A method and system for determining the vibration of a beam structure containing an acoustic black hole damping layer

Abstract

The present application belongs to the technical field of ship vibration and noise reduction, and discloses a method and system for determining the vibration of a beam structure containing an acoustic black hole damping layer. The method includes the following steps: S1. For a beam structure in a ship with an acoustic black hole damping layer attached, a coupled system containing a uniform beam and the acoustic black hole damping layer is selected as the research object, and the research object is simplified as two-layer beams coupled, with different material properties and cross-sectional forms; S2. Construct the motion control equation of the coupled system; S3. Solve the motion control equation 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, respectively. Through the present application, the problem of low efficiency and poor economy in quickly predicting the natural frequency and vibration response of the beam structure containing the acoustic black hole damping layer is solved.

Description

Technical Field

[0001] This invention belongs to the technical field of 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 Technology

[0002] Ship vibration and sound radiation originate from the propagation of elastic waves within the ship's structure and their coupling with surrounding acoustic media such as air and water. Regulating the propagation of elastic waves within the ship's structure is crucial for vibration reduction and noise control. Traditional vibration absorption, isolation, damping, and damping methods have played a significant role in suppressing and regulating elastic waves to achieve ship vibration reduction and noise control. However, among these methods, vibration absorption is only effective against line spectrum noise, isolation is costly, and is limited by factors such as overall weight, spatial dimensions, and material properties. Traditional damping and damping methods are only applicable to the mid-to-high frequency bands.

[0003] Acoustic black hole damping layers, as a lightweight, high-damping structural form, offer advantages such as strong design flexibility and a wide vibration suppression frequency band, providing new ideas for theoretical and technological breakthroughs in ship vibration reduction and noise control, and offering valuable insights for overcoming the challenge of broadband noise control in ships. However, for beam structures with acoustic black hole damping layers attached to ships, numerical methods for modeling and calculation suffer from disadvantages such as low efficiency and poor economic performance.

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

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method and system for determining the vibration of a beam structure with an acoustic black hole damping layer. The purpose is to solve the technical problems of low efficiency and poor economy in the rapid prediction of the natural frequency and vibration response of a beam structure with an acoustic black hole damping layer.

[0006] To achieve the above objectives, 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 beam structures in ships with acoustic black hole damping layers attached, a coupled system containing a uniform beam and the acoustic black hole damping layer is selected as the research object. This research object is simplified to two coupled beams with different material properties and cross-sectional shapes.

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

[0009] S3. Solve the motion control equations of the coupled system to obtain the natural frequencies of the coupled system under free vibration and the vibration response of the coupled system under external excitation.

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

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

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

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

[0014] Uniform beam:

[0015] Acoustic black hole damping:

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

[0017] Preferably, in step S21, the vibration control equations for the uniform beam and the acoustic black hole damping layer are:

[0018]

[0019] Wherein, the stiffness matrix coefficient K is the diagonal arrangement of matrices K1 and K2 according to the principle of block matrix, and 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 diagonal arrangement of matrices M1 and M2 according to the principle of block matrix, and 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, and 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 angular 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 For the thickness of a uniform beam, h a For the maximum thickness of the damping layer of an acoustic black hole, u 01 (x) and u 02 (x) represents the in-plane displacement of the neutral plane of the uniform beam and the acoustic black hole damping, respectively, and w1 and w2 represent the vertical displacement of the uniform beam and the acoustic black hole damping, respectively.

[0023] Preferably, in step S22, the continuity characteristic is that the in-plane displacement and 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 coupled system is:

[0025]

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

[0027] Preferably, in step S3, when solving for the natural frequency of the coupled system, the amplitude vector F of the external force is set to zero, and the determinant of the coefficient matrix of the motion control equation of the coupled system is obtained by... The angular frequency ω is obtained by setting it to zero, and then the natural frequency f of the coupled system is obtained by using the formula ω = 2πf.

[0028] Preferably, in step S3, solving the vibration response of the coupled system under external excitation is done by applying the external excitation to the coupled system, thereby updating the motion control equations of the coupled system, and then solving the problem using the determinant of the coefficient matrix. The displacement amplitude coefficient A in the motion control equation of the coupled system is obtained by inverting the value of the system and left-multiplying it with the amplitude vector F corresponding to the external force, and then the vibration response of the coupled system is obtained.

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

[0030] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0031] 1. In this invention, the coupled system containing a uniform beam and an acoustic black hole damping layer is first equivalent to two coupled beams; then, the motion control equations of the coupled system are constructed; finally, the natural frequencies and vibration responses of the coupled system are solved; this can effectively solve the vibration characteristics of beam structures containing acoustic black hole damping layers, providing a theoretical basis for the application of acoustic black holes in vibration reduction and noise reduction of ship structures, and has better efficiency and economic benefits compared with existing numerical methods;

[0032] 2. In this invention, the continuous in-plane and vertical displacements of the uniform beam and the acoustic black hole damping layer at the connection surface are utilized, which fully considers the influence of the shear characteristics between the two beam structures, making it more in line with actual application scenarios and practical application conditions.

[0033] 3. This invention provides theoretical modeling and computational analysis of beam structures with acoustic black hole damping layers. By changing the uniform beam and the acoustic black hole damping parameters, the vibration characteristics of beam structures with different acoustic black hole damping layers can be obtained. Compared with numerical methods, both modeling efficiency and computational efficiency are significantly improved.

[0034] 4. This invention obtains the natural frequency and vibration response of the coupled system under different excitations, and the results are in good agreement with the calculation results of finite element software. By rapidly predicting the vibration characteristics of the coupled system, the theoretical system of beam structure vibration containing acoustic black hole damping layer is further improved, providing theoretical support for the application of acoustic black holes in vibration reduction and noise reduction of ship structures. Attached Figure Description

[0035] Figure 1 This is a flowchart of a method for determining the vibration of a beam structure with an acoustic black hole damping layer, constructed according to a preferred embodiment of the present invention.

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

[0037] Figure 3 This is a schematic diagram of the coordinate system and parameters 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 This is a comparison diagram of the determination method of the beam structure with acoustic black hole damping layer constructed according to the preferred embodiment of the present invention and the results of the finite element method.

[0039] Figure 5 This is a comparison diagram of the mean square vibration velocities of a beam structure with an acoustic black hole damping layer constructed according to a preferred embodiment of the present invention and a beam structure with a uniform damping layer. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this 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 includes the following steps:

[0042] S1. For beam structures in ships with acoustic black hole damping layers, a coupled system comprising a uniform beam and the acoustic black hole damping layer is selected as the research object. This research object is simplified into two coupled beams with different material properties and cross-sectional shapes. A simplified model of this research object is performed, and the equivalent model is as follows: Figure 2 As shown, a structural coordinate system is established on the equivalent model, and the coordinate system and structural parameters are as follows. Figure 3 As shown; establish coordinate system origins O1 and O2 at the center of each layer of beam structure, where coordinates z1 and z2 represent the thickness directions of the uniform beam and the acoustic black hole damping layer, respectively, coordinate x represents the axial coordinate of the coupled system, L0 is the length of the uniform beam, and h u For the thickness of a uniform beam, h a Let h be the maximum thickness of the acoustic black hole damping layer, h0 be the cut-off thickness of the acoustic black hole damping layer, h(x) be the thickness variation function of the acoustic black hole, and R be the radius of the acoustic black hole.

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

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

[0045] The displacement function calculation formulas for a uniform beam and an acoustic black hole damping layer are 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, u 01 (x) and u 02 θ(x) represents the in-plane displacement of the uniform beam and the acoustic black hole damping at the neutral plane, respectively; w1 and w2 represent the vertical displacement of the uniform beam and the acoustic black hole damping, respectively; θ1(x) and θ2(x) represent the rotation angles of the uniform beam and the acoustic black hole damping about the neutral axis, respectively; t represents time; x represents the axial coordinate of the coupled system; and z represents the vertical coordinate of the coupled system. and It is the displacement shape function vector of a uniform beam. and It is the displacement shape function vector of the acoustic black hole damping, a 11 ,a 21 and a 31 It corresponds and The undetermined coefficients, a 12 ,a 22 and a 32 It corresponds and The undetermined coefficients can be expressed as an exponential function, such as a. 11 (t)=A 11 e iωt A 11 It is the coefficient a 11 The amplitude vector, where i is the imaginary unit and ω is the angular frequency.

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

[0049]

[0050] Here, 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 functions to form a displacement 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 It is the combination coefficient. Indicates a n Differentiate ρ with respect to time n b n and h n (x) represents the density, width, and thickness of the beam, respectively, M. n Let n be the mass matrix of each beam layer, where the subscript n represents the type of beam. When n is 1, it represents a uniform beam, and when n is 2, it represents an acoustic black hole damping layer. y is the coordinate along the width direction of the coupled system.

[0054] Combining 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 the acoustic black hole damping layer is solved. n :

[0055]

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

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

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

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

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

[0061]

[0062] Among them, the Lagrange operator L=T n -V n +W is represented by kinetic energy, potential energy, and work done by external forces. By rearranging formula (6), the vibration control equations for 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] Wherein, the stiffness matrix coefficient K is the diagonal arrangement of matrices K1 and K2 according to the principle of block matrix, and 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 diagonal arrangement of matrices M1 and M2 according to the principle of block matrix, and 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, and 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 angular frequency; and F is the amplitude vector corresponding to the external force.

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

[0068] The characteristic of displacement continuity between the uniform beam and the acoustic black hole damping layer is that at the coupling point of their connection surface, the in-plane displacement and vertical displacement of the uniform beam and the acoustic black hole damping layer at the connection surface are equal. Based on this, the coupling constraint conditions between the uniform beam and the acoustic black hole damping layer are:

[0069]

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

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

[0072]

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

[0074]

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

[0076]

[0077] S3. Solve the control equations of motion for the coupled system to obtain the natural frequencies 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, let the amplitude vector F of the external force be the zero vector, and solve the determinant of the coefficient matrix. The angular frequency ω is obtained by setting it to zero, and then the natural frequency f of the coupled system is obtained by using the formula ω = 2πf.

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

[0080] In the preferred embodiment of the present invention, the effectiveness of the method is determined by verifying the established coupled system model through simulation, and the results are as follows: Figure 4 As shown, the method proposed in this invention agrees well with the finite element method, verifying the effectiveness of the proposed method for determining the vibration of beam structures with acoustic black hole damping layers. The structural geometric parameters and material parameters used in the simulation verification are shown in Table 1.

[0081] Table 1 Geometric and Material Parameters

[0082]

[0083] Furthermore, the vibration levels of beam structures with acoustic black hole damping and beam structures with uniform thickness damping were compared, such as... Figure 5 As shown, the vibration level of the beam structure with acoustic black hole damping is significantly lower than that of the beam structure with uniform thickness damping, which verifies that the beam structure with acoustic black hole damping layer proposed in this invention has better vibration reduction and noise reduction effect.

[0084] Those skilled in the art will readily understand that the above description is merely 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 within the scope of protection of the present invention.

Claims

1. A method for calculating the vibration of a beam structure containing an acoustic black hole damping layer, characterized in that: The method includes the following steps: S1. For beam structures in ships with acoustic black hole damping layers attached, a coupled system containing a uniform beam and the acoustic black hole damping layer is selected as the research object. This research object is simplified to two coupled beams with different material properties and cross-sectional shapes. S2. Construct the vibration control equations for the two beam layers, namely the uniform beam and the acoustic black hole damping layer, and set the coupling constraint conditions between the two beam layers to construct the motion control equations of the coupled system. S21. Based on Timoshenko beam theory, the displacement functions of the uniform beam and the acoustic black hole damping layer are obtained, and the kinetic and potential energies of the uniform beam and the acoustic black hole damping layer are calculated. Based on Hamilton's principle and combining kinetic and potential energies, the vibration control equations of the uniform beam and the acoustic black hole damping layer are established. S22. Based on Layerwise theory, the continuity characteristics of in-plane and vertical displacements of the uniform beam and the acoustic black hole damping layer at the coupling position are considered. The coupling constraint conditions between the uniform beam and the acoustic black hole damping layer are set as follows: in, h u For a uniform beam thickness, h a This represents the maximum thickness of the damping layer in an acoustic black hole. u 01 ( x )and u 02 ( x The displacements in the neutral plane of a uniform beam and an acoustic black hole damper are respectively the in-plane displacements. w 1 and w 2 represents the vertical displacement of the uniform beam and the acoustic black hole damper, respectively. θ 1( x )and θ 2( x ) represent the rotation angles of the uniform beam and the acoustic black hole damping about the neutral axis, respectively; According to Hooke's Law, the coupling constraint condition can be transformed into the elastic potential energy of a virtual spring: in, E c This represents 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 This represents the stiffness coefficient of the virtual spring. L c The axial coordinate interval corresponds to the connection between the uniform beam and the acoustic black hole damping layer. K c Let be the stiffness matrix at the junction of the uniform beam and the acoustic black hole damping layer. Let be the displacement coefficient vector of the coupled system. u 01 ( x )and u 02 ( x The displacements in the neutral plane of a uniform beam and an acoustic black hole damper are respectively the in-plane displacements. w 1 and w 2 represents the vertical displacement of the uniform beam and the acoustic black hole damping, respectively; By combining the coupling constraint conditions, the vibration control equations of the uniform beam and the acoustic black hole damping layer in S21 are coupled using the virtual spring method to obtain the motion control equations of the coupled system. S3. Solve the motion control equations of the coupled system to obtain the natural frequencies of the coupled system under free vibration and the vibration response of the coupled system under external excitation; Solving for the natural frequencies of the coupled system involves using the coefficient matrix of the motion control equations of the coupled system. The determinant is zero, which gives the result where, Here is the stiffness matrix of the coupled system. ω It is the angular frequency. These are the coefficients of the quality matrix.

2. The method for calculating the vibration of a beam structure containing an acoustic black hole damping layer as described in claim 1, characterized in that: In step S21, the displacement function calculation formulas for the uniform beam and the acoustic black hole damping layer are as follows: in, u 1 and u 2 represents the in-plane displacement of the uniform beam and the acoustic black hole damping layer, respectively. u 01 ( x )and u 02 ( x The displacements in the neutral plane of a uniform beam and an acoustic black hole damper are respectively the in-plane displacements. w 1 and w 2 represents the vertical displacement of the uniform beam and the acoustic black hole damper, respectively. θ 1( x )and θ 2( x The angles of rotation about the neutral axis are the angles of rotation of the uniform beam and the acoustic black hole damping, respectively. t For time, x Let be the axial coordinates of the coupled system. z For the vertical coordinates of the coupled system, φ 11 , φ 21 and φ 31 Let be the displacement shape function vector of a uniform beam. φ 12 , φ 22 and φ 32 Let be the displacement shape function vector of the acoustic black hole damping. 11 , 21 and 31 For the corresponding φ 11 , φ 21 and φ 31 The undetermined coefficients, 12 , 22 and 32 For the corresponding φ 12 , φ 22 and φ 32 The undetermined coefficients.

3. The method for calculating the vibration of a beam structure with an acoustic black hole damping layer as described in claim 1, characterized in that: In step S21, the vibration control equations for the uniform beam and the acoustic black hole damping layer are as follows: Among them, stiffness matrix coefficients It is a matrix 1 and 2. Arrange diagonally according to the block matrix principle, matrix 1 and 2 represents the stiffness matrix for the uniform beam and the damping layer for the acoustic black hole, respectively; the mass matrix coefficients are... It is a matrix and Arranged diagonally according to the principle of block matrix, the matrix and These are the mass matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively. For displacement amplitude coefficients, matrix 1 and 2 are the amplitude vector matrices corresponding to the uniform beam and the acoustic black hole damping layer, respectively. ω It is the angular frequency. This is the magnitude vector corresponding to the external force.

4. The method for calculating the vibration of a beam structure containing an acoustic black hole damping layer as described in claim 1, characterized in that: In step S22, the continuity characteristic is that the in-plane displacement and vertical displacement of the uniform beam and the acoustic black hole damping layer at the coupling position are equal. Based on the continuity characteristic, the elastic potential energy of the virtual spring at the coupling position is calculated.

5. The method for calculating the vibration of a beam structure containing an acoustic black hole damping layer as described in claim 3, characterized in that: In step S22, the motion control equations of the coupled system are: in, Let be the stiffness matrix of the coupled system.

6. A method for calculating the vibration of a beam structure containing an acoustic black hole damping layer as described in claim 1 or 2, 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, thereby updating the motion control equation of the coupled system, obtaining the displacement amplitude coefficient in the motion control equation of the coupled system through the inversion operation of the coefficient matrix, and then obtaining the vibration response of the coupled system.

7. A calculation system for the vibration of a beam structure containing an acoustic black hole damping layer, characterized in that, The system includes a processor for executing a method for calculating the vibration of a beam structure with an acoustic black hole damping layer as described in any one of claims 1-6.

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