Method and system for determining vibration of beam structure containing acoustic black hole damping layer

Abstract

The invention belongs to the related technical field of ship vibration and noise reduction, and discloses a method and system for determining vibration of a beam structure containing an acoustic black hole damping layer. The method comprises the following steps that S1, for a beam structure attached with an acoustic black hole damping layer in a ship, a coupling system comprising a uniform beam and the acoustic black hole damping layer is selected as a research object, the research object is simplified into two layers of beams which are connected in a coupling mode, and material attributes and section forms of the two layers of beams are different; s2, constructing a motion control equation of the coupling system; and S3, solving the motion control equation of the coupling system, and respectively obtaining the inherent frequency of the coupling system under free vibration and the vibration response of the coupling system under external excitation. According to the invention, the problems of low efficiency and poor economical efficiency of rapid prediction of the inherent frequency and the vibration response of the beam structure containing the acoustic black hole damping layer are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to ship vibration reduction and noise reduction, and more specifically, relates to a method and system for determining the vibration of a beam structure containing an acoustic black hole damping layer. Background Art

[0002] The essence of ship vibration and sound radiation comes from the propagation of elastic waves in the ship structure and the mutual coupling with the surrounding sound media such as air and water. Regulating the propagation of elastic waves in the ship structure is of great significance for vibration and noise reduction. Traditional vibration and noise reduction methods such as vibration absorption, vibration isolation, damping and vibration resistance play an important role in suppressing and regulating elastic waves to achieve ship vibration and noise reduction. However, among these methods, vibration absorption is only effective for line spectrum noise, vibration isolation has a high cost, and is limited by overall weight, space size and material properties. Traditional damping and vibration resistance methods are only applicable to medium and high frequency bands.

[0003] As a lightweight and high-damping structure, the acoustic black hole damping layer has the advantages of strong designability and wide vibration suppression frequency band, which provides new ideas for theoretical and technical breakthroughs in ship vibration and noise reduction, and provides a good reference for breaking through the problem of wide-band noise control of ships. However, for the beam structure of the ship with an acoustic black hole damping layer attached, the modeling and calculation using numerical methods have the disadvantages of low efficiency and poor economy.

[0004] Therefore, it is urgent to propose an equivalent and reasonable acoustic vibration theoretical model and calculation method to quickly predict the natural frequency and vibration response of the beam structure containing the acoustic black hole damping layer, so as to provide theoretical support for the use of acoustic black holes in vibration and noise reduction of ship structures. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a method and system for determining the vibration of a beam structure containing an acoustic black hole damping layer, which aims to solve the technical problems of low efficiency and poor economy in rapid prediction of the natural frequency and vibration response of the beam structure containing an acoustic black hole damping layer.

[0006] To achieve the above object, according to one aspect of the present invention, a method for determining the vibration of a beam structure containing an acoustic black hole damping layer is provided, the method comprising the following steps:

[0007] S1. For a beam structure with an acoustic black hole damping layer attached in a ship, a coupled system including a uniform beam and the acoustic black hole damping layer is selected as a research object, and the research object is simplified into a two-layer beam coupled and connected, and the material properties and cross-sectional forms of the two-layer beams are different;

[0008] S2. Construct the vibration control equations of the two layers of beams, the uniform beam and the acoustic black hole damping layer, and set the coupling constraint conditions between the two layers of beams to construct the motion control equations of the coupling system;

[0009] S3. Solve the motion control equation of the coupling system to obtain the natural frequency of the coupling system under free vibration and the vibration response of the coupling system under external excitation.

[0010] Preferably, step S2 specifically includes the following steps:

[0011] S21. Based on the Timoshenko beam theory, the displacement functions of the uniform beam and the acoustic black hole damping layer are obtained, and the kinetic energy and potential energy of the uniform beam and the acoustic black hole damping layer are obtained. Based on the Hamilton principle and the kinetic energy and potential energy, the vibration control equations of the uniform beam and the acoustic black hole damping layer are established.

[0012] S22. Based on the Layerwise layered theory, the continuity characteristics of the in-plane displacement and vertical displacement of the uniform beam and the acoustic black hole damping layer at the coupling position are considered, and the coupling constraints of the uniform beam and the acoustic black hole damping layer are set; combined with the coupling constraints, the vibration control equations of the uniform beam and the acoustic black hole damping layer in S21 are coupled through the virtual spring method to obtain the motion control equation of the coupling system.

[0013] Preferably, in step S21, the displacement function calculation formula of the uniform beam and the acoustic black hole damping layer is as follows:

[0014] Uniform beam:

[0015] Acoustic Black Hole Damping:

[0016] Among them, u1 and u2 are the in-plane displacements of the uniform beam and the acoustic black hole damping layer, respectively, and u 01 (x) and u 02 (x) is the neutral plane displacement of the uniform beam and the acoustic black hole damper, w1 and w2 are the vertical displacements of the uniform beam and the acoustic black hole damper, θ1(x) and θ2(x) are the rotation angles of the uniform beam and the acoustic black hole damper around the neutral axis, t is the time, x is the axial coordinate of the coupled system, z is the vertical coordinate of the coupled system, and is the displacement shape function vector of the uniform beam, and is the displacement shape function vector of acoustic black hole damping, a 11 ,a 21 and a 31 For the corresponding and The unknown coefficient, a 12 ,a 22 and a 32 For the corresponding and The undetermined coefficient.

[0017] Preferably, in step S21, the vibration control equation of the uniform beam and the acoustic black hole damping layer is:

[0018]

[0019] Among them, the stiffness matrix coefficient K is the matrix K1 and K2 arranged diagonally according to the block matrix principle. The matrices K1 and K2 are the stiffness matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively; the mass matrix coefficient M is the matrix M1 and M2 arranged diagonally according to the block matrix principle. The matrices M1 and M2 are the mass matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively; A is the displacement amplitude coefficient, the matrices A1 and A2 are the amplitude vector matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively, ω is the circular frequency, and F is the amplitude vector corresponding to the external force.

[0020] Preferably, in step S22, the coupling constraint condition between the uniform beam and the acoustic black hole damping layer is:

[0021]

[0022] Among them, h u is the thickness of the uniform beam, h a is the maximum thickness of the acoustic black hole damping layer, u 01 (x) and u 02 (x) is the in-plane displacement of the neutral surface of the uniform beam and the acoustic black hole damper, w1 and w2 are the vertical displacements of the uniform beam and the acoustic black hole damper, respectively.

[0023] Preferably, in step S22, the continuity characteristic is that the in-plane displacement and the vertical displacement of the uniform beam and the acoustic black hole damping layer at the coupling position are equal.

[0024] Preferably, in step S22, the motion control equation of the coupling system is:

[0025]

[0026] in, is the stiffness matrix of the coupled system.

[0027] Preferably, in step S3, when solving the natural frequency of the coupling system, the amplitude vector F of the external force is set to be a zero vector, and the determinant of the coefficient matrix of the motion control equation of the coupling system is obtained by: The circular frequency ω is zero, and then the natural frequency f of the coupling system is obtained according to the formula ω=2πf.

[0028] Preferably, in step S3, the vibration response of the coupled system under external excitation is solved by applying the external excitation to the coupled system to update the motion control equation of the coupled system, and the determinant of the coefficient matrix is ​​obtained. The displacement amplitude coefficient A in the motion control equation of the coupling system is obtained by inverting and left-multiplying the amplitude vector F corresponding to the external force, and then the vibration response of the coupling system is obtained.

[0029] According to another aspect of the present invention, a system for determining the vibration of a beam structure containing an acoustic black hole damping layer is provided. The system includes a processor for executing the above-mentioned method for determining the vibration of a beam structure containing an acoustic black hole damping layer.

[0030] In general, the above technical solution conceived by the present invention has the following beneficial effects compared with the prior art:

[0031] 1. In the present invention, the coupling system including the uniform beam and the acoustic black hole damping layer is firstly equivalent to a two-layer beam connected by coupling; then the motion control equation of the coupling system is constructed; finally, the natural frequency and vibration response of the coupling system are solved; the vibration characteristics of the beam structure containing the acoustic black hole damping layer can be effectively solved, providing a theoretical basis for the application of acoustic black holes in vibration and noise reduction of ship structures, and compared with the existing numerical methods, it has better efficiency and economic benefits;

[0032] 2. The present invention uses the continuity of the in-plane displacement and vertical displacement of the uniform beam and the acoustic black hole damping layer at the connection surface, fully considering the influence of the shear characteristics between the two-layer beam structure, which is more in line with the actual application scenario and meets the actual application situation;

[0033] 3. The present invention performs theoretical modeling and computational analysis on the beam structure containing the acoustic black hole damping layer. By changing the uniform beam and the acoustic black hole damping parameters, the vibration characteristics of the beam structures with different acoustic black hole damping layers can be obtained. Compared with the numerical method, the modeling efficiency and the computational efficiency are significantly improved.

[0034] 4. The present invention obtains the natural frequency of the coupling system and the vibration response under different excitations, and the results are in good agreement with the calculation results of the finite element software; by quickly predicting the vibration characteristics of the coupling system, the theoretical system of the vibration of the beam structure containing the acoustic black hole damping layer is further improved, providing theoretical support for the use of acoustic black holes for vibration and noise reduction of ship structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flow chart of a method for determining vibration of a beam structure containing an acoustic black hole damping layer constructed according to a preferred embodiment of the present invention;

[0036] Figure 2is a schematic diagram of a beam structure model including an acoustic black hole damping layer constructed according to a preferred embodiment of the present invention;

[0037] Figure 3 It is a coordinate system and parameter diagram of an equivalent beam structure containing an acoustic black hole damping layer constructed according to a preferred embodiment of the present invention.

[0038] Figure 4 It is a comparison diagram of the results of the determination method of the beam structure containing the acoustic black hole damping layer constructed according to the preferred embodiment of the present invention and the finite element method.

[0039] Figure 5 It is a comparison diagram of the mean square vibration velocity of a beam structure containing an acoustic black hole damping layer and a beam structure containing a uniform damping layer constructed according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0041] like Figure 1 As shown, the present invention provides a method for determining the vibration of a beam structure containing an acoustic black hole damping layer, which comprises the following steps:

[0042] S1. For the beam structure with an acoustic black hole damping layer attached in the ship, a coupling system including a uniform beam and the acoustic black hole damping layer is selected as the research object, and the research object is simplified into a two-layer beam coupled and connected, and the material properties and cross-sectional forms of the two-layer beam are different; the research object is simplified and modeled, and the equivalent model is as follows Figure 2 As shown, a structural coordinate system is established on the equivalent model. The coordinate system and structural parameters are shown in Figure 3 As shown; the origins of the coordinate system O1 and O2 are established at the center of each layer of the beam structure, where the coordinates z1 and z2 represent the thickness directions of the uniform beam and the acoustic black hole damping layer, respectively, the coordinate x represents the axial coordinate of the coupling system, L0 is the length of the uniform beam, and h u is the thickness of the uniform beam, h a is the maximum thickness of the acoustic black hole damping layer, h0 is the cutoff thickness of the acoustic black hole damping layer, h(x) is the thickness variation function of the acoustic black hole, and R is the radius of the acoustic black hole.

[0043] S2. Construct the vibration control equations of the two layers of beams, the uniform beam and the acoustic black hole damping layer, and set the coupling constraint conditions between the two layers of beams to construct the motion control equations of the coupling system;

[0044] S21. Based on the Timoshenko beam theory, the displacement functions of the uniform beam and the acoustic black hole damping layer are obtained, and the kinetic energy and potential energy of the uniform beam and the acoustic black hole damping layer are obtained. Based on the Hamilton principle and the kinetic energy and potential energy, the vibration control equations of the uniform beam and the acoustic black hole damping layer are established.

[0045] The displacement function calculation formula of uniform beam and acoustic black hole damping layer is as follows:

[0046]

[0047] Where u1 and u2 are the in-plane displacements of the uniform beam and the acoustic black hole damping layer, respectively, and u 01 (x) and u 02 (x) is the neutral plane displacement of the uniform beam and the acoustic black hole damper, w1 and w2 are the vertical displacements of the uniform beam and the acoustic black hole damper, θ1(x) and θ2(x) are the rotation angles of the uniform beam and the acoustic black hole damper around the neutral axis, t is the time, x is the axial coordinate of the coupled system, z is the vertical coordinate of the coupled system, and is the displacement shape function vector of the uniform beam, and is the displacement shape function vector of acoustic black hole damping, a 11 ,a 21 and a 31 It corresponds to and The unknown coefficient, a 12 ,a 22 and a 32 It corresponds to and The unknown coefficients can be written in the form of exponential functions, such as a 11 (t) = A 11 e iωt , A 11 is the coefficient a 11 is the magnitude vector of , i is the imaginary unit, and ω is the circular frequency.

[0048] The displacement shape function vector in formula (1) and Each element in can be described by a Gaussian function, and the displacement shape function vector expression is as follows:

[0049]

[0050] Among them, exp represents the exponential function form, j represents the scaling factor, and k represents the translation factor. By changing the values ​​of j and k, the original Gaussian function can be scaled and translated, thereby constructing a series of Gaussian shape functions to form a displacement shape function vector.

[0051] Combining the displacement function expression in formula (1) and the displacement shape function vector expression in formula (2), the kinetic energy T of the uniform beam and the acoustic black hole damping layer is solved. n :

[0052]

[0053] in is the combination coefficient, Indicates a n Taking the derivative with respect to time, ρ n , b n and h n (x) are the density, width and thickness of the beam, M n is the mass matrix of each layer of beams, the subscript n represents the type of beam, n = 1 indicates a uniform beam, n = 2 indicates an acoustic black hole damping layer, and y is the coordinate along the width of the coupled system;

[0054] Combined with the displacement function expression in formula (1) and the displacement shape function vector expression in formula (2), the potential energy V of the uniform beam and acoustic black hole damping layer is solved: n :

[0055]

[0056] in is the first derivative of the displacement shape function along the x direction, the complex Young's modulus E n is the Young's modulus of the material, η n is the loss factor, i is the imaginary unit, ν n is the material Poisson’s ratio, K n is the stiffness matrix of each layer of beams.

[0057] If the uniform beam is at position x = x f If the position is subjected to an external excitation of magnitude f1, the external work W is:

[0058] W=f1w1(x f )=a T F (5)

[0059] The superscript "T" indicates the matrix transpose; F is the amplitude vector corresponding to the external force; the displacement coefficient vector of the coupled system

[0060] Based on Hamilton's principle, the kinetic energy, potential energy and external work expressed by formulas (3)-(5) are substituted into the Lagrange equation:

[0061]

[0062] Among them, the Lagrangian operator L = T n -V n +W is represented by kinetic energy, potential energy and external work. By rearranging formula (6), the vibration control equations of the uniform beam and the acoustic black hole damping layer can be established respectively:

[0063] (K-ω 2 M)A=F (7)

[0064]

[0065]

[0066] Among them, the stiffness matrix coefficient K is the matrix K1 and K2 arranged diagonally according to the block matrix principle. The matrices K1 and K2 are the stiffness matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively; the mass matrix coefficient M is the matrix M1 and M2 arranged diagonally according to the block matrix principle. The matrices M1 and M2 are the mass matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively; A is the displacement amplitude coefficient, the matrices A1 and A2 are the amplitude vector matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively, ω is the circular frequency, and F is the amplitude vector corresponding to the external force.

[0067] S22. Based on the Layerwise layered theory, the continuity characteristics of the in-plane displacement and vertical displacement of the uniform beam and the acoustic black hole damping layer at the coupling position are considered, and the coupling constraints of the uniform beam and the acoustic black hole damping layer are set; combined with the coupling constraints, the vibration control equations of the uniform beam and the acoustic black hole damping layer are coupled through the virtual spring method to obtain the motion control equation of the beam structure of the coupling system.

[0068] Among them, the displacement continuity characteristic of the uniform beam and the acoustic black hole damping layer is that at the coupling position of the connection surface between the two, the in-plane displacement and vertical displacement of the uniform beam and the acoustic black hole damping layer on the connection surface are equal. On this basis, the coupling constraint condition of the uniform beam and the acoustic black hole damping layer is:

[0069]

[0070] Among them, h u represents the thickness of the uniform beam, h a Represents the maximum thickness of the acoustic black hole damping layer.

[0071] According to Hooke's law, the coupling constraint condition of the uniform beam and the acoustic black hole damping layer expressed in formula (8) is converted into the elastic potential energy of the virtual spring according to the following relationship:

[0072]

[0073] Among them, E cis the elastic potential energy corresponding to the virtual spring at the connection between the uniform beam and the acoustic black hole damping layer, k s1 and k s2 is the stiffness coefficient of the virtual spring, L c is the axial coordinate interval corresponding to the connection between the uniform beam and the acoustic black hole damping layer, K c is the stiffness matrix corresponding to the connection between the uniform beam and the acoustic black hole damping layer. According to formula (9), the Lagrangian operator L in formula (6) is updated to L = T n -V n -E c +W. By bringing the Lagrangian operator that takes into account the coupling constraints back into the Langrange equation (6), we can obtain the motion control equation of the coupled system:

[0074]

[0075] in, is the stiffness matrix of the coupled system after considering the coupling conditions of the uniform beam and the acoustic black hole damping layer, The calculation formula is:

[0076]

[0077] S3. Solve the motion control equations of the coupled system to obtain the natural frequency of the coupled system under free vibration and the vibration response of the coupled system under external excitation:

[0078] (1) Under free vibration, according to the motion control equation of the coupled system, the amplitude vector F of the external force is set to zero vector, and the determinant of the coefficient matrix is ​​solved. The circular frequency ω is zero, and then the natural frequency f of the coupling system is obtained according to the formula ω=2πf.

[0079] (2) When subjected to external excitation, the motion control equations of the coupled system are updated by using the determinant of the coefficient matrix The displacement amplitude coefficient A in the motion control equation of the coupling system is obtained by inverting and left-multiplying the amplitude vector F corresponding to the external force, and then the vibration response of the coupling system is obtained.

[0080] In the preferred solution provided by the embodiment of the present invention, the effectiveness of the coupling system model determination method established is verified by simulation, and the results are as follows: Figure 4 As shown, it can be concluded that the method proposed in the present invention is in good agreement with the finite element method, which verifies the effectiveness of the method for determining the vibration of the beam structure containing the acoustic black hole damping layer proposed in the present invention. The structural geometric parameters and material parameters used in the simulation verification are shown in Table 1.

[0081] Table 1 Geometric parameters and material parameters

[0082]

[0083] Furthermore, the vibration levels of the beam structure with acoustic black hole damping and the beam structure with uniform thickness damping are compared, e.g. Figure 5 As shown, it can be concluded that the vibration level of the beam structure containing acoustic black hole damping is significantly lower than that of the beam structure containing uniform thickness damping, which verifies that the beam structure containing the acoustic black hole damping layer proposed in the present invention has better vibration reduction and noise reduction effects.

[0084] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for determining the vibration of a beam structure containing an acoustic black hole damping layer, characterized in that: The method comprises the following steps: S1. For a beam structure with an acoustic black hole damping layer attached in a ship, a coupled system including a uniform beam and the acoustic black hole damping layer is selected as a research object, and the research object is simplified into a two-layer beam coupled and connected, and the material properties and cross-sectional forms of the two-layer beams are different; S2. Construct the vibration control equations of the two layers of beams, the uniform beam and the acoustic black hole damping layer, and set the coupling constraint conditions between the two layers of beams to construct the motion control equations of the coupling system; S3. Solve the motion control equation of the coupling system to obtain the natural frequency of the coupling system under free vibration and the vibration response of the coupling system under external excitation.

2. A method for determining the vibration of a beam structure containing an acoustic black hole damping layer as claimed in claim 1, characterized in that: Step S2 specifically includes the following steps: S21. Based on the Timoshenko beam theory, the displacement functions of the uniform beam and the acoustic black hole damping layer are obtained, and the kinetic energy and potential energy of the uniform beam and the acoustic black hole damping layer are obtained. Based on the Hamilton principle and the kinetic energy and potential energy, the vibration control equations of the uniform beam and the acoustic black hole damping layer are established. S22. Based on the Layerwise layered theory, the continuity characteristics of the in-plane displacement and vertical displacement of the uniform beam and the acoustic black hole damping layer at the coupling position are considered, and the coupling constraints of the uniform beam and the acoustic black hole damping layer are set; combined with the coupling constraints, the vibration control equations of the uniform beam and the acoustic black hole damping layer in S21 are coupled through the virtual spring method to obtain the motion control equation of the coupling system.

3. A method for determining the vibration of a beam structure containing an acoustic black hole damping layer as claimed in claim 2, characterized in that: In step S21, the displacement function calculation formula of the uniform beam and the acoustic black hole damping layer is as follows: Uniform beam: Acoustic Black Hole Damping: Among them, u1 and u2 are the in-plane displacements of the uniform beam and the acoustic black hole damping layer, respectively, and u 01 (x) and u 02 (x) is the neutral plane displacement of the uniform beam and the acoustic black hole damper, w1 and w2 are the vertical displacements of the uniform beam and the acoustic black hole damper, θ1(x) and θ2(x) are the rotation angles of the uniform beam and the acoustic black hole damper around the neutral axis, t is the time, x is the axial coordinate of the coupled system, z is the vertical coordinate of the coupled system, and is the displacement shape function vector of the uniform beam, and is the displacement shape function vector of acoustic black hole damping, a 11 ,a 21 and a 31 For the corresponding and The undetermined coefficient, a 12 ,a 22 and a 32 For the corresponding and The undetermined coefficient of .

4. The method for determining the vibration of a beam structure containing an acoustic black hole damping layer according to claim 2, characterized in that: In step S21, the vibration control equation of the uniform beam and the acoustic black hole damping layer is: (K-oh 2 M)A=F Among them, the stiffness matrix coefficient K is the matrix K1 and K2 arranged diagonally according to the block matrix principle. The matrices K1 and K2 are the stiffness matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively; the mass matrix coefficient M is the matrix M1 and M2 arranged diagonally according to the block matrix principle. The matrices M1 and M2 are the mass matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively; A is the displacement amplitude coefficient, the matrices A1 and A2 are the amplitude vector matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively, ω is the circular frequency, and F is the amplitude vector corresponding to the external force.

5. The method for determining the vibration of a beam structure containing an acoustic black hole damping layer according to claim 2, characterized in that: In step S22, the coupling constraint condition between the uniform beam and the acoustic black hole damping layer is: Among them, h u is the thickness of the uniform beam, h a is the maximum thickness of the acoustic black hole damping layer, u 01 (x) and u 02 (x) is the in-plane displacement of the neutral surface of the uniform beam and the acoustic black hole damper, w1 and w2 are the vertical displacements of the uniform beam and the acoustic black hole damper, respectively.

6. A method for determining the vibration of a beam structure containing an acoustic black hole damping layer as claimed in claim 2, characterized in that: In step S22, the continuity characteristic is that the in-plane displacement and the vertical displacement of the uniform beam and the acoustic black hole damping layer at the coupling position are equal.

7. The method for calculating the vibration of a beam structure containing an acoustic black hole damping layer according to claim 4, characterized in that: In step S22, the motion control equation of the coupling system is: in, is the stiffness matrix of the coupled system.

8. A method for determining the vibration of a beam structure containing an acoustic black hole damping layer as claimed in claim 7, characterized in that: In step S3, when solving the natural frequency of the coupling system, the amplitude vector F of the external force is set to be a zero vector, and the determinant of the coefficient matrix of the motion control equation of the coupling system is obtained by The circular frequency ω is zero, and then the natural frequency f of the coupling system is obtained according to the formula ω=2πf.

9. A method for determining the vibration of a beam structure containing an acoustic black hole damping layer according to claim 7, characterized in that: In step S3, the vibration response of the coupled system under external excitation is solved by applying the external excitation to the coupled system to update the motion control equation of the coupled system, and the determinant of the coefficient matrix is ​​used to obtain the vibration response of the coupled system under external excitation. The displacement amplitude coefficient A in the motion control equation of the coupling system is obtained by inverting and left-multiplying the amplitude vector F corresponding to the external force, and then the vibration response of the coupling system is obtained.

10. A beam structure vibration system containing an acoustic black hole damping layer, characterized in that: The system includes a processor, which is used to execute the method for determining the vibration of a beam structure containing an acoustic black hole damping layer as described in any one of claims 1-9.

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