A method and system for hydrodynamic parameter analysis of a multi-module articulated laminated structure

Abstract

The application discloses a kind of water power parameter analysis method and system of multi-module articulated laminated structure, and the water power parameter analysis method is specifically as follows: design the complete boundary value problem of wave and the interaction of multi-module articulated laminated structure, based on the unknown complex expansion coefficient in velocity potential of complete boundary value problem, then unknown complex expansion coefficient is used to calculate the reflection coefficient, transmission coefficient, dimensionless deflection, dimensionless bending moment and dimensionless shear force of laminated structure, and the hydroelastic response of multi-module articulated laminated structure is characterized.The method of the application can quickly complete the water power parameter analysis of multi-module articulated laminated structure.

Description

Technical Field

[0001] This invention belongs to the technical field, specifically relating to a method and system for analyzing hydrodynamic parameters of a multi-module articulated laminated structure. Background Technology

[0002] Current marine floating body designs often treat ultra-large floating structures as homogeneous plates or beams, using classical fourth-order partial differential equations for hydroelastic calculations. However, in practical design and application, the self-weight and mechanical properties of ultra-large floating structures require continuous improvement. Laminated structures offer advantages such as geometric order and adjustable mechanical properties. High-stiffness panels maintain the overall structure's high stiffness, while the core layer utilizes perforated materials to reduce self-weight, overcoming the limitations of single-layer homogeneous plates in terms of their singular and unadjustable properties. Therefore, using laminated structures for ultra-large floating structures can meet the requirements for self-weight and mechanical performance. Furthermore, due to their enormous scale, designing ultra-large floating structures as a single unit is impractical, especially for floating structures like offshore photovoltaic systems, offshore ranches, and offshore cities, where prefabrication of such large-scale single structures is difficult. Therefore, a modular approach to designing and manufacturing ultra-large floating structures is considered, dividing the massive single structure into multiple smaller modules, which are then assembled later using suitable connectors. Offshore photovoltaics is one of the future directions for the development of the marine engineering industry. High-stiffness ultra-large floating structure arrays can be used for large-area, low-load offshore photovoltaic projects, and the hydroelastic design method of this type of structure has become the key. Summary of the Invention

[0003] In view of this, the present invention provides a method and system for analyzing hydrodynamic parameters of a multi-module articulated laminated structure.

[0004] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0005] A method for analyzing hydrodynamic parameters of a multi-module articulated laminated structure:

[0006] 1) Design a complete boundary value problem involving the interaction between waves and a multi-module articulated laminated structure.

[0007] The entire water area is divided into region 0, region j, and region J+1, and the velocity potential of each region must satisfy the Laplace equation, surface conditions, bottom boundary conditions, far-field conditions, and elastic plate boundary conditions. Specifically: region 0 is the open water area on the left, where x and z in two-dimensional Cartesian coordinates satisfy x≤0 and -h≤z≤0, respectively; region j is the covered area of ​​a multi-module articulated laminated structure, where x and z in two-dimensional Cartesian coordinates satisfy 0≤x≤b, respectively. J -h≤z≤0, region J+1 is the open water area on the right, and in two-dimensional Cartesian coordinates, x and z satisfy x≥b respectively. J-h≤z≤0, where h is the water depth and b J Let J represent the x-coordinate of the right edge of the J-th laminated structure in a two-dimensional Cartesian coordinate system, where j = 1, 2, ..., J;

[0008] For the wave-facing surface of the first laminated structure, zero deflection is applied to the entire first laminated structure, and zero bending moment is applied to both the panel and the core material of the first laminated structure:

[0009]

[0010]

[0011]

[0012] For the leeward side of the J-th laminated structure, zero deflection is applied to the entire J-th laminated structure, and zero bending moment is applied to both the panel and core material of the J-th laminated structure:

[0013]

[0014]

[0015]

[0016] For the hinge points of laminated structures, set the edge end constraints of the laminated structures as follows:

[0017]

[0018]

[0019] M jm (x)=M (j+1)m (x)=0,x=b j , j=1,2,3,…,J-1 (9)

[0020] Where: W1(x) represents the overall deflection of the first laminated structure, and φ1 is the velocity potential of the first laminated structure. ω represents the angular frequency of the wave, M 1u (x) represents the bending moment of the upper panel of the first laminated structure, M 1l (x) represents the bending moment of the lower panel of the first laminated structure, U u and U l The bending stiffness, M, represents the bending stiffness of the upper and lower panels, respectively. 1m (x) represents the bending moment of the first laminated core material, G t U t Both Y and Y are variables, and G is the shear modulus of the core material, h c E represents the core material thickness.u and E l The elastic modulus of the upper and lower panels, h, are respectively. u and h l The thicknesses of the top and bottom panels are respectively, U u and U l These represent the bending stiffness of the upper and lower panels, respectively, where d is the vertical distance between the centers of the upper and lower panels, and φ is the bending stiffness. j Let be the velocity potential of region j, ρ be the fluid density, and m be the velocity potential. s W is the mass of the laminated structure per unit area. J (x) represents the overall deflection of the J-th laminated structure, M Ju (x) represents the bending moment of the upper panel of the J-th laminated structure, M Jl (x) represents the bending moment of the lower panel of the J-th laminated structure, M Jm (x) represents the bending moment of the J-th laminated core material, μ1 is the vertical spring stiffness, μ2 is the torsional spring stiffness, and M jm (x) represents the bending moment of the j-th laminated core material, M (j+1)m (x) represents the bending moment of the core material of the right-hand laminate adjacent to the j-th laminate, b j φ represents the x-coordinate of the right edge of the j-th laminate in a two-dimensional Cartesian coordinate system. j+1 Let φ be the velocity potential of the region where the right-hand laminate adjacent to the j-th laminate is located. J Let J be the velocity potential of the J-th layered structure;

[0021] 2) Solve for the unknown complex expansion coefficients in the velocity potential.

[0022] Using the Laplace equation, surface conditions, bottom boundary conditions, far-field conditions, and elastic plate boundary conditions, solve for the velocity potentials in regions 0 and J+1. The velocity potential in region 0 includes the unknown complex expansion coefficient R. m The velocity potential in region J+1 contains unknown complex expansion coefficients T. m The velocity potential of region j is solved using the Laplace equation, the underwater boundary conditions, and the elastic plate boundary conditions. The velocity potential of region j includes the unknown complex expansion coefficient A. jn and B jn ;

[0023] Substituting the velocity potentials of regions 0, j, and J+1 into the continuity condition and then truncating them, and substituting the velocity potential of region j into formulas (1)-(9) and then truncating them, we obtain a system of linear equations. Solving the system of linear equations yields the unknown complex expansion coefficient R in the velocity potential. m T m A jn and B jn ;

[0024] 3) Calculate hydrodynamic parameters

[0025] Using the R m T m A jn and B jn The reflection coefficient, transmission coefficient, dimensionless deflection, dimensionless bending moment, and dimensionless shear force of the laminated structure are calculated to characterize the hydroelastic response of the multi-module articulated laminated structure.

[0026] Furthermore, the continuity condition is:

[0027] φ0=φ1,x=0,-h≤z≤0

[0028]

[0029] φ j =φ j+1 x=b j j = 1, 2, 3, ..., J-1, -h ≤ z ≤ 0

[0030]

[0031] φ J =φ J+1 x=b J -h≤z≤0

[0032]

[0033] Where: φ J+1 φ is the velocity potential of region J+1, and φ0 is the velocity potential of region 0.

[0034] Furthermore, the velocity potential expressions for region 0 and region J+1 are as follows:

[0035]

[0036]

[0037] Where: H is the wave height of the incident wave, intermediate quantity κ0 = -ik0, intermediate quantity κ m =k m k m They are eigenvalues, and k0, k m Positive real roots satisfying the following dispersion relation:

[0038] ω 2 =gk0 tanh(k0h)=-gk m tan(k m h),m≥1

[0039] Characteristic functions Z0(z), Z m The expression for (z) is:

[0040]

[0041] Where: g is the acceleration due to gravity, and k0 is the wave number.

[0042] Furthermore, the velocity potential expression for region j is:

[0043]

[0044] Where: Y n (z) represents the vertical characteristic function, and eigenvalue λ n Satisfies the dispersion equation:

[0045] Furthermore, substituting the velocity potentials of regions 0, j, and J+1 into the continuity condition, we obtain:

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] Among them, intermediate quantity intermediate quantity δ 00 =1,δ m0 =0. Furthermore, substituting the velocity potential of region j into formulas (1)-(9), we obtain:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065] A hydrodynamic parameter analysis system for a multi-module articulated laminated structure includes:

[0066] The complete boundary value problem design module is used to construct complete boundary value problems involving the interaction of waves with multi-module articulated laminated structures.

[0067] The unknown complex expansion coefficient solution module is used to solve the velocity potential in different regions and, in conjunction with the complete boundary value problem, determine the unknown complex expansion coefficients.

[0068] The hydrodynamic parameter calculation module calculates the hydrodynamic parameters of the laminated structure based on the unknown complex expansion coefficient.

[0069] An electronic device, comprising a memory and a processor;

[0070] The memory is used to store computer programs;

[0071] The processor is used to execute the computer program and, in executing the computer program, implement the above-mentioned hydrodynamic parameter analysis method.

[0072] A storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the above-described hydrodynamic parameter analysis method.

[0073] The beneficial effects of this invention are as follows: Firstly, this invention designs a complete boundary value problem involving the interaction between waves and a multi-module articulated laminated structure. This includes dividing the water area and setting the Laplace equation, surface conditions, bottom boundary conditions, far-field conditions, and elastic plate boundary conditions. Zero deflection is applied to the first and Jth laminated structures as a whole, zero bending moment conditions are applied to the panels and core materials of the first and Jth laminated structures, and edge constraints are set for the laminated structures. Then, based on the complete boundary value problem, the unknown complex expansion coefficients in the velocity potential are solved. Finally, the unknown complex expansion coefficients are used to calculate the reflection coefficient, transmission coefficient, dimensionless deflection, dimensionless bending moment, and dimensionless shear force of the laminated structure, characterizing the hydroelastic response of the multi-module articulated laminated structure. The method of this invention is fast, convenient, and simple. The time required to complete the hydrodynamic parameter analysis of the marine photovoltaic foundation structure is far less than the time required for CFD calculation simulation, which is conducive to promoting the rapid development of the marine engineering industry. Attached Figure Description

[0074] Figure 1 This is a schematic diagram illustrating the interaction between the wave and the multi-module hinged laminated structure described in this invention.

[0075] Figure 2(a) shows the deflection results of the laminated structure calculated according to an embodiment of the present invention;

[0076] Figure 2(b) shows the bending moment results of the laminated structure calculated according to the embodiment of the present invention;

[0077] Figure 2(c) shows the shear force results of the laminated structure calculated according to the embodiment of the present invention. Detailed Implementation

[0078] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0079] Figure 1 This is an idealized schematic diagram of the interaction between waves and a multi-module articulated laminated structure, where the physical properties of each laminated structure are completely identical. The water depth is assumed to be a constant h, and the total thickness of each laminated structure is c, neglecting the draft. This invention uses a two-dimensional Cartesian coordinate system to solve the hydroelastic problem of the interaction between waves and the multi-module articulated laminated structure. The origin is set at the left edge of the first laminated structure, the x-axis is located at the undisturbed water surface, and the z-axis is vertically upward. Selecting J laminated structures as the research object, the number of flexible joints is J-1. It is assumed that the right edge of the j-th (j=1,2,…,J) laminated structure is located at x=b j And the lateral length of each layered structure is L j (L j =b j -b j-1 =2a j The upper and lower panels of the adjacent laminated structure are hinged by vertical springs and torsion springs (the dimensions of the vertical springs and torsion springs are ignored in this invention); wherein b j Let a represent the x-coordinate of the right edge of the j-th laminate in a two-dimensional Cartesian coordinate system. j This indicates half of the transverse length of the laminated structure.

[0080] I. Complete Boundary Value Problem of the Interaction between Waves and Multi-Module Hinged Laminated Structures

[0081] 1) Assuming the fluid is incompressible and inviscid and irrotational, the fluid motion can still be described by the velocity potential Φ(x,z,t). Since this invention does not consider the time domain and only analyzes the frequency domain, the time factor is separated out:

[0082] Φ(x,z,t)=Re[φ(x,z)e -iωt (1)

[0083] Where: Re represents the real part, ω represents the angular frequency of the wave, and t represents time. φ(x,z) represents the complex velocity potential.

[0084] 2) Divide the entire water area into the following parts: Region 0 (x≤0, -h≤z≤0) is the open water area on the left; Region j (j=1,2,…,J) is the layered structure covered area (0≤x≤b) J -h≤z≤0); region J+1(x≥b J -h≤z≤0) represents the open water area on the right; the velocity potential of all regions must satisfy the Laplace equation (Equation (2)), surface conditions (Equation (3)), bottom boundary conditions (Equation (4)), far-field conditions (Equations (5), (6)) and elastic plate (laminated structure) boundary conditions (Equation (7)):

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091] Where the subscript j represents the fluid region variable; g is the gravitational acceleration; k0 is the wave number; φ Ⅰ Let G be the velocity potential of the incident wave. t U t Both Y and Y are variables, and G is the shear modulus of the core material, h c E represents the core material thickness. u and E l The elastic modulus of the upper and lower panels, h, are respectively. u and h l The thicknesses of the top and bottom panels are respectively, U u and U l These represent the bending stiffness of the upper and lower panels, respectively, where d is the vertical distance between the centers of the upper and lower panels, and φ is the bending stiffness. j Let be the velocity potential of region j, ρ be the fluid density, and m be the velocity potential. s φ is the mass per unit area of ​​the laminated structure. J+1 φ is the velocity potential of region J+1, and φ0 is the velocity potential of region 0.

[0092] 3) In order to form a closed boundary value problem, appropriate conditions must be applied to the edges of the laminated structure according to the support conditions.

[0093] For the wave-facing surface of the first laminated structure (i.e., x = 0), zero deflection is applied to the entire first laminated structure (Equation (8)), and zero bending moment conditions are applied to the panel and core material of the first laminated structure (Equations (9) and (10)). The mathematical expressions are as follows:

[0094]

[0095]

[0096]

[0097] Where: W1(x) represents the overall deflection of the first laminated structure, M 1u (x) represents the bending moment of the upper panel of the first laminated structure, M 1l (x) represents the bending moment of the lower panel of the first laminated structure, M 1m (x) represents the bending moment of the core material of the first laminated structure, and φ1 is the velocity potential of the first laminated structure.

[0098] For the leeward side of the Jth layered structure (i.e., x = b) J It also considers the conditions of zero deflection and zero bending moment, and the expression is:

[0099]

[0100]

[0101]

[0102] Among them: W J (x) represents the overall deflection of the J-th laminated structure, M Ju (x) represents the bending moment of the upper panel of the J-th laminated structure, M Jl (x) represents the bending moment of the lower panel of the J-th laminated structure, M Jm (x) represents the bending moment of the J-th laminated core material, φ J Let J be the velocity potential of the J-th layered structure;

[0103] For the hinge point (i.e., x = b) j The expression for the edge constraint condition of the laminated structure is:

[0104]

[0105]

[0106] M jm (x)=M (j+1)m (x)=0,x=b j, j=1,2,3,...,J-1 (16)

[0107] Where μ1 is the stiffness of the vertical spring, μ2 is the stiffness of the torsional spring, and M jm (x) represents the bending moment of the j-th laminated core material, M (j+1)m (x) represents the bending moment of the core material of the right-hand laminate adjacent to the j-th laminate.

[0108] Equations (1) to (16) constitute a complete boundary value problem of the interaction between waves and multi-module articulated laminated structures.

[0109] II. Solving for the unknown complex expansion coefficients in the velocity potential

[0110] 1) In regions 0 and J+1, the velocity potentials satisfying the governing equations (Laplace equation (2)) and conditions (3) to (7) are:

[0111]

[0112]

[0113] Where H is the wave height of the incident wave, and R... m and T m These are undetermined, unknown complex expansion coefficients, with intermediate quantity κ0 = -ik0, and intermediate quantity κ... m =k m (m≥1), k m They are eigenvalues, and k0, k m Positive real roots that satisfy the following dispersion relation:

[0114] ω 2 =gk0 tanh(k0h)=-gk m tan(k m h),m≥1 (19)

[0115] Characteristic functions Z0(z), Z m The expression for (z) is as follows:

[0116]

[0117] In the region j (j=1,2,3,…,J), the velocity potential satisfies the governing equation (Laplace equation (2)) and conditions (4) and (7):

[0118]

[0119]

[0120] Among them, A jn and B jn Y represents the unknown complex expansion coefficients.n (z) represents the vertical characteristic function, with eigenvalue λ. n Satisfy the following dispersion equation:

[0121]

[0122] 2) The unknown complex expansion coefficients in the velocity potential need to be determined by applying structural edge conditions and the following continuity conditions (including pressure continuity condition and horizontal velocity continuity condition) on the common boundary of adjacent regions:

[0123] φ0=φ1,x=0,-h≤z≤0(24)

[0124]

[0125] φ j =φ j+1 x=b j ,j=1,2,3,...,J-1,-h≤z≤0 (26)

[0126]

[0127] φ J =φ J+1 x=b J -h≤z≤0 (28)

[0128]

[0129] Where: φ j+1 Let be the velocity potential of the region where the rightmost laminate adjacent to the j-th laminate is located.

[0130] 3) Substitute the velocity potential expressions for the three regions into equations (24) to (29) respectively, and multiply both sides of the equations by the characteristic function Z. m Integrating (z) over z from -h to 0, we get:

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] Among them, intermediate quantity intermediate quantity δ00 =1,δ m0 =0 (m≠0).

[0138] Substituting the velocity potential expression for region j into formulas (8) to (16), we can obtain:

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151] By truncating m in equations (30) to (35) to N terms, and truncating n in equations (30) to (47) to N+1 terms, we obtain a system of linear equations containing 2(N+1)(J+1)+6J unknowns. Solving this system of linear equations yields the unknown complex expansion coefficients (R) in the velocity potential. m T m A jn and B jn The process of solving a system of linear equations is a current technology.

[0152] III. Calculation of hydrodynamic parameters

[0153] The reflection coefficient C of the laminated structure R and transmission coefficient C T The expression is as follows:

[0154] C R =|R0|,C T =|T0|(48)

[0155] For the hydroelasticity problem of this invention, wave motion still satisfies the energy relationship:

[0156]

[0157] The deflection W of each laminated structure j (x), bending moment and shear force The calculation expression is as follows:

[0158]

[0159]

[0160]

[0161] The dimensionless deflection C W Dimensionless bending moment C M and dimensionless shear force C S They are defined as follows:

[0162]

[0163]

[0164]

[0165] The aforementioned reflection coefficient, transmission coefficient, dimensionless deflection, dimensionless bending moment, and dimensionless shear force characterize the hydroelastic response of the multi-module articulated laminated structure.

[0166] Example

[0167] The method of this invention can be applied to practical engineering projects to reduce the hydroelastic response of laminated structures by selecting an appropriate number of hinge points. Specifically, 1 (J=2), 3 (J=4), and 4 (J=5) hinge points were selected for verification.

[0168] Figures 2(a), (b), and (c) show the hydroelastic response of multi-module hinged laminated structures with different numbers of hinges. The dimensionless wavenumber k0h is 3.5, the total length of the multi-module hinged laminated structures is 600m, and the abscissa is x / L0. For ease of calculation, L0 = 150m is taken. It can be observed that, with the total length remaining constant, the deflection, bending moment, and shear force of the laminated structure gradually decrease as the number of hinge points increases, indicating a weakening of the hydroelastic response of the laminated structure. When J > 2, the bending moment and shear force of the second laminated structure are significantly smaller than those of the other laminated structures. When J = 2, the bending moment and shear force of the second laminated structure are smaller than those of the first laminated structure. This indicates that under near total reflection conditions, the second laminated structure experiences the smallest bending moment and shear force, meaning that the shielding effect of the laminated structure is better for the second laminated structure.

[0169] In this embodiment, the time required to calculate hydrodynamic parameters is approximately 1 minute, which is far less than the time required for CFD calculation simulation.

[0170] The present invention provides a hydrodynamic parameter analysis system for a multi-module articulated laminated structure, comprising a complete boundary value problem design module, a module for solving unknown complex expansion coefficients in the velocity potential, and a hydrodynamic parameter calculation module.

[0171] The module for designing complete boundary value problems is used to construct complete boundary value problems involving the interaction between waves and multi-module articulated laminated structures. The module for solving unknown complex expansion coefficients is used to solve the velocity potential in different regions and, in conjunction with the complete boundary value problem, determine the unknown complex expansion coefficients. The module for calculating hydrodynamic parameters is used to calculate the hydrodynamic parameters of the laminated structure based on the determined unknown complex expansion coefficients.

[0172] Based on the same inventive concept as the hydrodynamic parameter analysis method for multi-module articulated laminated structures, this application also provides an electronic device comprising one or more processors and one or more memories. The memories store computer-readable code, which, when executed by the one or more processors, implements the hydrodynamic parameter analysis of the multi-module articulated laminated structure. The memories may include a non-volatile storage medium and internal memory; the non-volatile storage medium may store an operating system and the computer-readable code. The computer-readable code includes program instructions that, when executed, cause the processor to execute any hydrodynamic parameter analysis method for the multi-module articulated laminated structure. The processor provides computational and control capabilities to support the operation of the entire electronic device. The memories provide an environment for the execution of the computer-readable code in the non-volatile storage medium, which, when executed by the processor, causes the processor to execute any hydrodynamic parameter analysis method for the multi-module articulated laminated structure.

[0173] It should be understood that the processor can be a Central Processing Unit (CPU), but it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. Among these, a general-purpose processor can be a microprocessor or any conventional processor.

[0174] The embodiments of this application also provide a computer-readable storage medium storing computer-readable code, which includes program instructions. The processor executes the program instructions to implement the hydrodynamic parameter analysis method for the multi-module articulated laminated structure of this application.

[0175] The computer-readable storage medium can be an internal storage unit of the electronic device described in the foregoing embodiments, such as the hard disk or memory of the computer device. The computer-readable storage medium can also be an external storage device of the electronic device, such as a plug-in hard disk, SmartMedia Card (SMC), Secure Digital (SD) card, or Flash Card equipped on the electronic device.

[0176] The embodiments described above are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for analyzing hydrodynamic parameters of a multi-module articulated laminated structure, characterized in that: 1) Design a complete boundary value problem involving the interaction between waves and a multi-module articulated laminated structure. The entire water area is divided into region 0, region j, and region J+1, and the velocity potential of each region must satisfy the Laplace equation, surface conditions, bottom boundary conditions, far-field conditions, and elastic plate boundary conditions. Specifically: region 0 is the open water area on the left, where x and z in two-dimensional Cartesian coordinates satisfy x≤0 and -h≤z≤0, respectively; region j is the covered area of ​​a multi-module articulated laminated structure, where x and z in two-dimensional Cartesian coordinates satisfy 0≤x≤b, respectively. J -h≤z≤0, region J+1 is the open water area on the right, and in two-dimensional Cartesian coordinates, x and z satisfy x≥b respectively. J -h≤z≤0, where h is the water depth and b J Let J represent the x-coordinate of the right edge of the J-th laminated structure in a two-dimensional Cartesian coordinate system, where j = 1, 2, ..., J; For the wave-facing surface of the first laminated structure, zero deflection is applied to the entire first laminated structure, and zero bending moment is applied to both the panel and the core material of the first laminated structure: For the leeward side of the J-th laminated structure, zero deflection is applied to the entire J-th laminated structure, and zero bending moment is applied to both the panel and core material of the J-th laminated structure: For the hinge points of laminated structures, set the edge end constraints of the laminated structures as follows: M jm (x)=M (j+1)m (x)=0,x=b j ,j=1,2,3,...,J-1 (9) Where: W1(x) represents the overall deflection of the first laminated structure, and φ1 is the velocity potential of the first laminated structure. ω represents the angular frequency of the wave, M 1u (x) represents the bending moment of the upper panel of the first laminated structure, M 1l (x) represents the bending moment of the lower panel of the first laminated structure, U u and U l The bending stiffness, M, represents the bending stiffness of the upper and lower panels, respectively. 1m (x) represents the bending moment of the first laminated core material, G t U t Both Y and Y are variables, and G is the shear modulus of the core material, h c E represents the core material thickness. u and E l The elastic modulus of the upper and lower panels, h, are respectively. u and h l The thicknesses of the top and bottom panels are respectively, U u and U l These represent the bending stiffness of the upper and lower panels, respectively, where d is the vertical distance between the centers of the upper and lower panels, and φ is the bending stiffness. j Let be the velocity potential of region j, ρ be the fluid density, and m be the velocity potential. s W is the mass of the laminated structure per unit area. J (x) represents the overall deflection of the J-th laminated structure, M Ju (x) represents the bending moment of the upper panel of the J-th laminated structure, M Jl (x) represents the bending moment of the lower panel of the J-th laminated structure, M Jm (x) represents the bending moment of the J-th laminated core material, μ1 is the vertical spring stiffness, μ2 is the torsional spring stiffness, and M jm (x) represents the bending moment of the j-th laminated core material, M (j+1)m (x) represents the bending moment of the core material of the right-hand laminate adjacent to the j-th laminate, b j φ represents the x-coordinate of the right edge of the j-th laminate in a two-dimensional Cartesian coordinate system. j+1 Let φ be the velocity potential of the region where the right-hand laminate adjacent to the j-th laminate is located. J Let J be the velocity potential of the J-th layered structure; 2) Solve for the unknown complex expansion coefficients in the velocity potential. Using the Laplace equation, surface conditions, bottom boundary conditions, far-field conditions, and elastic plate boundary conditions, solve for the velocity potentials in regions 0 and J+1. The velocity potential in region 0 includes the unknown complex expansion coefficient R. m The velocity potential in region J+1 contains unknown complex expansion coefficients T. m The velocity potential of region j is solved using the Laplace equation, the underwater boundary conditions, and the elastic plate boundary conditions. The velocity potential of region j includes the unknown complex expansion coefficient A. jn and B jn ; Substituting the velocity potentials of regions 0, j, and J+1 into the continuity condition and then truncating them, and substituting the velocity potential of region j into formulas (1)-(9) and then truncating them, we obtain a system of linear equations. Solving the system of linear equations yields the unknown complex expansion coefficient R in the velocity potential. m T m A jn and B jn ; 3) Calculate hydrodynamic parameters Using the R m T m A jn and B jn The reflection coefficient, transmission coefficient, dimensionless deflection, dimensionless bending moment, and dimensionless shear force of the laminated structure are calculated to characterize the hydroelastic response of the multi-module articulated laminated structure.

2. The hydrodynamic parameter analysis method according to claim 1, characterized in that, The continuity condition is: φ0=φ1,x=0,-h≤z≤0 f j =φ j+1 ,x=b j ,j=1,2,3,...,J-1,-h≤z≤0 f J =φ J+1 ,x=b J ,-h≤z≤0 Where: φ J+1 φ is the velocity potential of region J+1, and φ0 is the velocity potential of region 0.

3. The hydrodynamic parameter analysis method according to claim 2, characterized in that, The velocity potential expressions for region 0 and region J+1 are as follows: Where: H is the wave height of the incident wave, intermediate quantity κ0 = -ik0, intermediate quantity κ m =k m k m They are eigenvalues, and k0, k m Positive real roots satisfying the following dispersion relation: ω 2 =gk0tanh(k0h)=-gk m tank m h),m≥1 Characteristic functions Z0(z), Z m The expression for (z) is: Where: g is the acceleration due to gravity, and k0 is the wave number.

4. The hydrodynamic parameter analysis method according to claim 3, characterized in that, The velocity potential expression for region j is: Where: Y n (z) represents the vertical characteristic function, and eigenvalue λ n Satisfies the dispersion equation:

5. The hydrodynamic parameter analysis method according to claim 4, characterized in that, Substituting the velocity potentials of regions 0, j, and J+1 into the continuity condition, we obtain: Among them, intermediate quantity intermediate quantity δ 00 =1,δ m0 =0.

6. The hydrodynamic parameter analysis method according to claim 4, characterized in that, Substituting the velocity potential of region j into formulas (1)-(9), we get:

7. A system for implementing the hydrodynamic parameter analysis method according to any one of claims 1-6, characterized in that, include: The complete boundary value problem design module is used to construct complete boundary value problems involving the interaction of waves with multi-module articulated laminated structures. The unknown complex expansion coefficient solution module is used to solve the velocity potential in different regions and, in conjunction with the complete boundary value problem, determine the unknown complex expansion coefficients. The hydrodynamic parameter calculation module calculates the hydrodynamic parameters of the laminated structure based on the unknown complex expansion coefficient.

8. An electronic device, characterized in that, Including memory and processor; The memory is used to store computer programs; The processor is used to execute the computer program and, in executing the computer program, implement the hydrodynamic parameter analysis method as described in any one of claims 1-6.

9. A storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, causes the processor to perform the hydrodynamic parameter analysis method as described in any one of claims 1-6.

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