Sound-vibration coupling analysis method for double-layer plate coupling system with mechanical connection

Abstract

The invention provides a sound and vibration coupling analysis method for a double-layer plate coupling system with mechanical connection. The sound and vibration coupling analysis method comprises the following steps: S1, establishing the double-layer plate coupling system with mechanical connection and a double-layer plate-sound cavity coupling system with mechanical connection; s2, establishing a vibration displacement tolerance function of the double-layer plate coupling system by adopting an improved Fourier series method; s3, analyzing plate-acoustic cavity coupling potential energy of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system by using an energy principle to obtain coupling energy functional of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system; s4, solving the coupling energy functional of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system by using a Rayleigh-Ritz method, and obtaining the acoustic vibration characteristics of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system; the method has important theoretical significance and engineering application value, can be used for establishment and verification of a theoretical model, and can also guide optimization design and performance evaluation of a double-layer board system in actual engineering.

Description

Technical Field

[0001] The invention relates to the field of structural dynamics technical analysis, and in particular to an acoustic-vibration coupling analysis method for a double-layer plate coupling system with mechanical connection. Background Art

[0002] Due to its excellent mechanical and acoustic properties, the double-layer panel structure has become a typical structure in aviation and ship equipment in actual engineering applications. For example, in an aircraft, its skin and inner decorative panel form a double-layer panel structure. There are two transmission pathways for sound energy to be transmitted in a double-layer panel system, namely, the acoustic transmission pathway and the structural transmission pathway. The existence of the structural transmission pathway causes the propagation of structure-borne noise, which makes the coupling between the structures in the system more complicated, thereby affecting the sound insulation performance of the double-layer panel system.

[0003] There are two main ways to control noise from a technical perspective: active control and passive control. Active control generally requires external energy and is complex, so passive control is mostly used in engineering structures. Existing passive control consumes sound energy through the interaction between noise sound waves and acoustic materials or acoustic structures, thereby achieving the purpose of noise reduction. For example, damping, noise reduction, and sound insulation are all passive controls. In existing research, most of the studies on the vibration characteristics of double-layer plate structures have not considered the impact of mechanical connections on the vibration energy transfer of double-layer plate structures, or have ignored the energy transmission of bounded fluids between the double-layer plates. Summary of the invention

[0004] In view of this, the purpose of the present invention is to propose an acoustic-vibration coupling analysis method for a double-layer plate coupling system with mechanical connection, so as to solve the technical problem that the existing passive noise control method does not consider the influence of mechanical connection.

[0005] The technical means adopted by the present invention are as follows:

[0006] A method for analyzing acoustic-vibration coupling of a mechanically connected double-layer plate coupling system comprises the following steps:

[0007] S1. Establish a double-layer plate coupling system with mechanical connection and a double-layer plate-acoustic cavity coupling system with mechanical connection, and realize arbitrary boundary conditions of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system according to the simulated spring technology;

[0008] S2. The vibration displacement allowable function of the double-layer plate coupling system is established by using the improved Fourier series method, and the sound pressure allowable function of the closed sound cavity of the double-layer plate-sound cavity coupling system is established by using the improved Fourier series method;

[0009] S3. Analyze the plate-acoustic cavity coupling potential energy of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system by using the energy principle, and obtain the coupling energy functional of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system;

[0010] S4. Using the Rayleigh-Ritz method to solve the coupling energy functional of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system, the acoustic vibration characteristics of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system are obtained;

[0011] S5, use the acoustic vibration characteristics obtained in S4 to verify the convergence and correctness of the model, analyze the influence of important parameters on the acoustic vibration characteristics, and conduct steady-state response analysis of the coupled system by introducing surface force, point sound source excitation and changing the connection mode of mechanical connection, such as Figure 3 shown.

[0012] Furthermore, the double-layer plate coupling system comprises an upper rectangular elastic plate and a lower rectangular elastic plate arranged in parallel, wherein the upper rectangular elastic plate and the lower rectangular elastic plate are connected with rigid walls on all sides; the upper rectangular elastic plate and the lower rectangular elastic plate are mechanically connected;

[0013] The double-layer plate-acoustic cavity coupling system comprises an upper rectangular elastic plate and a lower rectangular elastic plate arranged in a rectangular shell, the upper rectangular elastic plate and the lower rectangular elastic plate are arranged in parallel, the edges of the upper rectangular elastic plate and the lower rectangular elastic plate are connected to the inner wall of the shell, the upper rectangular elastic plate and the lower rectangular elastic plate are mechanically connected, the upper rectangular elastic plate and the shell above it form a first acoustic cavity, the upper rectangular elastic plate, the lower rectangular elastic plate and the shell form a second acoustic cavity, and the lower rectangular elastic plate and the shell below it form a third acoustic cavity;

[0014] The simulated spring technology is a lateral support spring and a rotational constraint spring uniformly distributed on the boundaries of the upper rectangular elastic plate and the lower rectangular elastic plate to simulate different boundary conditions of the bending vibration of the double-layer plate structure.

[0015] Furthermore, the vibration displacement allowable function is as follows:

[0016]

[0017] In the formula, The specific form of the supplementary function is:

[0018] ζ 1a (x p )=9asin(πx p / 2a) / 4π-asin(3πx p / 2a) / 12π(2.1a)

[0019] ζ 2a (x p)=-9acos(πx p / 2a) / 4π-acos(3πx p / 2a) / 12π(2.1b)

[0020] ζ 3a (x p )=a 3 sin(πx p / 2a) / π 3 -a 3 sin(3πx p / 2a) / 3π 3 (2.1c)

[0021] ζ 1a (x p )=-a 3 cos(πx p / 2a) / π 3 -a 3 cos(3πx p / 2a) / 3π 3 (2.1d)

[0022] in, is the unknown expansion coefficient.

[0023] Furthermore, the permissible function of the sound pressure of the closed acoustic cavity is as follows:

[0024] The sound pressure of the sound field in the first sound cavity and the third sound cavity are expressed as:

[0025]

[0026] in,

[0027]

[0028] The expression of the complementary function is expressed as:

[0029] ξ 1h (z c1 )=z c1 (z c1 / h1-1) 2 (2.5)

[0030]

[0031] The second acoustic cavity is an acoustic cavity with two flexible walls and four rigid walls. The sound pressure of its sound field is expressed as:

[0032]

[0033] in, The expression of the supplementary function is:

[0034] ξ 1h (z c2 )=z c2 (z c2 / h2-1) 2 (2.8)

[0035]

[0036] in, is the unknown expansion coefficient.

[0037] Further, in S4, the total energy functional includes the total potential energy of the upper rectangular elastic plate and the lower rectangular elastic plate, the total kinetic energy of the upper rectangular elastic plate and the lower rectangular elastic plate, the elastic potential energy stored in the mechanical connection, the work done by external excitation on the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system, and the work done on the plate structure by the sound pressure at the interface between the upper rectangular elastic plate and the lower rectangular elastic plate and the internal sound field of the first acoustic cavity, the second acoustic cavity and the third acoustic cavity in the double-layer plate-acoustic cavity coupling system.

[0038] Furthermore, the process of obtaining the acoustic vibration characteristics includes the following steps:

[0039] S41, taking partial derivatives of the expansion coefficients in the total energy functional and setting the result equal to zero, obtaining the overall mass matrix and stiffness matrix of the coupled system, and then obtaining the acoustic vibration characteristic equation of the coupled system;

[0040] S42. Solve the acoustic-vibration characteristic equation to obtain the acoustic-vibration characteristics of the coupled system.

[0041] Furthermore, the steady-state response analysis method is: substituting the surface force and the point sound source into the acoustic vibration characteristics to obtain the steady-state response.

[0042] The present invention also provides a storage medium, which includes a stored program, wherein when the program is run, any of the above-mentioned acoustic-vibration coupling analysis methods for a double-layer plate coupling system with mechanical connection is executed.

[0043] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes any of the above-mentioned acoustic-vibration coupling analysis methods for a double-layer plate coupling system with mechanical connection through the computer program.

[0044] Compared with the prior art, the present invention has the following advantages:

[0045] The present invention establishes an acoustic vibration theoretical model of a double-layer plate-acoustic cavity coupling system with mechanical connection, and adopts the improved Fourier series method and Rayleigh-Lee-Zehnder method to calculate the free mode and forced response characteristics of the coupling system, and analyzes the attenuation effect of the model on sound energy under different boundary conditions and different external excitations. On this basis, the mechanical connection between the double-layer plates is changed to explore the optimal configuration of the sound insulation performance of the coupling system, and the finite element analysis results are used for comparison and verification. It provides an effective reference and theoretical basis for the subsequent application of the sound insulation performance of the double-layer plate structure. The application of the double-layer plate structure can also improve the living conditions of people in a noisy environment and reduce the impact of noise on the accuracy of the instrument, which has certain theoretical value and practical engineering significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0047] Figure 1 The present invention is a flow chart of the method.

[0048] Figure 2 a is a three-dimensional diagram of the double-layer board structure. Figure 2 b is the cross-sectional view of the double-layer plate structure. Figure 2 c is a stereogram of the double-layer plate-acoustic cavity coupling system model. Figure 2 d is the cross-sectional view of the double-layer plate-acoustic cavity coupling system model.

[0049] Figure 3 a is a schematic diagram of the surface force excitation distribution of the present invention, Figure 3 b is a schematic diagram of the point sound source excitation distribution of the present invention.

[0050] Figure 4 It is the vibration response diagram of the single-point mechanical connection coupling system at different connection positions of the present invention.

[0051] Figure 5 a is Figure 4 The average vibration acceleration level of the single-point mechanical connection coupling system of the middle and upper rectangular elastic plate, Figure 5 b is Figure 4 Average vibration acceleration level of the single-point mechanical connection coupling system of the middle and lower rectangular elastic plates.

[0052] Figure 6 Schematic diagram of different numbers of mechanical connection coupling systems of the present invention.

[0053] Figure 7 a is Figure 6Average vibration acceleration level of the mechanical connection coupling system with different numbers of middle and upper rectangular elastic plates, Figure 7 b is Figure 6 Average vibration acceleration level of the coupling system with different numbers of mechanical connections of the middle and lower rectangular elastic plates.

[0054] Figure 8 a is the sound pressure response diagram of the coupled system under the excitation of the point sound source at observation point 1, Figure 8 b is the sound pressure response diagram of the coupled system under the excitation of the point sound source at observation point 2. DETAILED DESCRIPTION

[0055] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0056] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0057] As an embodiment of the present invention, the relevant parameters of the coupling system are: the upper thin plate is called the upper rectangular elastic plate, the length is a = 0.5m, the width is b = 0.4m, the thickness is δ1 = 0.002m, the lower thin plate is called the lower rectangular elastic plate, the length is a = 0.5m, the width is b = 0.4m, the thickness is δ2 = 0.002m, the material is aluminum, and the density, Poisson's ratio, and Young's modulus of the two aluminum plates are: ρ = 2750kg / m 3 , μ=0.3,E=71*10 9 Pa. The sound velocity and density of the middle cavity are: c0 = 340 m / s, ρ0 = 1.21 kg / m 3 The height of the acoustic cavity is h. There is a mechanical connection between the upper rectangular elastic plate and the lower rectangular elastic plate, and the position coordinate of the connection is (x l ,y l ).

[0058] A vibro-acoustic coupling analysis method for a mechanically connected double-layer plate coupling system, such as Figure 1 As shown, the following steps are included:

[0059] S1. Establish a structural analysis model of a double-layer plate coupling system with mechanical connections, such as Figure 2 As shown: Figure 2 (a) and (b) are the structural analysis models of the double-layer plate coupling system. They consist of two rectangular elastic thin plates, four rigid walls and a mechanical connection in the middle. The upper thin plate is called the upper rectangular elastic plate (plate 1), with a length of a = 0.5m, a width of b = 0.4m, and a thickness of δ1 = 0.002m. The lower thin plate is called the lower rectangular elastic plate (plate 2), with a length of a = 0.5m, a width of b = 0.4m, and a thickness of δ2 = 0.002m. The height of the sound cavity is h. There is a mechanical connection between the upper rectangular elastic plate and the lower rectangular elastic plate. The position coordinates of the connection are (x l ,y l ), the linear stiffness of the mechanical connection is k l , the rotational stiffness is K lx and K ly F is the point force excitation applied to the upper rectangular elastic plate. In order to simulate the different boundary conditions of the bending vibration of the double-layer plate structure, the lateral support springs and rotation constraint springs are evenly distributed on the boundaries of the upper rectangular elastic plate and the lower rectangular elastic plate. The boundary conditions of plate i (i=1,2) are expressed by the following formula:

[0060] On the boundary x = 0,

[0061]

[0062] On the boundary x = a,

[0063]

[0064] On the boundary y = 0,

[0065]

[0066] On the boundary y = b,

[0067]

[0068] Among them, w i (x i ,y i ) is the bending vibration displacement, are the lateral support spring constants, is the rotation constraint spring constant. Different boundary conditions can be obtained by changing the spring constants of each boundary. are the shear force in the x-axis direction and the shear force in the y-axis direction, They are the bending moment in the x-axis direction and the bending moment in the y-axis direction, respectively, and can be expressed by the following formula:

[0069]

[0070] Among them, v i is Poisson's ratio, D i is the bending stiffness.

[0071] Figure 2 (c) and (d) are the structural analysis models of the double-layer plate-acoustic cavity coupling system. The model is mainly composed of two upper and lower rectangular elastic thin plates and three acoustic cavities. The upper thin plate is called the upper rectangular elastic plate, with a length of a = 0.5m, a width of b = 0.4m, and a thickness of δ1 = 0.002m. The lower thin plate is called the lower rectangular elastic plate, with a length of a = 0.5m, a width of b = 0.4m, and a thickness of δ2 = 0.002m. The height of the acoustic cavity is h. There is a mechanical connection between the upper rectangular elastic plate and the lower rectangular elastic plate, and the position coordinates of the connection are (x l ,y l ), the linear stiffness of the mechanical connection is k l , the rotational stiffness is K lx and K ly . Transverse support springs and rotation constraint springs are evenly distributed on the boundaries of the upper rectangular elastic plate and the lower rectangular elastic plate, and arbitrary boundary conditions are achieved by setting the stiffness coefficient of the spring. The three sound cavities from top to bottom are the first sound cavity (sound cavity 1), the second sound cavity (sound cavity 2) and the third sound cavity (sound cavity 3), with heights of h1, h2 and h3 respectively. The boundary conditions of the three sound cavities are all impedance boundary conditions, and their internal sound fields and boundary conditions can be expressed by the following formulas:

[0072]

[0073] Where p(x, y, z) is the sound pressure distribution function in the sound cavity, k is the driving wave number, k = ω / c, where ω and c are the angular frequency and the speed of sound, respectively. n and ρ in formula (1.10) are the outer normal direction of the boundary wall and the mass density of the propagation medium in the sound cavity, respectively. i represents the complex acoustic impedance of the i-th wall.

[0074] S2. The vibration displacement allowable function of the double-layer plate coupling system is established by using the improved Fourier series method, and the sound pressure allowable function of the closed sound cavity of the double-layer plate-sound cavity coupling system is established by using the improved Fourier series method;

[0075] The vibration displacement allowable function of the double-layer plate coupling system structural analysis model is expressed as:

[0076]

[0077] In the formula, The formula is:

[0078] ζ 1a (x p )=9asin(πx p / 2a) / 4π-asin(3πx p / 2a) / 12π(2.1a)

[0079] ζ 2a (x p )=-9acos(πx p / 2a) / 4π-acos(3πx p / 2a) / 12π(2.1b)

[0080] ζ 3a (x p )=a 3 sin(πx p / 2a) / π 3 -a 3 sin(3πx p / 2a) / 3π 3 (2.1c)

[0081] ζ 1a (x p )=-a 3 cos(πx p / 2a) / π 3 -a 3 cos(3πx p / 2a) / 3π 3 (2.1d)

[0082] The function forms of the double-layer plate structure and the three acoustic cavities in a double-layer plate-acoustic cavity coupling system with mechanical connection are also described by the two-dimensional improved Fourier series method and the three-dimensional improved Fourier series method respectively. For the bending vibration of the double-layer plate structure, the displacement function is expressed as:

[0083]

[0084] Among them, the supplementary function form refers to formula (2.1a) to formula (2.1d).

[0085] The first acoustic cavity and the third acoustic cavity are both acoustic cavities with one flexible wall and five rigid walls. According to the three-dimensional improved Fourier series, the sound field pressure of the first acoustic cavity and the third acoustic cavity are respectively expressed as:

[0086]

[0087] in,

[0088]

[0089] The expression of the complementary function is expressed as:

[0090] ξ 1h (z c1 )=z c1 (z c1 / h1-1) 2 (2.5)

[0091]

[0092] The second acoustic cavity is an acoustic cavity with two flexible walls and four rigid walls. The sound pressure of its sound field is expressed as:

[0093]

[0094] in, The expression of the supplementary function is:

[0095] ξ 1h (z c2 )=z c2 (z c2 / h2-1) 2 (2.8)

[0096]

[0097] S3. Analyze the plate-acoustic cavity coupling potential energy of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system by using the energy principle, and obtain the coupling energy functional of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system;

[0098] The energy principle is used to describe the motion equations of the double-layer plate coupling system structural analysis model and the double-layer plate-acoustic cavity coupling system. First, the motion equation of the coupling system is described, and its Lagrangian function is expressed as:

[0099] L p =U1-T1+U2-T2+U link -W ext +W cp (2.10)

[0100] Among them, U1 and U2 are the total potential energies of the upper rectangular elastic plate and the lower rectangular elastic plate, respectively, T1 and T2 are the total kinetic energies of the two plate structures, and U link is the elastic potential energy stored in the mechanical connection, W ext is the work done by the external excitation on the coupled system. W cpIt represents the work done by the sound pressure on the plate structure at the interface between the plate structure and the sound field inside the middle sound cavity. The schematic diagram of the external excitation distribution is Figure 3 .

[0101] The total potential energy and total kinetic energy of the plate structure are described by the following expressions:

[0102]

[0103] In the formula, is the bending stiffness of the plate structure, μ is Poisson’s ratio, ρ i is the density, δ i is the thickness of the plate, and are the lateral support spring stiffness coefficient and the rotational constraint spring stiffness coefficient on the edge. meaning.

[0104] The potential energy stored in the spring torque of the mechanical connection is:

[0105]

[0106] In the formula, k l is the translational stiffness of the mechanical connection spring, K lx and K ly are the rotational spring stiffness around the x-axis and the y-axis, respectively, (x l ,y l ) are the position coordinates of the mechanical connection and the double-layer board connection.

[0107] When the system is subjected to forced vibration, it can be assumed that there is a point force acting on the upper rectangular elastic plate (x e ,y e ). The work done by the point force on the double-layer plate system is expressed as:

[0108] W ext =F0w1(x e ,y e )(2.14)

[0109] Where F0 is the point force amplitude.

[0110] The Lagrangian function of the middle cavity is:

[0111] L c =U c -T c -W pc (2.15)

[0112] Among them, U c is the total potential energy of the vocal cavity, T c is the total kinetic energy of the vocal cavity, W pcIt represents the work done by the bending vibration of the plate structure on the sound field inside the middle sound cavity. Due to the conservation of energy, W pc =W cp , which is expressed by the following formula:

[0113]

[0114] The total potential energy and total kinetic energy of the vocal cavity can be expressed by the following formula:

[0115]

[0116] Among them, ρ0 and c0 are the density and sound speed of the sound transmission medium respectively.

[0117] S4. Using the Rayleigh-Ritz method to solve the coupling energy functional of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system, the acoustic vibration characteristics of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system are obtained;

[0118] After obtaining the energy equation of the coupled system, each energy equation is substituted into the Lagrangian function, and the Rayleigh-Ritz method is applied to obtain the partial derivatives of the Fourier coefficients in the Lagrangian equation, and the results are equal to zero. The linear algebraic equations for the double-layer plate coupled system can be obtained and written in matrix form:

[0119]

[0120] Where K1, K2, K c are the stiffness matrices of the upper rectangular elastic plate, the lower rectangular elastic plate and the acoustic cavity system, M1, M2, M c are the mass matrices of the upper rectangular elastic plate, the lower rectangular elastic plate and the acoustic cavity system respectively; C 11 , C 12 , C 21 , C 22 are the coupling matrix of the upper rectangular elastic plate, the lower rectangular elastic plate and the mechanical connection, C 1c , C 2c , C c1 , C c2 The coupling matrix F1 of the upper rectangular elastic plate, the lower rectangular elastic plate and the acoustic cavity system is the external load vector caused by the point force acting on the upper rectangular elastic plate. W1, P and W2 are vectors containing all unknown Fourier expansion coefficients in the field function of the double-layer plate system. Among them:

[0121]

[0122] The bending displacement and sound pressure of the double-layer plate system can be directly obtained by using the response coefficient vector solved by the equation. In addition, the modal characteristics of the double-layer plate system can be obtained by solving the eigenvalue problem of the matrix equation.

[0123] Next, the equation of motion of the double-layer plate-acoustic cavity coupling system is described:

[0124] L p =U1-T1+U2-T2+U link -W ext +W c1p +W c2p +W c3p (2.23)

[0125] Among them, U1 and U2 are the total potential energies of the upper rectangular elastic plate and the lower rectangular elastic plate, respectively; T1 and T2 are the total kinetic energy of the double-layer plate structure; U link is the elastic potential energy stored in the mechanical connection, W ext is the work done by the external excitation on the coupled system. W c1p , W c2p and W c3p They respectively represent the work done on the panel structure by the sound pressure at the interface between the panel structure and the sound field inside the first acoustic cavity, the second acoustic cavity and the third acoustic cavity.

[0126] At this time, the total potential energy and total kinetic energy of the double-layer plate structure are described by the following formula:

[0127]

[0128] In the formula, is the bending stiffness of the double-layer plate structure, μ is the Poisson’s ratio, and are the lateral support spring stiffness coefficient and the rotation constraint spring stiffness coefficient on the edge, and similarly, The meaning of ρ i is the material density of the double-layer plate, δ i is the thickness of the double-layer board.

[0129] The potential energy stored in the spring torque of the mechanical connection is:

[0130]

[0131] Where k l is the translational stiffness of the mechanical connection spring, K lx and K ly are the rotational stiffness around the x-axis and the y-axis respectively, (x l ,y l ) are the coordinates of the mechanical connection with the upper rectangular elastic plate and the lower rectangular elastic plate.

[0132] When the coupled system is disturbed by external noise, it can be assumed that at the point (x e ,y e ,ze ) is set up on the surface. The work done by the point sound source on the coupled system is expressed as:

[0133]

[0134] Where V is the volume of the first acoustic cavity, Q is the sound source intensity distribution function, and the specific form is described by the following formula:

[0135] Q=Q0δ(x-x0)δ(y-y0)δ(z-z0)(2.28)

[0136] Where Q0 is the velocity amplitude of the sound source, and δ is the three-dimensional Dirac function.

[0137] The Lagrangian function of the first cavity is:

[0138] L c1 =U c1 -T c1 -W pc1 (2.29)

[0139] Among them, U c1 is the total potential energy of the first cavity, T c1 is the total kinetic energy of the first cavity, W pc1 represents the work done by the bending vibration of the upper rectangular elastic plate on the sound field inside the first sound cavity. Due to the conservation of energy, W c1p =W pc1 , which is described by the following formula:

[0140]

[0141] The total potential energy and total kinetic energy of the first acoustic cavity can be described by the following formula:

[0142]

[0143] Wherein, ρ1 and c1 are density and sound velocity of the sound transmission medium in the first sound cavity respectively.

[0144] The Lagrangian function of the second cavity is:

[0145] L c2 =U c2 -T c2 -W pc2 (2.33)

[0146] Among them, U c2 is the total potential energy of the second cavity, T c2 is the total kinetic energy of the second cavity, W pc2 represents the work done by the bending vibration of the upper rectangular elastic plate and the lower rectangular elastic plate on the sound field inside the second sound cavity. Also due to the conservation of energy, W c2p =Wpc2 , which is described by the following formula:

[0147]

[0148] The total potential energy and total kinetic energy of the first acoustic cavity can be described by the following formula:

[0149]

[0150] Wherein, ρ2 and c3 are density and sound velocity of the sound transmission medium in the second sound cavity respectively.

[0151] The Lagrangian function of the third cavity is:

[0152] L c3 =U c3 -T c3 -W pc3 (2.37)

[0153] Among them, U c3 is the total potential energy of the third cavity, T c3 is the total kinetic energy of the third cavity, W pc3 W represents the work done by the bending vibration of the lower rectangular elastic plate on the sound field inside the third sound cavity. c3p =W pc3 , which is described by the following formula:

[0154]

[0155] The total potential energy and total kinetic energy of the third cavity can be described by the following formula:

[0156]

[0157] Among them, ρ3 and c3 are the density and sound speed of the sound transmission medium in the third acoustic cavity respectively.

[0158] After obtaining the energy equation of the double-layer plate-acoustic cavity coupling system, the energy equation is substituted into the Lagrangian function, and the Rayleigh-Ritz method is applied to find the partial derivative of the Fourier coefficient in the Lagrangian equation, and the result is set equal to zero. The linear algebraic equation system for the double-layer plate-acoustic cavity coupling system can be obtained and written in matrix form:

[0159] [K0-ω 2 M0]W0=Q0(2.41)

[0160]

[0161] W0=[P1 W1 P2 W2 P3]' (2.44)

[0162] Q0=[Q 0 0 0 0]' (2.45)

[0163] In the formula, K c1 , K c2 , K c3 , K p1 , K p2 are the stiffness matrices of the first acoustic cavity, the second acoustic cavity, the third acoustic cavity, the upper rectangular elastic plate, and the lower rectangular elastic plate, respectively. c1 , M c2 , M c3 , M p1 , M p2 are the mass matrices of the first acoustic cavity, the second acoustic cavity, the third acoustic cavity, the upper rectangular elastic plate, and the lower rectangular elastic plate respectively; C 11 , C 12 , C 21 , C 22 are the coupling matrix of the upper rectangular elastic plate, the lower rectangular elastic plate and the mechanical connection, C p1c1 , C c1p1 is the coupling matrix between the first acoustic cavity and the upper rectangular elastic plate, C p1c2 , C c2p1 is the coupling matrix between the second acoustic cavity and the upper rectangular elastic plate, C p2c2 , C c2p2 is the coupling matrix between the second acoustic cavity and the lower rectangular elastic plate, C p2c3 , C c3p2 is the coupling matrix between the third acoustic cavity and the lower rectangular elastic plate, Q0 is the external load vector caused by the point sound source arranged in the first acoustic cavity. P1, W1, P2, W2 and P3 are vectors of all unknown Fourier expansion coefficients in the field function of the coupling system. Where:

[0164]

[0165] According to the above steps, an acoustic-vibration coupling analysis method for a double-layer plate coupling system with mechanical connections is calculated.

[0166] S5, use the acoustic vibration characteristics obtained by S4 to verify the convergence and correctness of the model, analyze the influence of important parameters on the acoustic vibration characteristics, and analyze the steady-state response of the coupling system by introducing surface force, point sound source excitation and changing the connection mode of mechanical connection. Table 1 and Table 2 are the comparative verification of the calculation results of this method and the finite element algorithm.

[0167] Table 1. Natural frequencies of double-layer plate systems with arbitrary boundary conditions

[0168]

[0169] Table 2. Natural frequency of double-layer plate-acoustic cavity coupling system

[0170]

[0171] The steady-state response analysis of the double-layer plate coupling system is as follows:

[0172] The vibration response of the single-point mechanical connection coupling system at different positions under the excitation of the surface force. The magnitude of the surface force is 1N, and the direction of the force is perpendicular to the xy plane and downward, acting on the upper rectangular elastic plate of the coupling system, as shown in Figure 4 and Figure 5 As shown, Figure 4 Position 1(x l ,y l )=(0.08,0.1)m、Position 2(x l ,y l )=(0.17,0.2)m, position 3(x l ,y l )=(0.33,0.3)m, position 4(x l ,y l )=(0.42,0.2)m;

[0173] The vibration response of the coupled system with different numbers of mechanical connections under the excitation of the surface force. The magnitude of the surface force is 1N, and the direction of the force is perpendicular to the xy plane and downward, acting on the upper rectangular elastic plate of the coupled system, as shown in Figure 6 and Figure 7 As shown, Figure 6 The order is quantity 1, quantity 2, quantity 3, quantity 4;

[0174] The sound pressure response of the coupled system under the excitation of a point sound source. The sound source is set at (0.45, 0.36, 0.45) in the first sound cavity. The sound source intensity is Q = 2 × 10-5 m3 / s. Observation point 1 and observation point 2 are set in the first sound cavity and the third sound cavity, respectively, at positions (0.25, 0.2, 0.45) and (0.45, 0.36, 0.1). Figure 8 Shown

[0175] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing acoustic-vibration coupling of a mechanically connected double-layer plate coupling system, characterized in that: The steps include: S1. Establish a double-layer plate coupling system with mechanical connection and a double-layer plate-acoustic cavity coupling system with mechanical connection, and realize arbitrary boundary conditions of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system according to the simulated spring technology; S2. The vibration displacement allowable function of the double-layer plate coupling system is established by using the improved Fourier series method, and the sound pressure allowable function of the closed sound cavity of the double-layer plate-sound cavity coupling system is established by using the improved Fourier series method; S3. Analyze the plate-acoustic cavity coupling potential energy of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system by using the energy principle, and obtain the coupling energy functional of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system; S4. Using the Rayleigh-Ritz method to solve the coupling energy functional of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system, the acoustic vibration characteristics of the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system are obtained; S5. Use the acoustic-vibration characteristics obtained in S4 to verify the convergence and correctness of the model, analyze the influence of important parameters on the acoustic-vibration characteristics, and perform steady-state response analysis on the coupled system by introducing surface forces, point sound source excitations, and changing the connection method of mechanical connections.

2. The acoustic-vibration coupling analysis method of a double-layer plate coupling system with mechanical connection according to claim 1, characterized in that: The double-layer plate coupling system comprises an upper rectangular elastic plate and a lower rectangular elastic plate arranged in parallel, wherein the upper rectangular elastic plate and the lower rectangular elastic plate are connected with rigid walls on all sides; the upper rectangular elastic plate and the lower rectangular elastic plate are mechanically connected; The double-layer plate-acoustic cavity coupling system comprises an upper rectangular elastic plate and a lower rectangular elastic plate arranged in a rectangular shell, the upper rectangular elastic plate and the lower rectangular elastic plate are arranged in parallel, the edges of the upper rectangular elastic plate and the lower rectangular elastic plate are connected to the inner wall of the shell, the upper rectangular elastic plate and the lower rectangular elastic plate are mechanically connected, the upper rectangular elastic plate and the shell above it form a first acoustic cavity, the upper rectangular elastic plate, the lower rectangular elastic plate and the shell form a second acoustic cavity, and the lower rectangular elastic plate and the shell below it form a third acoustic cavity; The simulated spring technology is a lateral support spring and a rotational constraint spring uniformly distributed on the boundaries of the upper rectangular elastic plate and the lower rectangular elastic plate to simulate different boundary conditions of the bending vibration of the double-layer plate structure.

3. The acoustic-vibration coupling analysis method of a double-layer plate coupling system with mechanical connection according to claim 1, characterized in that: The vibration displacement allowable function is as follows: In the formula, The specific form of the supplementary function is: ζ 1a (x p )=9asin(πx p / 2a) / 4π-asin(3πx p / 2a) / 12π (2.1a) ζ 2a (x p )=-9acos(πx p / 2a) / 4π-acos(3πx p / 2a) / 12π (2.1b) g 3a (x p )=a 3 sin(πx p / 2a) / p 3 -a 3 sin(3πx p / 2a) / 3π 3 (2.1c) g 1a (x p )=-a 3 cos(πx p / 2a) / p 3 -a 3 cos(3πx p / 2a) / 3π 3 (2.1d) in, is the unknown expansion coefficient.

4. The acoustic-vibration coupling analysis method of a double-layer plate coupling system with mechanical connection according to claim 1, characterized in that: The permissible function of the sound pressure in the closed acoustic cavity is as follows: The sound pressure of the sound field in the first sound cavity and the third sound cavity are expressed as: in, The expression of the complementary function is expressed as: ξ 1h (With c1 )=z c1 (With c1 / h1-1) 2 (2.5) The second acoustic cavity is an acoustic cavity with two flexible walls and four rigid walls. The sound pressure of its sound field is expressed as: in, The expression of the supplementary function is: ξ 1h (z c2 )=z c2 (z c2 / h2-1) 2 (2.8) in, is the unknown expansion coefficient.

5. The acoustic-vibration coupling analysis method of a double-layer plate coupling system with mechanical connection according to claim 2, characterized in that: In S4, the total energy functional includes the total potential energy of the upper rectangular elastic plate and the lower rectangular elastic plate, the total kinetic energy of the upper rectangular elastic plate and the lower rectangular elastic plate, the elastic potential energy stored in the mechanical connection, the work done by external excitation on the double-layer plate coupling system and the double-layer plate-acoustic cavity coupling system, and the work done on the plate structure by the sound pressure at the interface between the upper rectangular elastic plate and the lower rectangular elastic plate and the internal sound field of the first acoustic cavity, the second acoustic cavity and the third acoustic cavity in the double-layer plate-acoustic cavity coupling system.

6. The acoustic-vibration coupling analysis method of a double-layer plate coupling system with mechanical connection according to claim 1, characterized in that: The process of obtaining the acoustic vibration characteristics comprises the following steps: S41, taking partial derivatives of the expansion coefficients in the total energy functional and setting the result equal to zero, obtaining the overall mass matrix and stiffness matrix of the coupled system, and then obtaining the acoustic vibration characteristic equation of the coupled system; S42. Solve the acoustic-vibration characteristic equation to obtain the acoustic-vibration characteristics of the coupled system.

7. The acoustic-vibration coupling analysis method of a double-layer plate coupling system with mechanical connection according to claim 1, characterized in that: The steady-state response analysis method is: substituting the surface force and the point sound source into the acoustic vibration characteristics to obtain the steady-state response.

8. A storage medium, characterized in that: The storage medium includes a stored program, wherein when the program is run, the acoustic-vibration coupling analysis method of the double-layer plate coupling system with mechanical connection according to any one of claims 1 to 7 is executed.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: The processor executes the acoustic-vibration coupling analysis method for a double-layer plate coupling system with mechanical connection according to any one of claims 1 to 7 by running the computer program.

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