A method, system and device for predicting the dynamic performance of a composite rectangular plate

Abstract

The present application relates to the technical field of acoustics, in particular to a method, system and device for predicting the dynamic performance of a composite rectangular plate. The method for predicting the dynamic performance of the composite rectangular plate comprises: setting parameters and elastic boundaries of a numerical model of the composite rectangular plate; establishing a dynamic model of the composite rectangular plate by using an energy method to obtain a Lagrange functional; dividing the composite rectangular plate into units to further obtain a vibration equation; applying forced excitation to the numerical model of the composite rectangular plate to obtain expressions of vibration displacement and vibration velocity of the composite rectangular plate structure; solving the vibration equation to obtain a Fourier coefficient matrix, and substituting the Fourier coefficient matrix into the expressions of the vibration displacement and the vibration velocity to obtain the vibration displacement and the vibration velocity of the composite rectangular plate, thereby realizing the prediction of the dynamic performance of the composite rectangular plate. The method improves the efficiency of predicting the dynamic performance of the composite rectangular plate.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of acoustics, in particular to a method, system and device for predicting the dynamic performance of a composite rectangular plate. BACKGROUND

[0002] At present, in the field of engineering and science, the lightweight application of plate structure is an important part of engineering design and construction.

[0003] A composite plate refers to a combined plate composed of two or more than two substances with completely different properties according to a certain comprehensive method. The continuous phase in the composite plate is called the main substance, and the dispersed phase is called the reinforcing substance. The main function of the main substance is to support the reinforcing material and avoid wear and tear and corrosion of the reinforcing material, while the reinforcing material is distributed in the matrix in a relatively independent form. For this technical field, the composite plate is widely used in lightweight development due to its high strength, small mass, fast forming and other advantages.

[0004] In the design process of the composite plate, it is usually necessary to first construct a dynamic model of the composite plate to predict its dynamic performance, and then put it into production after the performance meets the standard. In the prior art, the dynamic model of the composite plate is usually constructed by using the finite element method. This construction method is relatively complex in calculation, and the applicable scene is limited, which leads to low efficiency in predicting the dynamic performance of the composite plate in actual application. SUMMARY

[0005] Therefore, the technical problem to be solved by the present application is to overcome the low efficiency of predicting the dynamic performance of the composite plate in the prior art.

[0006] To solve the above technical problems, the present application provides a method for predicting the dynamic performance of a composite rectangular plate, comprising:

[0007] S1, setting parameters and elastic boundary of a numerical model of a composite rectangular plate;

[0008] S2, establishing a dynamic model of the composite rectangular plate by using energy method to obtain a Lagrange functional of the composite rectangular plate; dividing the composite rectangular plate into units to further obtain a vibration equation;

[0009] S3, applying forced excitation to the numerical model of the composite rectangular plate to obtain a vibration displacement expression and a vibration velocity expression of the composite rectangular plate structure; solving the vibration equation to obtain a Fourier coefficient matrix, substituting the Fourier coefficient matrix into the vibration displacement expression and the vibration velocity expression to calculate the vibration displacement and the vibration velocity of the composite rectangular plate, and realizing the prediction of the dynamic performance of the composite rectangular plate.

[0010] In one embodiment of the present application, the Lagrangian function of the composite rectangular plate in S2 is expressed as:

[0011] L plate =U plate -T plate -W F

[0012] wherein U plate represents the potential energy of the composite rectangular plate, T plate represents the kinetic energy of the composite rectangular plate, and W F represents the work done by the external force.

[0013] In one embodiment of the present application, the maximum potential energy of the composite rectangular plate is expressed as:

[0014]

[0015] wherein D is the bending stiffness of the composite rectangular plate, and D = Eh 3 / (12(1-μ 2 )), E represents the Young's modulus of the material, S represents the surface area of the composite rectangular plate, w represents the displacement of each point of the composite rectangular plate during vibration, x represents the horizontal coordinate of the composite rectangular plate, y represents the vertical coordinate of the composite rectangular plate, μ represents the Poisson's ratio of the material, a represents the length of the composite rectangular plate, b represents the width of the composite rectangular plate, k x0 , k xa , k y0 , k yb represent the horizontal springs in the boundary springs of the composite rectangular plate, K x0 , K xa , K y0 , K yb represent the torsional springs in the boundary springs of the composite rectangular plate.

[0016] The maximum kinetic energy of the composite rectangular plate is expressed as:

[0017]

[0018] wherein ρ represents the material density, ω represents the frequency of the external force, h represents the thickness of the composite rectangular plate, S represents the surface area of the composite rectangular plate, and w represents the displacement of each point of the composite rectangular plate during vibration.

[0019] In one embodiment of the present application, the numerical model of the composite rectangular plate is obtained by regarding different materials as different thicknesses and different densities of the unit assembly of the rectangular plate, and dividing the composite rectangular plate into V×T units. The expression of the potential energy of the entire rectangular plate is calculated from the potential energy of each unit as:

[0020]

[0021] The expression for calculating the kinetic energy of the whole rectangular plate from the kinetic energy of each unit is as follows:

[0022]

[0023] Wherein, V and T are the number of units in x and y directions respectively, U(v, t) and T(v, t) are the potential energy and kinetic energy of the unit cell (v, t) respectively; the unit cell (v, t) is discriminated, if the geometric center of (v, t) is located on the composite rectangular plate, then R1(v, t) = 1, R2(v, t) = 1, otherwise R1(v, t) = V1, R2(v, t) = V2;

[0024] There are Wherein, E1 represents the Young's modulus of the main material in the composite rectangular plate, E2 represents the Young's modulus of the auxiliary material in the composite rectangular plate, h1 represents the thickness of the main material, h2 represents the thickness of the auxiliary material, ρ1 represents the density of the main material, and ρ2 represents the density of the auxiliary material.

[0025] In one embodiment of the present application, a simple harmonic point force with size F and frequency f is taken as the external force, and the expression for the work done by the composite rectangular plate is as follows:

[0026] w F =∫∫ S Fwδ(x-x0)δ(y-y0)dxdy

[0027] S represents the surface area of the composite rectangular plate, x represents the horizontal coordinate of the composite rectangular plate, y represents the vertical coordinate of the composite rectangular plate, w represents the displacement of each point of the composite rectangular plate in the vibration process, δ represents the Dirac function, x0 represents the horizontal coordinate of the point of action of the external force on the composite rectangular plate, and y0 represents the vertical coordinate of the point of action of the external force on the composite rectangular plate.

[0028] In one embodiment of the present application, the potential energy of the whole rectangular plate calculated from the potential energy of each unit, the kinetic energy of the whole rectangular plate calculated from the kinetic energy of each unit, and the external force work expression are substituted into the Lagrangian functional, and the coefficients in the Fourier series are derived to obtain the vibration equation of the composite rectangular plate as follows:

[0029] {[K p_h ]-ω 2 [M p_h ]}{A}={F}

[0030] Wherein, K p_h represents the stiffness matrix of the composite rectangular plate, ω represents the frequency of the external force, M p_hLet A represent the mass matrix of the composite rectangular plate, A represent the Fourier coefficient matrix to be solved, and F represent the force matrix.

[0031] In one embodiment of the present invention, in S3, the vibration displacement expression of the composite rectangular plate structure is:

[0032]

[0033] Where x represents the abscissa of the composite rectangular plate, y represents the ordinate of the composite rectangular plate, and A mn , λ represents the expansion coefficients of the Fourier series, M and N represent the number of terms in the Fourier series expansion, and m and n represent the m-th and n-th terms in the Fourier series expansion, respectively; am =mπ / a,λ bn =nπ / b; and For auxiliary functions, the expression is:

[0034]

[0035]

[0036]

[0037]

[0038] Where a represents the length of the composite rectangular plate and b represents the width of the composite rectangular plate.

[0039] In one embodiment of the present invention, in S3, the Fourier series expression of the vibration velocity of the composite rectangular plate is:

[0040]

[0041] Where i represents a complex number in mathematics, i 2 =-1;

[0042] and The supplementary terms of the Fourier series are obtained by Rayleigh's method and are derived through the supplementary terms. and Use the Fourier cosine expansion as an expression to refine

[0043]

[0044] Will and A mn Restated in matrix form: Wherein the elements in the matrix A are unknown coefficients to be solved, and T is the change matrix of the process.

[0045] The application further provides a dynamic performance prediction system of a composite material rectangular plate, comprising:

[0046] A parameter setting module is configured to set parameters of the numerical model of the composite material rectangular plate and an elastic boundary;

[0047] A model construction module is configured to establish a dynamic model of the composite material rectangular plate by using an energy method to obtain a Lagrange functional of the composite material rectangular plate, and further divide the composite material rectangular plate into units to obtain a vibration equation.

[0048] A data analysis module is configured to apply a forced excitation to the numerical model of the composite material rectangular plate to obtain an expression of a vibration displacement and an expression of a vibration velocity of the composite material rectangular plate structure, and solve the vibration equation to obtain a Fourier coefficient matrix, and substitute the Fourier coefficient matrix into the expression of the vibration displacement and the expression of the vibration velocity to calculate the vibration displacement and the vibration velocity of the composite material rectangular plate, thereby realizing dynamic performance prediction of the composite material rectangular plate.

[0049] The application further provides a dynamic performance prediction device of a composite material rectangular plate, comprising:

[0050] A memory is configured to store a computer program;

[0051] A processor is configured to execute the computer program to realize the steps of the dynamic performance prediction method of the composite material rectangular plate.

[0052] The above technical solution of the application has the following advantages over the prior art:

[0053] The dynamic performance prediction method of the composite material rectangular plate provided by the application regards different materials as different thickness and different density unit assemblies of the plate during establishment of the numerical model of the composite material rectangular plate, and performs unit division, in which the mass density and the Young's modulus are set respectively. According to the Lagrange functional and the expression of the vibration displacement, the vibration equation of the composite material rectangular plate is derived, and under the premise of ensuring the accuracy of the dynamic performance prediction of the composite material rectangular plate, the calculation parameters and the dimension used are less, the operation of the numerical model is simplified, and the efficiency of the dynamic performance prediction of the composite material rectangular plate is improved. The numerical model of the composite material rectangular plate provided by the application only needs to input parameter values to obtain good prediction results when predicting the dynamic performance, and therefore is more widely applicable and has higher prediction efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to make the content of the present application more easily understood, the present application is further described in detail below according to specific embodiments of the present application and in conjunction with the accompanying drawings, in which

[0055] Figure 1 is a flowchart of a method for predicting the dynamic performance of a composite material rectangular plate provided by the present application;

[0056] Figure 2 is a numerical model schematic diagram provided by an embodiment of the present application;

[0057] Figure 3 is a comparison schematic diagram of the sound radiation results obtained by using the method provided by the present application and the results obtained by using the finite element method in an embodiment of the present application;

[0058] Figure 4 is a comparison schematic diagram of the results obtained by changing the sound pressure point according to the method provided by the present application and the results obtained by using the finite element method in an embodiment of the present application;

[0059] Figure 5 is a comparison schematic diagram of the modes of each order of the method provided by the present application and the method using the finite element method provided by an embodiment of the present application;

[0060] Figure 6 is a structure schematic diagram of a system for predicting the dynamic performance of a composite material rectangular plate provided by the present application. DETAILED DESCRIPTION

[0061] The present application is further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present application and implement it, but the embodiments are not limiting to the present application. Embodiment One

[0063] Referring to Figure 1 , the present application provides a method for predicting the dynamic performance of a composite material rectangular plate, comprising:

[0064] S1, setting the parameters and elastic boundary of the numerical model of the composite material rectangular plate.

[0065] In the present application, different materials are regarded as different thickness and different density unit assemblies of the rectangular plate, and the unit division is performed, and the thickness, density and Young's modulus of different materials are set respectively. For the sake of simplifying the description, two composite material rectangular plates are taken as examples in the present application, in which the main material density is p1, the auxiliary material density is p2, the main material thickness is h1, the auxiliary material thickness is h2, the main material Young's modulus is E1, and the auxiliary material Young's modulus is E1.

[0066] The numerical model established by the embodiment of the present application can refer to Figure 2 , and the numerical model comprises different material plate domains and elastic boundary conditions. Figure 2 The rectangular thin plate in the formula does not consider the rotational inertia in the plate and the transverse shear of the plate, and the plate boundary is supported by transverse springs and torsional springs to establish an elastic mounting boundary.

[0067] The size of the plate is: length x=a, width y=b, and thickness h. The boundary springs are transverse springs k x0 , k xa , k y0 , k yb and torsional springs K x0 , K xa , K y0 , K yb . Taking k xa as an example, the meaning of the variable is introduced, and k xa represents the spring stiffness value at the coordinate x=a in the x direction.

[0068] S2, the energy method is used to establish the dynamic model of the composite rectangular plate, and the Lagrange functional of the composite rectangular plate is obtained; the composite rectangular plate is divided into units, and the vibration equation is further obtained.

[0069] Suppose that there is a force F(x i , y i ) acting on the composite rectangular plate, then the Lagrange functional of the composite rectangular plate is:

[0070] L plate =U plate -T plate -W F

[0071] Wherein U plate represents the potential energy of the composite rectangular plate, T plate represents the kinetic energy of the composite rectangular plate, and W F represents the work done by the external force.

[0072] Wherein, the maximum potential energy expression of the composite rectangular plate is:

[0073]

[0074] The maximum kinetic energy expression of the composite rectangular plate is:

[0075]

[0076] The expression of the work done by the external force on the composite rectangular plate is:

[0077] wF =∫∫ S Fwδ(x-x0)δ(y-y0)dxdy

[0078] where D is the bending stiffness of the composite rectangular plate, and D=Eh 3 / (12(1-μ 2 ))。

[0079] S represents the surface area of the composite rectangular plate, w represents the displacement of each point of the composite rectangular plate in the vibration process, x represents the horizontal coordinate of the composite rectangular plate, y represents the vertical coordinate of the composite rectangular plate, μ represents the Poisson's ratio of the material, a represents the length of the composite rectangular plate, b represents the width of the composite rectangular plate, k x0 , k xa , k y0 , k yb represents the transverse spring in the boundary spring of the composite rectangular plate, K x0 , K xa , K y0 , K yb represents the torsional spring in the boundary spring of the composite rectangular plate; ρ represents the material density, ω represents the frequency of the external force, h represents the thickness of the composite rectangular plate, E represents the Young's modulus of the material; δ represents the Dirac function, x0 represents the horizontal coordinate of the point of action of the external force on the composite rectangular plate, and y0 represents the vertical coordinate of the point of action of the external force on the composite rectangular plate.

[0080] In order to simplify the integral operation, the composite rectangular plate is divided into VxT units in the embodiment of the present application, and the expression for calculating the potential energy of the entire rectangular plate from the potential energy of each unit is as follows:

[0081]

[0082] The expression for calculating the kinetic energy of the entire rectangular plate from the kinetic energy of each unit is as follows:

[0083]

[0084] where V and T are the number of units in the x and y directions, respectively, and U(v, t) and T(v, t) are the potential energy and kinetic energy of the unit cell (v, t), respectively.

[0085] The unit cell (v, t) is discriminated, if the geometric center of (v, t) is located on the composite rectangular plate, then R1(v, t)=1, R2(v, t)=1, otherwise R1(v, t)=V1, R2(v, t)=V2. Wherein

[0086] The potential energy, kinetic energy and work done by external force obtained after the above division unit are substituted into Lagrange functional, and derivation is performed on the coefficients in the Fourier series to obtain a vibration equation of the composite material rectangular plate as follows:

[0087] {[K p_h ]-ω 2 [M p_h ]}{A}={F}

[0088] Wherein, K p_h represents the stiffness matrix of the composite material rectangular plate, ω represents the frequency of the external force, M p_h represents the mass matrix of the composite material rectangular plate, A represents the Fourier coefficient matrix to be solved, and F represents the force matrix.

[0089] S3, a forced excitation is applied on the numerical model of the composite material rectangular plate to obtain a vibration displacement expression and a vibration velocity expression of the composite material rectangular plate structure; the vibration equation is solved to obtain a Fourier coefficient matrix, the Fourier coefficient matrix is substituted into the vibration displacement expression and the vibration velocity expression, and the vibration displacement and the vibration velocity of the composite material rectangular plate are calculated to realize the prediction of the dynamic performance of the composite material rectangular plate.

[0090] The Fourier series is improved in the embodiment, an additional term is added on the basis of the traditional Fourier cosine function to process the discontinuity of the original cosine function at the elastic constraint boundary, and the vibration displacement expression of the composite material rectangular plate structure is as follows:

[0091]

[0092] Wherein, A mn 、 are expansion coefficients of the Fourier series, M and N represent the number of expansion terms of the Fourier series respectively, and m and n represent the mth expansion term and the nth expansion term of the Fourier series respectively; λ am =mπ / a, λ bn =nπ / b; and are auxiliary functions, and the expression is as follows:

[0093]

[0094]

[0095]

[0096]

[0097] The normal vibration velocity expression of a point on the composite material rectangular plate is as follows:

[0098] u(x, y) = iωw(x, y)

[0099] wherein the Fourier series form expression of the rectangular plate vibration velocity is:

[0100]

[0101] wherein represents the complex number in mathematics, has i 2 = -1;

[0102] and are the supplementary terms of the Fourier series, which are obtained by the Rayleigh method, and the Fourier cosine expansion of and is used as the expression to perfect

[0103]

[0104] wherein and are the supplementary terms of the Fourier series.

[0105] The and A mn are restated in the matrix form: wherein the elements in the A matrix are all unknown coefficients to be solved in the vibration equation of the composite rectangular plate, and T is the change matrix in the process.

[0106] By solving the vibration equation of the composite rectangular plate, the Fourier coefficient matrix A is obtained, which is substituted into the vibration displacement expression and the vibration velocity expression of the composite rectangular plate, so that the vibration displacement and the vibration velocity of the composite rectangular plate can be obtained, and the dynamic performance prediction of the composite rectangular plate is realized. Specific embodiment two:

[0108] To verify the correctness of the method proposed in the application, in the embodiments of the application, the prediction results of the dynamic performance of the composite rectangular plate by the application are compared with the prediction results by the finite element method, so as to illustrate the effectiveness of the method of the application.

[0109] Taking the addition of a secondary material in the center circular area of the composite rectangular plate as an example, the parameters of the rectangular plate are as follows: length a = 0.5 m, width b = 0.6 m, density of the primary material 7850 kg / m 3 , density of the secondary material 2700 kg / m 3 , Young's modulus of the primary material 200 GPa, Young's modulus of the secondary material 70.3 GPa, thickness of the primary material 3 mm, thickness of the secondary material 2 mm. The center coordinates are (0.25, 0.3), and the radius r = 0.1 m.

[0110] The parameters of air are set as: sound speed c0=343m / s, air density p0=1.23kg / m 3 The coordinates of the point force F are (0.1, 0.5). The elastic boundary conditions of the composite rectangular plate are set as four edges being fixed, i.e. the transverse spring stiffness and the torsional spring stiffness of the four edges are infinite, i.e. x0 , xa , y0 , yb , x0 , xa , y0 , yb are all 10 11 N / m.

[0111] The plate vibration displacement results of the composite rectangular plate are shown in Figure 3 By comparison, it can be obviously seen that the method has high consistency with the finite element results in calculating the forced excitation dynamic model.

[0112] In order to ensure the applicability of the method, the sub-material region is set as a square with a side length of 0.1m and a center point coordinate of (0.25, 0.3), and the coordinates of the point force F are changed to (0.1, 0.1), so that the composite rectangular plate is subjected to the action of the point force F at different positions again, and the results are compared. The comparison results are shown in Figure 4 It can be seen that the method has good consistency with the results obtained by the finite element method.

[0113] By comparison in Table 1, it can be obviously seen that the method has high consistency with the finite element results in predicting the natural frequency of the composite rectangular plate, and there is a slight difference, which is caused by the difference in plate damping in the calculation of the two methods.

[0114]

[0115] Table 1, comparison of the natural frequency of each modal order of the method and the finite element method

[0116] The dynamic performance prediction method provided by the application can also calculate the modal of each order of the composite rectangular plate. Referring to Figure 5 The upper image is the plate modal distribution diagram of the method, and the lower image is the plate modal distribution diagram of the finite element method. By comparison, it can be obviously seen that the method has high consistency and accuracy in calculating the plate modal with the finite element results.

[0117] To sum up, under the premise of ensuring the accuracy of the dynamic performance prediction of the composite rectangular plate, compared with the finite element method, the method provided by the application uses fewer calculation parameters and dimensions, simplifies the operation of the numerical model, and improves the efficiency of the dynamic performance prediction of the composite rectangular plate. When predicting the dynamic performance, the numerical model of the composite rectangular plate provided by the application only needs to input parameter values to obtain good prediction results, without the need to draw images, divide units, and re-model according to specific situations as in the finite element method, and therefore, the applicability is more extensive, and the prediction efficiency is higher. Embodiment three

[0119] Referring to Figure 6 The embodiment of the application provides a dynamic performance prediction system of a composite rectangular plate, which comprises:

[0120] A parameter setting module is configured to set parameters of a numerical model of the composite rectangular plate and an elastic boundary.

[0121] A model construction module is configured to establish a dynamic model of the composite rectangular plate by using an energy method to obtain a Lagrange functional of the composite rectangular plate, and to further obtain a vibration equation by dividing units of the composite rectangular plate.

[0122] A data analysis module is configured to apply a forced excitation to the numerical model of the composite rectangular plate to obtain an expression of a vibration displacement and an expression of a vibration velocity of the composite rectangular plate structure, and to solve the vibration equation to obtain a Fourier coefficient matrix, and to substitute the Fourier coefficient matrix into the expression of the vibration displacement and the expression of the vibration velocity to calculate the vibration displacement and the vibration velocity of the composite rectangular plate, so as to realize the dynamic performance prediction of the composite rectangular plate.

[0123] The embodiment of the application further provides a dynamic performance prediction device of a composite rectangular plate, which comprises:

[0124] A memory is configured to store a computer program.

[0125] A processor is configured to execute the computer program to realize the steps of the dynamic performance prediction method of the composite rectangular plate.

[0126] Those skilled in the art should understand that the embodiments of the application can be provided as a method, a system, or a computer program product. Therefore, the application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the application can adopt a computer program product in the form of one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program codes.

[0127] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 means for functionally implementing the steps of the flowchart block or blocks

[0128] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 means for functionally implementing the steps of the flowchart block or blocks

[0129] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks Figure 1 means for functionally implementing the steps of the flowchart block or blocks

[0130] Obviously, the above-described embodiments are only examples for clarity of description and are not limiting on the implementation. Based on the above description, other different forms of changes or variations can be made by those of ordinary skill in the art. Here, it is not necessary and impossible to enumerate all the embodiments. The obvious changes or variations derived therefrom are still within the protection scope of the present application.

Claims

1. A method of predicting the dynamic performance of a composite rectangular panel, characterized in that, The method comprises the following steps: S1, setting parameters of a numerical model of a composite material rectangular plate and an elastic boundary; S2, establishing a dynamic model of the composite material rectangular plate by using an energy method to obtain a Lagrange functional of the composite material rectangular plate; regarding different materials as different thicknesses and different densities of a unit assembly of the rectangular plate, performing unit division on the composite material rectangular plate, and further obtaining a vibration equation; S3, applying forced excitation on the numerical model of the composite material rectangular plate to obtain an expression of vibration displacement and an expression of vibration velocity of the composite material rectangular plate structure; The expression of vibration velocity of the composite material rectangular plate structure in a Fourier series form is: ； wherein represents a complex number in mathematics, has ; , and are complementary terms to the Fourier series, obtained by the method of Swillings and completed by the Fourier cosine expansion of the complementary terms and as expressions of the form : ； will be and restated in matrix form: where is the Fourier coefficient matrix to be solved, is the change matrix for the process; Solving the vibration equation to obtain a Fourier coefficient matrix, substituting the Fourier coefficient matrix into the expression of vibration displacement and the expression of vibration velocity, and calculating to obtain the vibration displacement and the vibration velocity of the composite material rectangular plate, so as to realize the prediction of the dynamic performance of the composite material rectangular plate.

2. The method of predicting the dynamic behavior of a composite rectangular panel according to claim 1, wherein In S2, the Lagrange functional of the composite material rectangular plate is expressed as: ； wherein represents the potential energy of the composite rectangular plate, represents the kinetic energy of the composite rectangular plate, represents the work done by the external forces.

3. The method of predicting the dynamic performance of a composite rectangular panel according to claim 2, wherein The maximum potential energy expression of the composite material rectangular plate is: ； wherein is the bending stiffness of the composite rectangular plate, has , denotes the Young's modulus of the material; denotes the surface area of the composite rectangular plate, denotes the displacement of each point of the composite rectangular plate during the vibration process, denotes the abscissa of the composite rectangular plate, denotes the ordinate of the composite rectangular plate, denotes the Poisson's ratio of the material, denotes the length of the composite rectangular plate, denotes the width of the composite rectangular plate, , , , denotes the transverse spring in the boundary spring of the composite rectangular plate, , , , denotes the torsional spring in the boundary spring of the composite rectangular plate; The maximum kinetic energy expression of the composite material rectangular plate is: ； wherein denotes the density of the material, denotes the frequency of the external force, denotes the thickness of the composite rectangular plate, denotes the surface area of the composite rectangular plate, denotes the displacement of each point of the composite rectangular plate during the vibration.

4. The method of predicting the dynamic performance of a composite rectangular panel according to claim 3, wherein The numerical model of the composite rectangular plate is divided into units by regarding different materials as different thicknesses and different densities of the unit assembly of the rectangular plate. The expression for calculating the potential energy of the entire rectangular plate from the potential energy of each unit is: ； The expression of kinetic energy of the entire rectangular plate calculated from the kinetic energy of each unit is: ； wherein , are respectively , number of cells in the direction , are respectively potential energy and kinetic energy of the cell ; the cell is discriminated, if the geometric center of the cell is located on the composite rectangular plate, then , , otherwise , ; There are , wherein E1represents the Young's modulus of the main material in the composite rectangular plate, E2represents the Young's modulus of the secondary material in the composite rectangular plate, h1represents the thickness of the main material, h2represents the thickness of the secondary material, p1represents the density of the main material, p2represents the density of the secondary material.

5. The method of predicting the dynamic performance of a composite rectangular panel according to claim 2, wherein The expression of the work done by the external force on the composite rectangular plate is as follows: , the frequency of the simple harmonic point force is ​ ； represents the surface area of the composite rectangular plate, represents the abscissa of the composite rectangular plate, represents the ordinate of the composite rectangular plate, represents the displacement of each point of the composite rectangular plate during the vibration process, represents the Dirac function, represents the abscissa of the point of action of the external force on the composite rectangular plate, represents the ordinate of the point of action of the external force on the composite rectangular plate.

6. The method of predicting the dynamic behavior of a composite rectangular panel according to any one of claims 4 to 5, characterized in that, Substituting the potential energy of the entire rectangular plate calculated from the potential energy of each unit, the kinetic energy of the entire rectangular plate calculated from the kinetic energy of each unit, and the expression of work done by external force into the Lagrange functional, and deriving the coefficients in the Fourier series to obtain the vibration equation of the composite material rectangular plate: ； wherein, represents the stiffness matrix of the composite rectangular plate, represents the frequency of the external force, represents the mass matrix of the composite rectangular plate, represents the Fourier coefficient matrix to be solved, represents the force matrix.

7. The method of predicting the dynamic performance of a composite rectangular panel according to claim 1, wherein In S3, the expression of vibration displacement of the composite material rectangular plate structure is: ； wherein denotes the abscissa of the composite rectangular plate, denotes the ordinate of the composite rectangular plate, , , are the expansion coefficients of the Fourier series, respectively, , denote the number of expansion terms of the Fourier series, respectively, and denote the first expansion term and the first expansion term of the Fourier series, respectively; , ; and are auxiliary functions, the expressions of which are: ； ； ； ； wherein represents the length of the composite rectangular plate, represents the width of the composite rectangular plate.

8. A system for predicting the dynamic performance of a composite rectangular panel, characterized in that, The method comprises the following steps: A parameter setting module is configured to set parameters of a numerical model of a composite material rectangular plate and an elastic boundary; A model construction module is configured to establish a dynamic model of the composite material rectangular plate by using an energy method to obtain a Lagrange functional of the composite material rectangular plate; regarding different materials as different thicknesses and different densities of a unit assembly of the rectangular plate, performing unit division on the composite material rectangular plate, and further obtaining a vibration equation; A data analysis module is configured to apply forced excitation on the numerical model of the composite material rectangular plate to obtain an expression of vibration displacement and an expression of vibration velocity of the composite material rectangular plate structure; The expression of vibration velocity of the composite material rectangular plate structure in a Fourier series form is: ； wherein represents a complex number in mathematics, has ; , and are supplementary terms of the Fourier series, obtained by the method of Swedberg and completed by the Fourier cosine expansion of the supplementary terms and as expressions : ； The and are restated in matrix form: where is the Fourier coefficient matrix to be solved, is the change matrix for the process; Solving the vibration equation to obtain a Fourier coefficient matrix, substituting the Fourier coefficient matrix into the expression of vibration displacement and the expression of vibration velocity, and calculating to obtain the vibration displacement and the vibration velocity of the composite material rectangular plate, so as to realize the prediction of the dynamic performance of the composite material rectangular plate.

9. An apparatus for predicting the dynamic performance of a composite rectangular panel, characterized by The method comprises the following steps: A memory is configured to store a computer program; A processor is configured to execute the computer program to implement the steps of the method for predicting the dynamic performance of the composite material rectangular plate according to any one of claims 1 to 7.

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