An arbitrary shell structure quasi-three-dimensional vibration sound radiation analysis method, device, equipment and medium

Abstract

This invention proposes a quasi-three-dimensional vibration and acoustic radiation analysis method, apparatus, equipment, and medium for arbitrary plate and shell structures, belonging to the field of dynamics and acoustic-structure coupling analysis technology. It solves the problem in existing technologies where complex plate and shell structures are difficult to simultaneously account for thickness direction effects and achieve unified acoustic-vibration coupling modeling. It includes extracting the geometric parameters, material parameters, and boundary condition parameters of the plate and shell structure; constructing a quasi-three-dimensional displacement function capable of simultaneously describing in-plane deformation and bending deformation; constructing the quasi-three-dimensional strain vector and stress vector of the structure to obtain the structural mass matrix and structural stiffness matrix; establishing an acoustic radiation model of the external fluid domain; establishing a unified acoustic-structure coupling dynamic equation; solving for the vibration response and acoustic radiation characteristics of the plate and shell structure; and outputting the structural vibration response and acoustic radiation characteristics results. It is mainly used for quasi-three-dimensional vibration and acoustic radiation analysis of plate and shell structures.

Description

Technical Field

[0001] This invention belongs to the field of structural dynamics and acoustic-structure coupling analysis technology, and in particular relates to a method, device, equipment and medium for quasi-three-dimensional vibration acoustic radiation analysis of arbitrary plate and shell structures. Background Technology

[0002] Vibration and acoustic radiation analysis of plate and shell structures is a key technical issue in fields such as shipbuilding, aerospace, and marine engineering. A typical analysis approach involves first establishing a structural dynamics model to obtain the normal vibration response of the plate and shell surface, then using this as boundary conditions to establish an external acoustic field model based on the Helmholtz equations, and finally obtaining the vibratory-acoustic response through frequency domain simultaneous analysis or weak coupling. Currently, the mainstream theoretical methods for vibration and acoustic radiation analysis of plate and shell structures are mainly divided into three categories, each with its own advantages and disadvantages. The first category is based on classical shell theory (such as the Kirchhoff-Love theory), which has the advantages of simple models and high computational efficiency, making it suitable for the preliminary analysis of thin-shell structures; however, it neglects transverse shear deformation and nonlinear strain in the thickness direction, resulting in significant errors for medium-thick plate shells or composite laminate structures. The second category is based on first-order or higher-order shear deformation shell theory. Compared to classical theory, this method can account for transverse shear effects, improving accuracy, and the computational cost is still much lower than that of three-dimensional models; however, it is essentially still a two-dimensional plate and shell theory, and the displacement distribution in the thickness direction usually adopts a polynomial assumption, which cannot accurately describe the complex deformation and nonlinear stress distribution in the thickness direction. The third category is the plate and shell vibration and acoustic modeling method based on three-dimensional linear elasticity theory. Its advantage lies in its ability to completely and accurately describe the mechanical behavior of the structure in the thickness direction, making it suitable for plates and shells of arbitrary thickness. However, its disadvantages include a huge number of degrees of freedom and excessively high computational scale, making it difficult to use for vibration and acoustic radiation analysis and optimization design of large and complex structures. In summary, existing methods have a clear trade-off between computational efficiency and thickness-direction modeling accuracy. Low-dimensional theories are difficult to meet the accuracy requirements of medium-thickness / composite structures, while high-dimensional theories are difficult to balance with engineering practicality.

[0003] Therefore, how to rationally utilize the advantages of classical shell theory, first-order shear deformation shell theory, higher-order shear deformation shell theory and three-dimensional elasticity theory to form a quasi-three-dimensional vibration and acoustic radiation analysis method for plate and shell structures that integrates multiple theories, has strong applicability, and balances solution accuracy and computational efficiency, and is applicable to arbitrary curved surface shapes and complex boundary conditions, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0004] In view of this, the present invention aims to propose a quasi-three-dimensional vibration and acoustic radiation analysis method, device, equipment and medium for arbitrary plate and shell structures, so as to solve the problem in the prior art that it is difficult to simultaneously take into account the expression of thickness direction effects and unified acoustic-vibration coupling modeling of complex plate and shell structures.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: According to a first aspect of the present invention, a quasi-three-dimensional vibration and acoustic radiation analysis method for arbitrary plate and shell structures includes the following steps: Extract the geometric parameters, material parameters, and boundary condition parameters of the plate and shell structure; A curvilinear coordinate system is established with the neutral plane of the plate and shell structure as the reference. Independent variables are introduced in the thickness direction to construct a quasi-three-dimensional displacement function that can simultaneously describe in-plane deformation and bending deformation. Based on the quasi-three-dimensional displacement function, a strain-displacement relationship is established, and a stress-strain relationship is obtained by combining the linear elastic constitutive relationship. Then, the quasi-three-dimensional strain vector and stress vector of the structure are constructed, and the structural vibration control equation is established by the variational principle to obtain the structural mass matrix and structural stiffness matrix. Using the normal vibration response of the plate and shell structure surface as the acoustic radiation boundary condition, an acoustic radiation model of the external fluid domain is established based on the acoustic boundary integral theory. The structural vibration control equations are combined with the acoustic boundary integral equations to establish a unified acoustic-structure coupled dynamic equation. The vibration response and acoustic radiation characteristics of the plate and shell structure are then solved, and the results of the structural vibration response and acoustic radiation characteristics are output.

[0006] Furthermore, the specific expression for the quasi-three-dimensional displacement function is as follows: in, and These are the in-plane coordinates of the neutral plane of the plate and shell structure along the directions of the two orthogonal curves; Let u(α, β, γ) be the coordinates along the thickness direction; u(α, β, γ) be the three-dimensional displacement vector of the plate and shell structure; u τ (α, β) represents the neutral surface displacement component corresponding to the τth thickness expansion term; F τ (γ) represents the basis function in the thickness direction; Y represents the truncation order of the thickness direction expansion, τ=1,2,……,Y+1. Classical shell theory, first-order and higher-order shear deformation shell theory can be regarded as special cases of the above formulas.

[0007] Furthermore, the first The neutral plane displacement component u corresponding to the thickness expansion term τ (α, β) is discretized using orthogonal function expansion or finite element method, and the generalized coordinates of the structure are obtained by finite term truncation or finite degree of freedom discretization.

[0008] When using the orthogonal function expansion method, we have: in, and To map to the interval [ Dimensionless coordinates of [1,1]; and These are orthogonal basis functions; N is the expansion coefficient; t N is the truncation order.

[0009] When using the finite element method for discretization, the neutral surface region is... Divide into a finite number of units, that is: in For the e-th unit region, This represents the total number of units.

[0010] Within the e-th element, the neutral surface displacement component corresponding to the τ-th thickness expansion term is expressed as: in, For unit shape functions; This represents the number of unit nodes; This represents the degree of freedom vector at the i-th node and the τ-th thickness expansion term.

[0011] Therefore, the quasi-three-dimensional displacement field within the element can be uniformly expressed as: like Figure 2 The diagram illustrates the finite element discretization of a curved surface shell and the local element division. This method enables quasi-three-dimensional displacement modeling on complex curved surface shells, providing a foundation for further structural vibration and acoustic radiation coupling analysis.

[0012] Furthermore, the specific expression for the strain vector is as follows: Where, ε α ε β ε γ and ε αβ ε βγ ε αγ Let represent normal strain and shear strain, respectively. Each strain component is calculated from the partial derivative of the displacement function with respect to spatial coordinates. After discretization using the finite element method, the element strain can be written as: in, For the element strain-displacement matrix, is the vector of unit degrees of freedom. Furthermore, the specific expression for the relationship between the stress vector and the strain vector is as follows: Where, σα σ β and σ γ τ is the quasi-three-dimensional normal stress component calculated from the displacement function. αβ τ βγ and τ αγ For the corresponding shear stress component, C 11 C 12 C 13 C 21 C 22 C 23 C 31 C 32 C 33 C 44 C 55 and C 66 The elastic coefficient is determined by the material's elastic modulus and Poisson's ratio.

[0013] Furthermore, the specific expression for the acoustic radiation model of the external fluid domain is as follows: Where p0 is the sound pressure level; Let be the sound wave number, and its expression is: ω is the angular frequency, c f The speed of sound in the acoustic medium; When using the boundary element method for discretization, the fluid boundary integral equation can be written as: Where p is the sound pressure vector at the boundary node, v n Let H be the normal vibration velocity vector of the structural surface, and let H and G be the acoustic influence matrices formed by discretization of the Green's function.

[0014] Furthermore, the specific expression of the acoustic-structure coupling dynamic equation is as follows: Wherein, q is the generalized coordinate vector of the structure composed of the Chebyshev expansion coefficients, M is the overall mass matrix of the plate and shell structure, K is the overall stiffness matrix of the plate and shell structure, D is the matrix that maps the structural normal velocity or displacement to the acoustic boundary, i is the imaginary unit, and T represents the matrix transpose.

[0015] According to a second aspect of the present invention, a quasi-three-dimensional vibration and acoustic radiation analysis device for arbitrary plate and shell structures is provided, comprising: The parameter input module is used to extract the geometric parameters, material parameters, and boundary condition parameters of the plate and shell structure. The quasi-3D modeling module is used to establish a curved coordinate system based on the neutral plane of the plate and shell structure, introduce independent variables in the thickness direction, and construct a quasi-3D displacement function that can simultaneously describe in-plane deformation and bending deformation. The structural analysis module is used to establish the strain-displacement relationship based on the quasi-three-dimensional displacement function, obtain the stress-strain relationship by combining the linear elastic constitutive relationship, and then construct the quasi-three-dimensional strain vector and stress vector of the structure. The structural vibration control equation is established through the variational principle to obtain the structural mass matrix and structural stiffness matrix. The acoustic modeling module is used to establish an acoustic radiation model of the external fluid domain based on the acoustic boundary integral theory, using the normal vibration response of the plate and shell structure surface as the acoustic radiation boundary condition. The coupled solution and output module combines the structural vibration control equation with the acoustic boundary integral equation to establish a unified acoustic-structure coupled dynamic equation, solves for the vibration response and acoustic radiation characteristics of the plate and shell structure, and outputs the results of the structural vibration response and acoustic radiation characteristics.

[0016] According to a third aspect of the present invention, an electronic device is provided, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the quasi-three-dimensional vibration and acoustic radiation analysis method for any plate and shell structure as described above.

[0017] According to a fourth aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being configured to cause the computer to perform the quasi-three-dimensional vibration and acoustic radiation analysis method for any plate and shell structure as described above.

[0018] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention provides a quasi-three-dimensional vibration and acoustic radiation analysis method for arbitrary plate and shell structures. It introduces independent variables in the thickness direction to construct a quasi-three-dimensional displacement field, no longer limited to the simplified treatment of shear deformation in the thickness direction in traditional two-dimensional plate and shell theory. Therefore, it can simultaneously consider the in-plane deformation, bending deformation and transverse shear deformation of the plate and shell structure. For medium-thick plate and shell or complex structures with significant curvature changes, this method can more realistically reflect the actual deformation characteristics of the structure, and the analysis results are more reliable. 2. This invention does not separate structural vibration analysis and acoustic radiation analysis, but directly combines the structural vibration control equation with the acoustic boundary integral equation of the external fluid domain to establish a unified acoustic-structure coupling analysis model. This can reduce the problems of numerous interface conversions and insufficient coupling in the traditional step-by-step analysis process, and is conducive to improving the consistency and stability of joint vibration and acoustic radiation analysis. 3. The present invention has strong flexibility in the mid-surface discretization method. It can use both orthogonal function expansion method and finite element discretization method. Therefore, it does not depend on a fixed numerical implementation form. This not only makes it easy to select the appropriate discretization method according to different structural forms and calculation requirements, but also makes the present invention easier to extend to the analysis of different types of plate and shell structures. 4. This invention ensures both modeling capability and computational efficiency. Compared with the method of directly using full three-dimensional solid discretization, this invention can effectively reduce the computational scale while retaining the main deformation characteristics in the thickness direction. Therefore, it is more suitable for vibration and acoustic radiation analysis of arbitrary plate and shell structures in complex boundary and external fluid environments. Attached Figure Description

[0019] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart illustrating a quasi-three-dimensional vibration and acoustic radiation analysis method for arbitrary plate and shell structures according to the present invention. Figure 2 This is a schematic diagram of the plate shell structure of the rotating shell structure described in the embodiment of the present invention; Figure 3 This is a schematic diagram of the overall structure of the rotating shell structure described in this embodiment of the invention; Figure 4 This is a block diagram of a quasi-three-dimensional vibration and acoustic radiation analysis device for arbitrary plate and shell structures according to the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Figure 1 This is a flowchart illustrating a quasi-three-dimensional vibration and acoustic radiation analysis method for arbitrary plate and shell structures according to the present invention.

[0022] like Figure 1 As shown, the quasi-three-dimensional vibration and acoustic radiation analysis method for this arbitrary plate and shell structure includes the following steps: In step S1, the geometric parameters, material parameters, and boundary condition parameters of the plate and shell structure are extracted; The geometric parameters include the geometric shape information of the neutral surface of the plate and shell structure, the thickness distribution function, the characteristic dimension parameters, and the curvature parameters of the neutral surface in the two principal directions. The curvature parameters can be characterized by the principal radii of curvature. The material parameters include the elastic modulus E and Poisson's ratio. and density .

[0023] In step S2, a curved coordinate system is established with the neutral surface of the plate and shell structure as the reference, and an independent variable is introduced in the thickness direction to construct a quasi-three-dimensional displacement function that can simultaneously describe in-plane deformation and bending deformation.

[0024] In some embodiments, the three-dimensional displacement function of the plate and shell structure adopts a quasi-three-dimensional unfolded form along the thickness direction, introducing independent variables along the thickness direction to describe the transverse shear deformation of the plate and shell structure. The specific expression of the quasi-three-dimensional displacement function is as follows: in, and These are the in-plane coordinates of the neutral plane of the plate and shell structure along the directions of the two orthogonal curves; Let u(α, β, γ) be the coordinates along the thickness direction; u(α, β, γ) be the three-dimensional displacement vector of the plate and shell structure; u τ (α, β) represents the neutral surface displacement component corresponding to the τth thickness expansion term; F τ (γ) represents the basis function in the thickness direction; Y represents the truncation order of the thickness direction expansion, τ=1,2,……,Y+1. Classical shell theory, first-order and higher-order shear deformation shell theory can be regarded as special cases of the above formulas.

[0025] The quasi-three-dimensional displacement function is used to describe the nonlinear distribution characteristics of the transverse shear deformation and displacement along the thickness direction of the plate and shell structure, and the transverse shear effect and displacement nonlinear distribution characteristics along the thickness direction of the plate and shell structure can be uniformly characterized.

[0026] The neutral surface displacement component u corresponding to the τth thickness expansion term τ (α, β) are discretized using orthogonal function expansion or finite element method, and the generalized coordinates of the structure are obtained through finite term truncation or finite degree of freedom discretization. When using orthogonal function expansion, we have: in, And η is mapped to the interval [ Dimensionless coordinates of [1,1]; and These are orthogonal basis functions; N is the expansion coefficient; t N is the truncation order.

[0027] When using the finite element method for discretization, the neutral surface region is... Divide into a finite number of units, that is: in For the e-th unit region, This represents the total number of units.

[0028] Within the e-th element, the neutral surface displacement component corresponding to the τ-th thickness expansion term is expressed as: in, For unit shape functions; This represents the number of unit nodes; Let represent the degree of freedom vector at the 0th node and the τth thickness expansion term. Therefore, the quasi-three-dimensional displacement field within the element can be uniformly represented as: In step S3, a strain-displacement relationship is established based on the quasi-three-dimensional displacement function, and a stress-strain relationship is obtained by combining the linear elastic constitutive relationship. Then, the quasi-three-dimensional strain vector and stress vector of the structure are constructed, and the structural vibration control equation is established through the variational principle to obtain the structural mass matrix and structural stiffness matrix.

[0029] In some embodiments, after obtaining the discrete expression of displacement, a strain-displacement relationship is established based on the quasi-three-dimensional displacement function, and a stress-strain relationship is obtained by combining the linear elastic constitutive relation, thereby constructing the quasi-three-dimensional strain vector and stress vector of the structure. The specific expression of the strain vector is as follows: Where, ε α ε β ε γ and ε αβ ε βγ ε αγ Let represent normal strain and shear strain, respectively. Each strain component is calculated from the partial derivative of the displacement function with respect to spatial coordinates. After discretization using the finite element method, the element strain can be written as: in, For the element strain-displacement matrix, The element is the degree-of-freedom vector. The stress vector is obtained through the three-dimensional linear elastic constitutive relation, and the specific expression for the relationship between the stress vector and the strain vector is: Where, σ α σ β and σ γ τ is the quasi-three-dimensional normal stress component calculated from the displacement function.αβ τ βγ and τ αγ For the corresponding shear stress component, C 11 C 12 C 13 C 21 C 22 C 23 C 31 C 32 C 33 C 44 C 55 and C 66 The elastic coefficient is determined by the material's elastic modulus and Poisson's ratio.

[0030] The structural strain energy is constructed based on the strain vector and stress vector. ,kinetic energy and boundary energy Furthermore, the structural vibration control equations are established using Hamilton's principle or Lagrange's variational principle, and after discretization, the following equations are obtained. Where q is the generalized coordinate vector of the structure, M is the mass matrix of the plate and shell structure, K is the stiffness matrix of the plate and shell structure, and F is the generalized force vector corresponding to the external load. For the free vibration problem, let the external load F=0, and assume the system response is q=G0e iωt Then, the characteristic equation of the plate and shell structure can be further obtained: Where G0 is the complex amplitude matrix of q; denoted as the structural angular frequency, and i is the imaginary unit.

[0031] In step S4, the normal vibration response of the plate and shell structure surface is used as the acoustic radiation boundary condition, and an acoustic radiation model of the external fluid domain is established based on the acoustic boundary integral theory.

[0032] In the acoustic analysis section, the normal vibration response of the shell structure surface is used as the acoustic radiation boundary condition. An acoustic model of the external fluid domain is established based on the Kirchhoff–Helmholtz boundary integral theory. The sound pressure field satisfies the Helmholtz equation, and the specific expression of the acoustic radiation model of the external fluid domain is as follows: Where p0 is the sound pressure level; k is the sound wave number, and its expression is: ω is the angular frequency, c f The velocity of sound in the acoustic medium.

[0033] The acoustic boundary integral equation is expanded circumferentially and discretized along the structural generatrix using Chebyshev polynomials of the first kind. The acoustic algebraic equation is obtained using the collocation method. Where p is the Fourier coefficient vector of the sound pressure on the structural surface; Let G be the Fourier coefficient vector of the structural normal displacement; G and H are the influence matrices formed by discretization of the acoustic boundary integral, respectively. The normal velocity of the structural surface and the generalized coordinates of the structure satisfy a mapping relationship: Where D is the mapping matrix from the structural displacement expansion coefficients to the normal displacement.

[0034] In step S5, the structural vibration control equation and the acoustic boundary integral equation are combined to establish a unified acoustic-structure coupled dynamic equation. The vibration response and acoustic radiation characteristics of the plate and shell structure are solved, and the results of the structural vibration response and acoustic radiation characteristics are output.

[0035] In some embodiments, the structural vibration control equations and the acoustic boundary integral discretization equations are combined to establish a unified acoustic-structure coupled dynamic equation, the specific expression of which is as follows: Where q is the generalized coordinate vector of the structure composed of the Chebyshev expansion coefficients, p is the sound pressure coefficient vector of the structural surface, M is the overall mass matrix of the plate and shell structure, K is the overall stiffness matrix of the plate and shell structure, and T represents the transpose.

[0036] By solving the acoustic-structure coupled dynamic equations, the vibration response, surface sound pressure distribution, far-field sound pressure, and radiated sound power of the plate and shell structure are obtained.

[0037] In actual implementation, the error of the truncation order Y in the thickness direction is evaluated. Specifically, the initial truncation order Y = Y0 is first set, and the truncation order is gradually increased. Then, the differences in analysis results under adjacent truncation orders are compared, and the relative error index is defined as: Where Y represents the truncation order in the thickness direction, ΔY represents the order increment, and R represents the selected result quantity, which can be the natural frequency, key point displacement response, surface acoustic pressure, far-field acoustic pressure, or radiated acoustic power. R(Y) is the structural response vector calculated for the corresponding truncation order. || represents the Euclidean norm, used to measure response differences. When e(Y) is less than or equal to the requirement, the current truncation order is considered to meet the preset accuracy requirement and is determined as the optimal truncation order; otherwise, the truncation order is increased and the above calculation is repeated.

[0038] The following example uses an axisymmetric variable radius shell of revolution as an analysis object to demonstrate the specific application process of the present invention.

[0039] Its structure is as follows Figure 3 As shown, its total length L = 10.0 m, shell thickness h = 0.05 m, and circumferential angle range of 0 ≤ θ ≤ 2π. The mid-surface of the structure is formed by generatrices. Formed by rotation about an axis. The material is isotropic steel, E = 210 GPa, ρ = 7850 kg / m². 3 , The boundary condition is CF (fixed at x=0, free at the other boundary).

[0040] First, the geometric parameters, material parameters, and boundary condition parameters of the shell of revolution structure are extracted, and an orthogonal curvilinear coordinate system is established with the neutral surface of the shell of revolution as the reference. In this coordinate system, the three-dimensional displacement function of the quasi-three-dimensional plate and shell theory is constructed, and the specific expression is as follows: in, As a basis function in the thickness direction, it can characterize bending and shear deformation in the thickness direction; , , It is the neutral surface displacement function; the thickness direction truncation order is Y=3.

[0041] To improve computational efficiency and ensure the accuracy of displacement field representation, this paper uses orthogonal function expansion or finite element discretization to represent the neutral surface displacement function. For regular plate and shell structures, the first-kind Chebyshev polynomial can be used as the orthogonal basis function to perform a spectral expansion of the neutral surface displacement function, i.e.: in and N represents dimensionless coordinates in the axial and circumferential directions, mapped to [-1, 1]; t =N=12 is the truncation order to ensure sufficient spatial resolution; U τmn V τmn W τmn The Chebyshev expansion coefficients are used as generalized coordinates for solving the subsequent vibration equations.

[0042] For complex geometries, locally irregular regions, or plate and shell structures requiring meshing, the neutral surface can be discretized into a finite number of elements, and the neutral surface displacement component corresponding to the r-th thickness expansion term can be represented by a finite element shape function within each element, i.e.: Based on the quasi-three-dimensional displacement function, the strain-displacement relationship of the shell of revolution structure is established, and the stress expression is further obtained by combining the three-dimensional linear elastic constitutive relation. The strain vector can be expressed as: Each strain component is calculated using the partial derivative relationship of the displacement function: , , , , The stress is calculated using the three-dimensional linear elastic constitutive relation: in , , E is the Young's modulus of the material, E = 210 GPa; υ is the Poisson's ratio of the material, υ = 0.25. The structural strain energy is then constructed based on the strain vector and stress vector. ,kinetic energy and boundary energy Furthermore, the structural vibration control equations are established using Hamilton's principle or Lagrange's variational principle, and after discretization, the following is obtained: Where q is the generalized coordinate vector of the structure composed of the Chebyshev expansion coefficients, M is the overall mass matrix of the plate and shell structure, and K is the overall stiffness matrix of the plate and shell structure. For the free vibration problem, let the external load F=0, and assume the system response form is q=G0e iωt Then, the characteristic equation of the plate and shell structure can be further obtained: Where G0 is the complex amplitude matrix of q. denoted as the structural angular frequency, and i is the imaginary unit.

[0043] In the acoustic radiation analysis section, the normal vibration response of the cylindrical shell surface is used as the acoustic boundary condition to establish an acoustic boundary integral model for the external fluid domain. The external sound field satisfies the Helmholtz equation: Where p0 is the sound pressure level; For sound wave number, Angular frequency, Let be the speed of sound in the acoustic medium. The acoustic boundary integral equation is expanded circumferentially using a Fourier expansion and discretized along the generatrix of the structure using a Chebyshev polynomial of the first kind. The acoustic algebraic equation is obtained using the collocation method: Where p is the sound pressure vector at the boundary node, v n Let H be the normal vibration velocity vector of the structural surface, and G be the acoustic influence matrices formed by discretization using Green's functions. The normal velocity of the structural surface and the generalized coordinates of the structure satisfy a mapping relationship: Where D is the mapping matrix from the structural displacement expansion coefficient to the normal displacement. By solving the above coupled equations, the vibration response, surface sound pressure distribution, far-field sound pressure, and radiated sound power of the shell of revolution structure under given parameters and boundary conditions can be obtained.

[0044] By combining the structural vibration control equations with the acoustic boundary integral discretization equations, a unified acoustic-structure coupled dynamic equation is established: Where q is the structural generalized coordinate vector composed of the Chebyshev expansion coefficients, p is the structural surface acoustic pressure coefficient vector, M is the overall mass matrix of the plate and shell structure, K is the overall stiffness matrix of the plate and shell structure, and T denotes transpose. The overall mass matrix and overall stiffness matrix are obtained by assembling each structural unit.

[0045] In actual implementation, the error of the truncation order Y in the thickness direction is evaluated. Specifically, the initial truncation order Y = Y0 is first set, and the truncation order is gradually increased. Then, the differences in analysis results under adjacent truncation orders are compared, and the relative error index is defined as: Where Y represents the truncation order in the thickness direction, ΔY represents the order increment, and R represents the selected result quantity, which can be the natural frequency, key point displacement response, surface acoustic pressure, far-field acoustic pressure, or radiated acoustic power. R(Y) is the structural response vector calculated for the corresponding truncation order. || represents the Euclidean norm, used to measure response differences. When e(Y) is less than or equal to the requirement, the current truncation order is considered to meet the preset accuracy requirement and is determined as the optimal truncation order; otherwise, the truncation order is increased and the above calculation is repeated. This method achieves a better balance between analytical accuracy and computational cost.

[0046] In this embodiment, MATLAB can be used to implement the above analysis process. By inputting the structural parameters of the shell of revolution, establishing a quasi-three-dimensional structural model and an acoustic model, solving the coupled equations simultaneously, and combining the truncation order error assessment, the analysis can be output. Analysis results of the shell structure including natural frequency, mode shape, displacement response, velocity response, stress distribution, surface sound pressure, far-field sound pressure, and radiated sound power.

[0047] The quasi-three-dimensional vibration and acoustic radiation analysis method for arbitrary plate and shell structures proposed in this invention has the following advantages: 1. This method introduces independent variables in the thickness direction to construct a quasi-three-dimensional displacement field, no longer limited to the simplified treatment of thickness direction deformation in traditional two-dimensional plate and shell theory. Therefore, it can simultaneously consider the in-plane deformation, bending deformation and transverse shear deformation of plate and shell structures. For medium-thick plate and shell or complex structures with significant curvature changes, this treatment can more realistically reflect the actual deformation characteristics of the structure, and the analysis results are more reliable. 2. This method does not separate structural vibration analysis and acoustic radiation analysis, but directly combines the structural vibration control equation with the acoustic boundary integral equation of the external fluid domain to establish a unified acoustic-structure coupling analysis model. This can reduce the problems of many interface conversions and insufficient coupling relationship in the traditional step-by-step analysis process, and is conducive to improving the consistency and stability of joint vibration and acoustic radiation analysis. 3. This method has strong flexibility in the discretization of the mid-surface. It can use either the orthogonal function expansion method or the finite element discretization method. Therefore, it does not depend on a fixed numerical implementation. This not only makes it easier to select the appropriate discretization method according to different structural forms and calculation requirements, but also makes it easier to extend this method to the analysis of different types of plate and shell structures. 4. This method ensures both modeling capability and computational efficiency. Compared with the method of directly discretizing the full three-dimensional solid, this method can effectively reduce the computational scale while preserving the main deformation characteristics in the thickness direction. Therefore, it is more suitable for vibration and acoustic radiation analysis of arbitrary structural plates and shells in complex boundary and external fluid environments.

[0048] Figure 4 This is a block diagram of a quasi-three-dimensional vibration and acoustic radiation analysis device for arbitrary plate and shell structures according to the present invention.

[0049] like Figure 4 As shown, the quasi-three-dimensional vibration and acoustic radiation analysis device 40 for arbitrary plate and shell structures includes: The parameter input module 401 is used to extract the geometric parameters, material parameters and boundary condition parameters of the plate and shell structure. The quasi-3D modeling module 402 is used to establish a curved coordinate system based on the neutral plane of the plate and shell structure, introduce independent variables in the thickness direction, and construct a quasi-3D displacement function that can simultaneously describe in-plane deformation and bending deformation. The structural analysis module 403 is used to establish the strain-displacement relationship based on the quasi-three-dimensional displacement function, obtain the stress-strain relationship by combining the linear elastic constitutive relationship, and then construct the quasi-three-dimensional strain vector and stress vector of the structure. The structural vibration control equation is established by the variational principle to obtain the structural mass matrix and structural stiffness matrix. The acoustic modeling module 404 is used to establish an acoustic radiation model of the external fluid domain based on the acoustic boundary integral theory, using the normal vibration response of the plate and shell structure surface as the acoustic radiation boundary condition. The coupling solution and output module 405 is used to combine the structural vibration control equation with the acoustic boundary integral equation to establish a unified acoustic-structure coupled dynamic equation, solve for the vibration response and acoustic radiation characteristics of the plate and shell structure, and output the structural vibration response and acoustic radiation characteristics results.

[0050] It should be noted that the foregoing explanation of the embodiment of the quasi-three-dimensional vibration and acoustic radiation analysis method for arbitrary plate and shell structures also applies to the quasi-three-dimensional vibration and acoustic radiation analysis device for arbitrary plate and shell structures in this embodiment, and will not be repeated here.

[0051] The quasi-three-dimensional vibration and acoustic radiation analysis device for arbitrary plate and shell structures proposed in the embodiments of the present invention has the following beneficial effects: 1. This device introduces independent variables in the thickness direction to construct a quasi-three-dimensional displacement field, no longer limited to the simplified treatment of thickness direction deformation in traditional two-dimensional plate and shell theory. Therefore, it can simultaneously consider the in-plane deformation, bending deformation and transverse shear deformation of plate and shell structures. For medium-thick plate and shell or complex structures with significant curvature changes, this treatment method can more realistically reflect the actual deformation characteristics of the structure, and the analysis results are more reliable. 2. This device does not separate structural vibration analysis and acoustic radiation analysis, but directly combines the structural vibration control equation with the acoustic boundary integral equation of the external fluid domain to establish a unified acoustic-structure coupling analysis model. This can reduce the problems of many interface conversions and insufficient coupling relationship in the traditional step-by-step analysis process, and is conducive to improving the consistency and stability of joint vibration and acoustic radiation analysis. 3. This device has strong flexibility in the mid-surface discretization method. It can use both orthogonal function expansion method and finite element discretization method. Therefore, it does not depend on a fixed numerical implementation form. This not only makes it easy to select the appropriate discretization method according to different structural forms and calculation requirements, but also makes it easier to extend this device to the analysis of different types of plate and shell structures. 4. This device ensures both modeling capabilities and computational efficiency. Compared with the method of directly using full three-dimensional solid discretization, this device can effectively reduce the computational scale while retaining the main deformation characteristics in the thickness direction. Therefore, it is more suitable for vibration and acoustic radiation analysis of arbitrary structural plates and shells in complex boundary and external fluid environments.

[0052] This invention proposes an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the quasi-three-dimensional vibration and acoustic radiation analysis method for arbitrary plate and shell structures.

[0053] This invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the quasi-three-dimensional vibration and acoustic radiation analysis method for arbitrary plate and shell structures.

[0054] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DRRAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0055] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state drives (SSDs)).

[0056] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0057] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0058] The foregoing has provided a detailed description of the quasi-three-dimensional vibration and acoustic radiation analysis of arbitrary plate and shell structures proposed in this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A quasi-three-dimensional vibration and acoustic radiation analysis method for arbitrary plate and shell structures, characterized in that: Includes the following steps: Extract the geometric parameters, material parameters, and boundary condition parameters of the plate and shell structure; A curvilinear coordinate system is established with the neutral plane of the plate and shell structure as the reference. Independent variables are introduced in the thickness direction to construct a quasi-three-dimensional displacement function that can simultaneously describe in-plane deformation and bending deformation. Based on the quasi-three-dimensional displacement function, a strain-displacement relationship is established, and a stress-strain relationship is obtained by combining the linear elastic constitutive relationship. Then, the quasi-three-dimensional strain vector and stress vector of the structure are constructed, and the structural vibration control equation is established by the variational principle to obtain the structural mass matrix and structural stiffness matrix. Using the normal vibration response of the plate and shell structure surface as the acoustic radiation boundary condition, an acoustic radiation model of the external fluid domain is established based on the acoustic boundary integral theory. The structural vibration control equations are combined with the acoustic boundary integral equations to establish a unified acoustic-structure coupled dynamic equation. The vibration response and acoustic radiation characteristics of the plate and shell structure are then solved, and the results of the structural vibration response and acoustic radiation characteristics are output.

2. The method for quasi-three-dimensional vibration and acoustic radiation analysis of arbitrary plate and shell structures according to claim 1, characterized in that: The specific expression for the quasi-three-dimensional displacement function is as follows: in, and These are the in-plane coordinates of the neutral plane of the plate and shell structure along the directions of the two orthogonal curves; Let α be the coordinate along the thickness direction; u(α, β, γ) be the three-dimensional displacement vector of the plate and shell structure; u τ (α, β) represents the neutral surface displacement component corresponding to the τth thickness expansion term; F τ (γ) represents the basis functions in the thickness direction; Y represents the truncation order of the thickness direction expansion, τ=1,2,……,Y+1. Classical shell theory, first-order and higher-order shear deformation shell theory can be regarded as special cases of the above formulas.

3. The method for quasi-three-dimensional vibration and acoustic radiation analysis of arbitrary plate and shell structures according to claim 2, characterized in that: The neutral surface displacement component u corresponding to the τth thickness expansion term τ (α, β) are discretized using orthogonal function expansion or finite element method, and the generalized coordinates of the structure are obtained through finite term truncation or finite degree of freedom discretization. When using orthogonal function expansion, we have: in, And η is mapped to the interval [ Dimensionless coordinates of [1,1]; and These are orthogonal basis functions; N is the expansion coefficient; t N is the truncation order. When using the finite element method, the neutral surface region Ω is divided into a finite number of elements, i.e.: in For the e-th unit region, This represents the total number of units. Within the e-th element, the neutral surface displacement component corresponding to the τ-th thickness expansion term is expressed as: in, For unit shape functions; This represents the number of unit nodes; Let represent the degree of freedom vector at the 0th node and the τth thickness expansion term. Therefore, the quasi-three-dimensional displacement field within the element can be uniformly represented as:

4. The method for quasi-three-dimensional vibration and acoustic radiation analysis of arbitrary plate and shell structures according to claim 1, characterized in that: The specific expression for the strain vector is: Where, ε α ε β ε γ and ε αβ ε βγ ε αγ Let represent normal strain and shear strain, respectively. Each strain component is calculated from the partial derivative of the displacement function with respect to spatial coordinates. After discretization using the finite element method, the element strain can be written as: in, For the element strain-displacement matrix, is the vector of unit degrees of freedom.

5. The method for quasi-three-dimensional vibration and acoustic radiation analysis of arbitrary plate and shell structures according to claim 4, characterized in that: The specific expression for the relationship between the stress vector and the strain vector is as follows: Where, σ α σ β and σ γ τ is the quasi-three-dimensional normal stress component calculated from the displacement function. αβ τ βγ and τ αγ For the corresponding shear stress component, C 11 C 12 C 13 C 21 C 22 C 23 C 31 C 32 C 33 C 44 C 55 and C 66 The elastic coefficient is determined by the material's elastic modulus and Poisson's ratio.

6. The method for quasi-three-dimensional vibration and acoustic radiation analysis of arbitrary plate and shell structures according to claim 1, characterized in that: The specific expression for the acoustic radiation model of the external fluid domain is as follows: Where p0 is the sound pressure level; Let be the sound wave number, and its expression is: , Angular frequency, The speed of sound in the acoustic medium; When using the boundary element method for discretization, the fluid boundary integral equation can be written as: Where p is the sound pressure vector at the boundary node, v n Let H be the normal vibration velocity vector of the structural surface, and let H and G be the acoustic influence matrices formed by discretization of the Green's function.

7. The method for quasi-three-dimensional vibration and acoustic radiation analysis of arbitrary plate and shell structures according to claim 1, characterized in that: The specific expression for the acoustic-structure coupling dynamic equation is as follows: Where q is the generalized coordinate vector of the structure composed of the Chebyshev expansion coefficients, M is the overall mass matrix of the plate and shell structure, K is the overall stiffness matrix of the plate and shell structure, D is the matrix that maps the structural normal velocity or displacement to the acoustic boundary, i is the imaginary unit, and T represents the matrix transpose.

8. A quasi-three-dimensional vibration and acoustic radiation analysis device for arbitrary plate and shell structures, characterized in that: It includes: The parameter input module is used to extract the geometric parameters, material parameters, and boundary condition parameters of the plate and shell structure. The quasi-3D modeling module is used to establish a curved coordinate system based on the neutral plane of the plate and shell structure, introduce independent variables in the thickness direction, and construct a quasi-3D displacement function that can simultaneously describe in-plane deformation and bending deformation. The structural analysis module is used to establish the strain-displacement relationship based on the quasi-three-dimensional displacement function, obtain the stress-strain relationship by combining the linear elastic constitutive relationship, and then construct the quasi-three-dimensional strain vector and stress vector of the structure. The structural vibration control equation is established through the variational principle to obtain the structural mass matrix and structural stiffness matrix. The acoustic modeling module is used to establish an acoustic radiation model of the external fluid domain based on the acoustic boundary integral theory, using the normal vibration response of the plate and shell structure surface as the acoustic radiation boundary condition. The coupled solution and output module is used to combine the structural vibration control equation with the acoustic boundary integral equation to establish a unified acoustic-structure coupled dynamic equation, solve for the vibration response and acoustic radiation characteristics of the plate and shell structure, and output the structural vibration response and acoustic radiation characteristics results.

9. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a quasi-three-dimensional vibration and acoustic radiation analysis method for any plate and shell structure as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, It stores a computer program that enables the computer to execute a quasi-three-dimensional vibration and acoustic radiation analysis method for any plate and shell structure as described in any one of claims 1-7.

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