the velocity potential in the outer region; It is the acceleration due to gravity;

[0077] In this embodiment, optionally, solving for the modal eigenvalues ​​of the outer region velocity potential based on the outer region dispersion relation includes: iteratively solving for the modal eigenvalues ​​of the outer region velocity potential using a bisection method on the outer region dispersion relation. Specifically, in In the case of complex numbers, that is, when the wavenumber of the outer region of a circular open elastic structure is complex, for... The dominant wavenumber, represented by a real number, is physically a propagating wave. It is solved iteratively within a reasonable range using the bisection method. For example, when the normalized frequency parameter is determined, the wave component corresponding to this dominant wavenumber can be found to propagate continuously in the far field and is a major component of the far-field scattered wave. For The wavenumber, where is an imaginary number, represents a decaying wave and must satisfy the imaginary value characteristic (let ). ), transforming the outer region dispersion relation into Then, the bisection method is used to solve the problem. The wave component corresponding to this type of wave number decays exponentially along the radial direction, and its influence is only in the vicinity of the circular open elastic structure, while it can be ignored in the far field. The effect of this solution process is to accurately distinguish between the propagating wave and the attenuated wave in the outer region of the circular open elastic structure, ensuring the physical rationality of the velocity potential expansion in the outer region.

[0078] In this embodiment, the dispersion relation of the inner region of the circular permeable elastic structure is obtained by combining the coupling equation of the circular permeable elastic structure with the fluid motion in the fluid domain and the velocity potential of the inner region. That is, the dispersion relation of the inner region is obtained by formula (6) and formula (12):

[0079] (15);

[0080] The determination of the modal eigenvalues ​​of the velocity potential in the inner region based on the dispersion relation of the inner region includes: solving the dispersion relation of the inner region using Newton's method combined with the homotopy method to obtain the modal eigenvalues ​​of the velocity potential in the inner region. Specifically, the inner region of the circular permeable elastic structure is constrained by the circular permeable elastic structure, and the dispersion relation of the inner region needs to take into account the influence of porosity and bending stiffness. The homotopy method is used for the solution: the principle is to start from the known wavenumber when there is no porosity (P=0), gradually increase the porosity parameter, and iterate to obtain the wavenumber corresponding to the target value, avoiding the difficulty of directly solving the complex wavenumber; while the wavenumber when P=0 can be obtained using Newton's method. The wavenumber is divided into real propagating waves and imaginary attenuating waves, and a pair of complex conjugate wavenumbers appear at the same time. The wave components corresponding to this type of complex wavenumber have dual characteristics of propagation and attenuation, which is a direct manifestation of energy dissipation caused by porosity.

[0081] S160: At the boundary between the outer and inner regions of the circular permeable elastic structure, a relational equation between the velocity potential of the outer region and the velocity potential of the inner region is constructed based on the continuity condition of the velocity potential and the radial derivative of the velocity potential. This equation serves as the target relational equation. A set of linear equations containing the target modal amplitude is determined based on the target relational equation through inner product operations, and this set serves as the first set of linear equations. The target modal amplitude includes the modal amplitude of the velocity potential of the outer region and the modal amplitude of the velocity potential of the inner region.

[0082] In this embodiment, the boundary continuity condition of the circular permeable elastic structure is coupled with the edge condition of the circular permeable elastic structure to determine the unknown coefficients in the velocity potential expansion. The principle is that the pressure and radial velocity of the fluid at the boundary must be continuous (otherwise there will be non-physical abrupt changes). At the same time, the mechanical constraints of the edge of the circular permeable elastic structure need to be transformed into linear constraints on the coefficients, thus obtaining a complete velocity potential expression.

[0083] Specifically, the boundary continuity conditions for a circular permeable elastic structure include pressure continuity and radial velocity continuity. The physical meaning of the pressure continuity condition is that there are no abrupt changes in fluid pressure at the inner and outer interfaces of the circular permeable elastic structure. Since fluid pressure is proportional to velocity potential, this can be converted into velocity potential continuity. The physical meaning of the radial velocity continuity condition is that there are no abrupt changes in the radial velocity of the fluid at the inner and outer interfaces of the circular permeable elastic structure. The fluid radial velocity is the radial derivative of the velocity potential, thus converting into the continuity of the radial derivative of the velocity potential. The boundary conditions for the circular permeable elastic structure are... Therefore, at the boundary between the outer and inner regions of the circular permeable elastic structure, i.e. The continuity conditions for the velocity potential and its radial derivative include: at the boundary between the outer and inner regions of the circular open elastic structure, the velocity potential of the outer region and the velocity potential of the inner region are equal, and the radial derivative of the velocity potential of the outer region is equal to the radial derivative of the velocity potential of the inner region. The specific expression is:

[0084] (16);

[0085] Therefore, at the boundary between the outer and inner regions of the circular open elastic structure, the target relation equation constructed based on the continuity condition of the velocity potential and its radial derivative is the above formula (16). The above formula (16) is simplified by inner product operation. The principle is to use the orthogonality of the circumferential eigenfunctions and multiply both sides of the equation (16) by the circumferential eigenfunctions. ,in Then, the circular open elastic structure is integrated in the circumferential direction;

[0086] (17);

[0087] in, When the modal eigenvalue is And the radial coordinate is time First-order Bessel function of the first kind; The first of the velocity potentials in the outer region First mode amplitude; When the modal eigenvalue is And the radial coordinate is time Hankel function of the first kind; The first of the velocity potentials in the inner region First mode amplitude; When the modal eigenvalue is And the radial coordinate is time The first-order Bessel function of the first kind; based on the above formula (17), using the orthogonality of the vertical eigenfunctions, multiply both sides of the equality in the above formula (17) by the vertical eigenfunction. ,in Then, the integral is performed vertically from the bottom of the water to the free surface:

[0088] (18);

[0089] in, (19);

[0090] in, ; These are the modal cutoff values ​​for the circumferential and vertical eigenfunctions, respectively. These are the integrals of the vertical eigenfunctions of the outer region and the inner region over the entire water depth, respectively. The modal eigenvalue is The integral of the vertical eigenfunctions of the outer region over the full water depth; , These are the orders of the circumferential mode and the radial mode, respectively.

[0091] Among them, the vertical eigenfunctions It has orthogonality, that is, eigenfunctions of different orders change from... The integral of the product of the two eigenfunctions is zero, and only the integral of the eigenfunctions of the same order is non-zero. Multiplying both sides of the equality in formula (17) by the vertical eigenfunction and integrating along the water depth direction transforms the three-dimensional problem into a two-dimensional problem, yielding the result containing only the vertical eigenfunctions. The linear equations; similarly, the circumferential eigenfunctions It also employs the orthogonality principle. The thread equation system of the above formula (18) contains The first system of linear equations consists of 10 equations.

[0092] S170: Based on the vertical displacement equation and the free edge condition of the circular open elastic structure, determine the deformation equation of the free edge condition, and determine the linear equation system containing the target mode based on the deformation equation of the free edge condition through inner product operation, as the second linear equation system.

[0093] Specifically, substituting formula (13) into formula (7) yields the deformation equation for the free edge condition, which is:

[0094] (20);

[0095] Similarly, utilizing the orthogonality of circumferential eigenfunctions, multiply both sides of the equality in formula (20) by the circumferential eigenfunction. Then, by integrating over the circular open elastic structure in the circumferential direction, we obtain:

[0096] (twenty one);

[0098] Among them, the above formula (21) can provide These equations form a system of linear equations, namely the second system of linear equations.

[0099] S180: Based on the first linear equation set, the second linear equation set, the modal eigenvalues ​​of the outer region velocity potential and the inner region velocity potential, solve for the target modal amplitude, and use the modal amplitude of the inner region velocity potential in the solved target modal amplitude as the modal amplitude of the vertical displacement equation.

[0100] In this embodiment, the modal eigenvalues ​​of the outer region velocity potential and the inner region velocity potential are substituted into the first and second linear equation systems to solve for the target modal amplitude, obtaining the modal amplitudes of the outer and inner region velocity potentials. The modal amplitude of the inner region velocity potential is then used as the modal amplitude of the vertical displacement equation. The LU decomposition method can be used to solve the first and second linear equation systems. This method has the advantage of high solution efficiency and stability for dense linear equation systems, taking into account the attenuation characteristics of far-field attenuated waves. The order of the vertical eigenfunction is truncated as follows: The order of the circumferential eigenfunction is truncated as (This cutoff parameter has been verified to ensure that the displacement calculation error is less than a certain value, meeting the engineering accuracy requirements.)

[0101] Specifically, by solving the first and second linear equation systems, we obtain... It can Substituting the modal eigenvalues ​​of the velocity potential in the inner region into formula (13) yields the final result, which can quantitatively describe the vibration response of a circular permeable elastic structure under water wave action. The principle is that the vertical displacement of the circular permeable elastic structure is directly related to the vertical velocity of the fluid on the lower surface of the circular permeable elastic structure. In effect, it can intuitively reflect the influence of parameters such as porosity and bending stiffness on the motion of the circular permeable elastic structure, providing key data for engineering structure design. Among them, in the circular permeable elastic structure under water wave action, the vertical displacement of the circular permeable elastic structure is directly related to the vertical velocity of the fluid on the lower surface of the circular permeable elastic structure. Time, expressed in dimensionless form. azimuth of incident wave In this case, , and A schematic diagram of the vertical displacement at that time can be referenced. Figures 3-5 Where PH is a dimensionless pore parameter.

[0102] It should be noted that in formula (13), The value is ,but Finally captured That is The value is The solution obtained by solving the first and second linear equation systems mentioned above In the future When substituted into formula (13), The value is also ,and The values ​​are the same, therefore, can be Substituting the modal eigenvalues ​​of the velocity potential in the inner region and the inner region into formula (13) yields the final result.

[0103] The technical solution provided in this application embodiment determines the coupling equations of the permeability effect, elastic deformation, and fluid motion of a circular permeable elastic structure through the kinematic and dynamic equations in the frequency domain. This allows for a deep integration of the permeability effect, elastic deformation, and fluid motion of the circular permeable elastic structure. The outer and inner velocity potentials of the circular permeable elastic structure are determined through the Laplace equation, bottom conditions, free surface boundary conditions, object surface boundary conditions, and far-field radiation conditions in the fluid domain. The vertical displacement equation of the circular permeable elastic structure is constructed using the inner velocity potential and kinematic equations with the vertical coordinates at zero. The modal eigenvalues ​​of the outer velocity potential are solved using the dispersion relation obtained from the outer velocity potential and free surface boundary conditions. Similarly, the modal eigenvalues ​​of the inner velocity potential are solved using the dispersion relation obtained from the inner velocity potential and coupling equations, serving as the modal eigenvalues ​​in the vertical displacement equation. Furthermore, the solution is applied to a circular permeable elastic structure... The first linear equation set is constructed by using the target relationship equation at the boundary between the outer and inner regions of the permeable elastic structure and inner product operations. The second linear equation set is determined based on the vertical displacement equation and the free edge conditions of the circular permeable elastic structure using inner product operations. The modal amplitude of the vertical displacement equation is obtained through the first and second linear equation sets, the modal eigenvalues ​​of the velocity potential in the outer and inner regions, and the modal eigenvalues ​​of the velocity potential in the inner region. In other words, the vertical displacement equation is obtained by integrating the coupled equations of the permeability effect, elastic deformation, and fluid motion of the circular permeable elastic structure. Solving the modal eigenvalues ​​and modal amplitudes in the vertical displacement equation quantifies the correlation mechanism between pore parameters and wave energy dissipation, achieving synergistic optimization of the water permeability and structural stability of the thin-film floating photovoltaic platform. This fundamentally alleviates vibration damage to flexible thin-film photovoltaic modules and reduces the risk of salt spray corrosion. The vertical displacement of the circular permeable elastic structure is quantitatively output using the above method, providing data support for the vibration control of the thin-film floating photovoltaic platform.

[0104] The technical solution provided by the embodiments of the present application performs analysis and solution based on a cylindrical coordinate system, adapts to the axisymmetric characteristics of circular permeable elastic structures, and is highly compatible with the array layout requirements of flexible thin-film photovoltaic modules; compared with existing methods that rely on empirical simplification, the homotopy method is used to solve eigenvalues, that is, the homotopy-based wavenumber solving strategy effectively solves the complex wavenumber problem caused by the permeable effect, ensures the physical consistency of the coupling relationship between fluid and circular permeable elastic structures, can more accurately handle the complex fluid-structure interaction between thin-film floating photovoltaic platforms and waves, and provides key technical support for the coupled vibration analysis of integrated offshore wind-photovoltaic platforms in deep and open seas.

[0105] The calculation accuracy and engineering adaptability of the solution provided by the embodiments of the present application fully match the design requirements of thin-film floating photovoltaic platforms. The vertical displacement solution results can be in good agreement with hydroelastic model tests, can accurately reflect the variation law of vibration response of thin-film floating photovoltaic platforms under different pore parameters, provide a quantitative basis for suppressing wave-induced deformation of thin-film floating photovoltaic platforms, and ensure the structural integrity of flexible thin-film photovoltaic modules. The solution has strong scenario adaptability: only by adjusting parameters such as water depth and angular frequency, it can meet the thin-film photovoltaic deployment requirements in different sea areas from inshore shallow waters to deep and open seas. There is no need to reconstruct the model framework for specific scenarios, which greatly improves design flexibility; under severe sea conditions, optimizing pore parameters can significantly weaken high-order modal vibration induced by nonlinear waves, which can not only protect flexible thin-film photovoltaic modules from impact damage, but also avoid the instability risk of the mooring system of the thin-film floating photovoltaic platform caused by drastic tension changes, and achieves technical synergy with the core requirement of long-term stable operation of thin-film floating photovoltaic platforms.

[0106] The high efficiency and universality of the technical solution provided by the embodiments of the present application can significantly reduce the engineering application threshold of thin-film floating photovoltaic platforms. Its calculation process can quickly complete comparative analysis of multiple sets of structural parameters, adapts to the entire design cycle of thin-film floating photovoltaic platforms from preliminary selection to detailed optimization, greatly reduces the R&D cost and cycle that rely on physical prototype trial and error, and is highly consistent with the development trends of automated production and low cost in the manufacturing field of thin-film floating photovoltaic platforms. In addition to the application of thin-film floating photovoltaic platforms, it can also be extended horizontally to the "photovoltaic-wind power" co-platform system, providing coupled vibration analysis support for the composite floating structure after adding wind turbines, and assisting the safety design of multi-energy complementary projects in deep and open seas; meanwhile, the accurate analysis capability of the technical solution provided by the embodiments of the present application on the interaction between permeable structures and waves can also provide a basis for the design of wave prevention and vibration reduction components supporting photovoltaic platforms, promote the development of thin-film floating photovoltaic platforms towards high efficiency, safety and ecology, and lay a technical foundation for the large-scale implementation of the marine photovoltaic industry.

[0107] Figure 6 is a motion response solving device for circular permeable elastic structures suitable for thin-film floating photovoltaic platforms provided by an embodiment of the present application, the device comprises:

[0108] The first processing module 610 is used to determine the kinematic equation and dynamic equation of the circular permeable elastic structure in the frequency domain, and to determine the coupling equation of the permeability effect, elastic deformation and fluid motion in the fluid domain of the circular permeable elastic structure based on the kinematic equation and the dynamic equation.

[0109] The second processing module 620 is used to determine the free edge conditions of the circular permeable elastic structure.

[0110] The third processing module 630 is used to determine the velocity potential of the outer region and the velocity potential of the inner region of the circular permeable elastic structure based on the Laplace equation of the scattering potential in the fluid domain, the bottom condition, the free liquid surface boundary condition, the object surface boundary condition that satisfies the circular permeable elastic structure and the far-field radiation condition.

[0111] The fourth processing module 640 is used to construct the vertical displacement equation of the circular permeable elastic structure based on the velocity potential of the inner region and the kinematic equation, and when the vertical coordinate is zero.

[0112] The fifth processing module 650 constructs the outer region dispersion relation of the circular permeable elastic structure based on the outer region velocity potential and the free liquid surface boundary conditions, solves the modal eigenvalues ​​of the outer region velocity potential based on the outer region dispersion relation, determines the inner region dispersion relation of the circular permeable elastic structure based on the inner region velocity potential and the coupling equation, and determines the modal eigenvalues ​​of the inner region velocity potential based on the inner region dispersion relation, which are used as the modal eigenvalues ​​in the vertical displacement equation;

[0113] The sixth processing module 660 is used to construct a relational equation between the velocity potential of the outer region and the velocity potential of the inner region at the boundary between the outer and inner regions of the circular open elastic structure, based on the velocity potential and the continuity condition of the radial derivative of the velocity potential, as the target relational equation. It then determines a set of linear equations containing the target modal amplitude based on the target relational equation through inner product operations, and uses this set as the first set of linear equations. The target modal amplitude includes the modal amplitude of the velocity potential in the outer region and the modal amplitude of the velocity potential in the inner region.

[0114] The seventh processing module 670 is used to determine the deformation equation of the free edge condition based on the vertical displacement equation and the free edge condition of the circular open elastic structure, and to determine a linear equation set containing the target mode amplitude based on the deformation equation of the free edge condition through inner product operation, as the second linear equation set.

[0115] The eighth processing module 680 solves for the target modal amplitude based on the first linear equation set, the second linear equation set, the modal characteristic value of the velocity potential in the outer region, and the modal characteristic value of the velocity potential in the inner region, and uses the modal amplitude of the velocity potential in the inner region in the solved target modal amplitude as the modal amplitude of the vertical displacement equation.

[0116] like Figure 7 As shown in the figure, this application provides an electronic device, including a processor 111, a communication interface 112, a memory 113, and a communication bus 114, wherein the processor 111, the communication interface 112, and the memory 113 communicate with each other through the communication bus 114.

[0117] Memory 113 is used to store computer programs;

[0118] In one embodiment of this application, when the processor 111 executes a program stored in the memory 113, it implements the method provided in any of the foregoing method embodiments, including:

[0119] The kinematic and dynamic equations of the circular permeable elastic structure in the frequency domain are determined, and the coupling equations of the permeability effect, elastic deformation and fluid motion in the fluid domain of the circular permeable elastic structure are determined based on the kinematic and dynamic equations.

[0120] Determine the free edge conditions of the circular perforated elastic structure;

[0121] Based on the Laplace equation of scattering potential in the fluid domain, the bottom condition, the free liquid surface boundary condition, the object surface boundary condition satisfying the circular open elastic structure, and the far-field radiation condition, the velocity potential of the outer region and the velocity potential of the inner region of the circular open elastic structure are determined.

[0122] Based on the velocity potential of the inner region and the kinematic equations, and with the vertical coordinates being zero, the vertical displacement equations of the circular permeable elastic structure are constructed.

[0123] The outer region dispersion relation of the circular permeable elastic structure is constructed based on the outer region velocity potential and the free liquid surface boundary conditions. The modal eigenvalues ​​of the outer region velocity potential are solved based on the outer region dispersion relation. The inner region dispersion relation of the circular permeable elastic structure is determined based on the inner region velocity potential and the coupling equation. The modal eigenvalues ​​of the inner region velocity potential are determined based on the inner region dispersion relation and used as the modal eigenvalues ​​in the vertical displacement equation.

[0124] At the boundary between the outer and inner regions of the circular permeable elastic structure, a relational equation between the velocity potential of the outer region and the velocity potential of the inner region is constructed based on the velocity potential and the continuity condition of the radial derivative of the velocity potential. This equation serves as the target relational equation. A set of linear equations containing the target modal amplitude is determined based on the target relational equation through inner product operations, and this set serves as the first set of linear equations. The target modal amplitude includes the modal amplitude of the velocity potential of the outer region and the modal amplitude of the velocity potential of the inner region.

[0125] Based on the vertical displacement equation and the free edge condition of the circular open elastic structure, the deformation equation of the free edge condition is determined, and a linear equation set containing the target mode amplitude is determined based on the deformation equation of the free edge condition through inner product operation, as the second linear equation set.

[0126] Based on the first set of linear equations, the second set of linear equations, the modal eigenvalues ​​of the velocity potential in the outer region and the modal eigenvalues ​​of the velocity potential in the inner region, the target modal amplitude is solved, and the modal amplitude of the velocity potential in the inner region in the solved target modal amplitude is used as the modal amplitude of the vertical displacement equation.

[0127] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method provided in any of the foregoing method embodiments.

[0128] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0129] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented using software plus a general-purpose hardware platform, or of course, using hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the related technology, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0130] The above embodiments are merely illustrative examples and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this application.

Claims

1. A method for solving the motion response of a circular open elastic structure suitable for thin-film floating photovoltaic platforms, characterized by, include: The kinematic and dynamic equations of the circular permeable elastic structure in the frequency domain are determined, and the coupling equations of the permeability effect, elastic deformation and fluid motion in the fluid domain of the circular permeable elastic structure are determined based on the kinematic and dynamic equations. Determine the free edge conditions of the circular perforated elastic structure; Based on the Laplace equation of scattering potential in the fluid domain, the bottom condition, the free liquid surface boundary condition, the object surface boundary condition satisfying the circular open elastic structure, and the far-field radiation condition, the velocity potential of the outer region and the velocity potential of the inner region of the circular open elastic structure are determined. Based on the velocity potential of the inner region and the kinematic equations, and with the vertical coordinates being zero, the vertical displacement equations of the circular permeable elastic structure are constructed. The outer region dispersion relation of the circular permeable elastic structure is constructed based on the outer region velocity potential and the free liquid surface boundary conditions. The modal eigenvalues ​​of the outer region velocity potential are solved based on the outer region dispersion relation. The inner region dispersion relation of the circular permeable elastic structure is determined based on the inner region velocity potential and the coupling equation. The modal eigenvalues ​​of the inner region velocity potential are determined based on the inner region dispersion relation and used as the modal eigenvalues ​​in the vertical displacement equation. At the boundary between the outer and inner regions of the circular permeable elastic structure, a relational equation between the velocity potential of the outer region and the velocity potential of the inner region is constructed based on the velocity potential and the continuity condition of the radial derivative of the velocity potential. This equation serves as the target relational equation. A set of linear equations containing the target modal amplitude is determined based on the target relational equation through inner product operations, and this set serves as the first set of linear equations. The target modal amplitude includes the modal amplitude of the velocity potential of the outer region and the modal amplitude of the velocity potential of the inner region. Based on the vertical displacement equation and the free edge condition of the circular open elastic structure, the deformation equation of the free edge condition is determined, and a linear equation set containing the target mode amplitude is determined based on the deformation equation of the free edge condition through inner product operation, as the second linear equation set. Based on the first set of linear equations, the second set of linear equations, the modal eigenvalues ​​of the velocity potential in the outer region and the modal eigenvalues ​​of the velocity potential in the inner region, the target modal amplitude is solved, and the modal amplitude of the velocity potential in the inner region in the solved target modal amplitude is used as the modal amplitude of the vertical displacement equation.

2. The method of claim 1, wherein, The determination of the outer and inner velocity potentials of the circular permeable elastic structure based on the Laplace equation of scattering potential in the fluid domain, bottom conditions, free liquid surface boundary conditions, surface boundary conditions satisfying the circular permeable elastic structure, and far-field radiation conditions includes: Based on the Laplace equation, the bottom conditions, the free liquid surface boundary conditions, the object surface boundary conditions, and the far-field radiation conditions, the scattering potential of the outer region of the circular permeable elastic structure constructed by the Hankel function and the scattering potential of the inner region of the circular permeable elastic structure constructed by the Bessel function are determined. The outer region velocity potential is constructed based on the incident wave potential, the outer region scattering potential, and the condition that the outer region scattering potential satisfies when the radial coordinate of the circular open elastic structure tends to 0. The velocity potential of the inner region is constructed based on the scattering potential of the inner region and the bounded condition of the center of the circular open elastic structure.

3. The method according to claim 2, characterized in that, The velocity potential in the outer region is: ； in, The velocity potential of the outer region; Let be the order of the circumferential mode; The order of the radial modes; The eigenvalues ​​are the 0th order radial mode eigenvalues ​​of the velocity potential in the outer region; The coordinates of the circular perforated elastic structure are circumferential. The radial coordinates of the circular permeable elastic structure; The azimuth angle of the incident wave; The vertical coordinates of the circular permeable elastic structure; Water depth; The first of the velocity potentials in the outer region First mode amplitude; for Hankel function of the first kind; The velocity potential of the outer region First-order radial modal eigenvalues; It is a hyperbolic cosine function; When the modal eigenvalue is And the radial coordinate is time First-order Bessel function of the first kind; Let A be a point in the flow field; Let it be the set of midpoints of the flow field; The velocity potential of the inner region is: ； in, The velocity potential of the inner region; The first of the velocity potentials in the inner region First mode amplitude; The first of the velocity potentials in the inner region First-order radial modal eigenvalues; When the modal eigenvalue is And the radial coordinate is time The first-order Bessel function of the order.

4. The method according to claim 3, characterized in that, The equation for the vertical displacement is: ； in, This represents the vertical displacement in the frequency domain; ω is the angular frequency of the incident wave; Pore ​​parameters; It is the hyperbolic tangent function.

5. The method according to claim 1, characterized in that, The free edge condition is: ； in, This represents the vertical displacement in the frequency domain; ω is the angular frequency of the incident wave; The coordinates of the circular perforated elastic structure are circumferential. The radial coordinates of the circular permeable elastic structure; The radius of the circular permeable elastic structure; and These are the bending moment and shear force at the edge of the circular permeable elastic structure, respectively. The Poisson's ratio of the circular permeable elastic structure; The boundary conditions of the object surface are as follows: ； in, The scattering potential is the stated scattering potential. Pore ​​parameters; The vertical coordinates of the circular permeable elastic structure; This represents the vertical displacement in the frequency domain; ω is the angular frequency of the incident wave; Let A be a point in the flow field; Let be the set of points in the flow field.

6. The method according to claim 3, characterized in that, The dispersion relation of the outer region is as follows: ； in, It is the ratio of the square of the angular frequency to the acceleration due to gravity; The modal characteristic value of the velocity potential in the outer region; It is the acceleration due to gravity; Accordingly, solving for the modal eigenvalues ​​of the velocity potential in the outer region based on the dispersion relation of the outer region includes: The modal eigenvalues ​​of the velocity potential in the outer region are solved iteratively by using the bisection method to solve the dispersion relation of the outer region.

7. The method according to claim 3, characterized in that, The coupling equation is: ； The dispersion relation of the inner region is as follows: ； in, It is the ratio of the square of the angular frequency to the acceleration due to gravity. To normalize surface quality; Normalized bending stiffness; The total velocity potential of the flow field in the frequency domain; ; The modal characteristic value of the velocity potential in the inner region; Pore ​​parameters; It is the hyperbolic tangent function; Determining the modal eigenvalues ​​of the velocity potential in the inner region based on the dispersion relation of the inner region includes: The dispersion relation of the inner region is solved by combining Newton's method with the homotopy method to obtain the modal eigenvalues ​​of the velocity potential of the inner region.

8. The method according to claim 3, characterized in that, The continuity conditions for the velocity potential and its radial derivative include: at the boundary between the outer and inner regions of the circular open elastic structure, the velocity potential of the outer region and the velocity potential of the inner region are equal, and the radial derivative of the velocity potential of the outer region is equal to the radial derivative of the velocity potential of the inner region.

9. An electronic device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed in a computer, causes the computer to perform the method of any one of claims 1-8.

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