Modulus power law acoustic black hole dynamic vibration absorber design method

Abstract

The application discloses a design method of a modulus power-law acoustic black hole dynamic vibration absorber, and designs an acoustic black hole structure with the modulus of elasticity of material changing in a power-law along the length direction of the structure as a dynamic vibration absorber device based on the acoustic black hole principle. Compared with the traditional acoustic black hole dynamic vibration absorber with the same mass and the same length and width and the geometric thickness changing in a power-law, the acoustic black hole dynamic vibration absorber with the modulus of elasticity changing in a power-law can not only effectively reduce the threshold frequency of damping enhancement, but also effectively improve the structural modal loss factor, so as to realize excellent low-frequency super-wideband damping enhancement and dynamic vibration absorption effect.

Description

Technical Field

[0001] This invention relates to the field of vibration reduction and noise reduction of acoustic black hole structures, specifically, to a design method for an acoustic black hole dynamic vibration absorber based on Young's modulus power law variation. Background Technology

[0002] The acoustic black hole (ABH) effect, as a novel wave manipulation mechanism, combined with a dynamic vibration absorber (DVA) to form an ABH-DVA, serves as an additional acoustic black hole, offering a new approach for lightweight low-frequency broadband vibration suppression. However, traditional thickness power-law ABH-DVAs often face drawbacks in practical engineering, such as high threshold frequencies and high processing precision requirements. Current research lacks a general design method for power-law acoustic black hole dynamic vibration absorbers (DVAs) where the Young's modulus varies along the structural length. Summary of the Invention

[0003] The purpose of this invention is to provide a design method for an acoustic black hole dynamic vibration absorber with Young's modulus power law variation.

[0004] To achieve the above objectives, the technical solution adopted by this invention is as follows: A design method for a modulus power-law acoustic black hole dynamic vibration absorber, comprising the following steps:

[0005] (1) Based on the principle of acoustic black holes, a structural model of an acoustic black hole dynamic vibration absorber with power-law variation of Young's modulus is constructed by utilizing the power-law variation of Young's modulus of the material.

[0006] (2) Determine the geometric and material parameters of each part of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation;

[0007] (3) Using the multibody system transfer matrix method, calculate the modal loss factor of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation;

[0008] (4) The main structure adopts a beam structure. Determine the geometric parameters and material parameters of the main structure;

[0009] (5) Determine the installation position of the dynamic vibration absorber on the main structure and use it as an additional vibration damping device on the main structure.

[0010] Compared with the prior art, the present invention has the following significant advantages: 1. The modal loss factor of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation is higher than that of the traditional geometric thickness power law acoustic black hole dynamic vibration absorber with the same mass, length and width; 2. The damping enhancement threshold frequency of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation is lower than that of the traditional geometric thickness power law acoustic black hole dynamic vibration absorber with the same mass, length and width, and it can achieve low-frequency ultra-wideband dynamic vibration absorption. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of an acoustic black hole dynamic vibration absorber with Young's modulus power law variation.

[0012] Figure 2 This is a schematic diagram of a power-law acoustic black hole dynamic vibration absorber with the same mass, length, and width, and a traditional geometric thickness.

[0013] Figure 3 This is a comparison chart of the modal loss factors of a dynamic vibration absorber for acoustic black holes with the same mass, length, and width, based on the power-law variation of Young's modulus and the power-law variation of traditional geometric thickness.

[0014] Figure 4 This is a schematic diagram of the main structure of an acoustic black hole dynamic vibration absorber with added Young's modulus power law variation.

[0015] Figure 5 It is the admittance frequency response of the main structure driving point of the acoustic black hole dynamic vibration absorber with the addition of Young's modulus power law variation, with the admittance frequency response of the same main structure driving point without the addition of dynamic vibration absorber as a reference. Detailed Implementation

[0016] The technical solution adopted by the design method of the modulus power-law acoustic black hole dynamic vibration absorber of the present invention is as follows: designing a modulus power-law acoustic black hole dynamic vibration absorber in which the Young's modulus of the material varies along the length of the structure; determining the geometric parameters and material parameters of each part of the acoustic black hole dynamic vibration absorber with the Young's modulus power-law variation; calculating the modal loss factor of the acoustic black hole dynamic vibration absorber with the Young's modulus power-law variation; using the acoustic black hole dynamic vibration absorber with the Young's modulus power-law variation as an additional vibration reduction device on the main structure; and calculating the steady-state response of the driving point on the main structure before and after the additional dynamic vibration absorber to verify its vibration reduction performance.

[0017] The specific process includes the following 5 steps:

[0018] (1) Based on the principle of acoustic black holes, an acoustic black hole dynamic vibration absorber with power law variation of Young's modulus is designed by utilizing the power law variation of Young's modulus of the material.

[0019] (2) Determine the geometric and material parameters of each part of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation;

[0020] (3) Using the multibody system transfer matrix method, calculate the modal loss factor of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation;

[0021] (4) The main structure adopts a beam structure. Determine the geometric parameters and material parameters of the main structure;

[0022] (5) Determine the installation position of the dynamic vibration absorber on the main structure and use it as an additional vibration damping device on the main structure;

[0023] The dynamic vibration absorber in step (1) includes a one-dimensional acoustic black hole element whose Young's modulus varies along the length of the structure, wherein the formula for the variation of Young's modulus is: ,in , and For coefficients, The thickness of a uniform segment of an acoustic black hole exhibiting a power-law variation in Young's modulus. For positive integers greater than or equal to 2, beams with uniform cross-sections are used as connectors between the acoustic black hole units, forming a dynamic vibration absorber for an acoustic black hole structure with a power-law variation of Young's modulus.

[0024] The geometric parameters in step (2) include the length of the uniform segment of the acoustic black hole unit. ,thickness Length of material change section Damping layer thickness Connector length ,high Material parameters include the Young's modulus of the uniform section. ,density Loss factor Young's modulus of viscoelastic damping layer ,density Loss factor The connector is made of aluminum, and its Young's modulus is... ,density Loss factor Overall width of the structure .

[0025] In step (3), the linear bifurcation multibody system transfer matrix method is used to perform dynamic modeling of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation. The acoustic black hole unit and connector both adopt the Euler Bernoulli beam model, simplifying it into a multi-element bifurcation multibody system. The parameters given in step (2) are substituted into the transfer matrix of the Euler Bernoulli beam to obtain the transfer matrix of each element. Then, according to the topology of the bifurcation multibody system corresponding to the acoustic black hole dynamic vibration absorber with Young's modulus power law variation, the transfer matrices of each element are "assembled" to obtain the total transfer matrix. The boundary conditions are substituted into the total transfer matrix to obtain the corresponding characteristic equation. The modal loss factor of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation can be obtained by solving the characteristic equation using the recursive eigenvalue search algorithm.

[0026] In step (4), the main structure is taken as a cantilever beam, but it can also be a beam structure with other arbitrary boundary conditions, given the length of the cantilever beam. and thickness The cantilever beam is made of aluminum, and the Young's modulus, density and loss factor of aluminum have been given in step (2).

[0027] In step (5), the acoustic black hole dynamic vibration absorber is used as an additional vibration reduction device on the main structure, and the installation position is selected near the maximum displacement or velocity response of the main structure within the target vibration reduction frequency range.

[0028] After completing the modulus power-law acoustic black hole dynamic vibration absorber, the steady-state response of the driving point on the main structure before and after the addition of the dynamic vibration absorber can be calculated to verify its vibration reduction performance. A point load is applied to the main structure, and the steady-state response of the driving point on the main structure is calculated using the multibody system transfer matrix method, with and without the addition of the acoustic black hole dynamic vibration absorber with Young's modulus power-law variation.

[0029] The specific method is as follows: Calculate the steady-state response of the driving point on the main structure under point load conditions with and without an acoustic black hole dynamic vibration absorber with a power-law variation in Young's modulus. The combined system is dynamically modeled using the linear bifurcation multibody system transfer matrix method. The main structure also adopts the Euler Bernoulli beam model, simplifying the combined system into a multi-element bifurcation multibody system. Substitute the parameters given in steps (2) and (4) into the transfer matrix of the Euler Bernoulli beam to obtain the transfer matrix of each element. Based on the topology of the bifurcation multibody system corresponding to the combined system, "assemble" the transfer matrices of each element to obtain the total transfer matrix. Substitute the boundary conditions and the applied point loads of the combined system into the total transfer equation to calculate the steady-state response of the driving point on the main structure with an acoustic black hole dynamic vibration absorber with a power-law variation in Young's modulus. When the main structure is not equipped with a dynamic vibration absorber, simply set the relevant dynamic vibration absorber geometric parameters in steps (2) and (4) to 0 to obtain the steady-state response of the driving point on the main structure without a dynamic vibration absorber under the same boundary conditions and load conditions.

[0030] The following simulation experiment, in conjunction with the accompanying drawings, further illustrates this point.

[0031] A power-law modulus of a material whose Young's modulus varies along the length of the structure; an acoustic black hole dynamic vibration absorber, such as... Figure 1 .

[0032] Determine the geometric and material parameters of each part of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation:

[0033] The lower limit of the target vibration reduction frequency range for acoustic black hole structures with Young's modulus power law variation is: The damping layer on the acoustic black hole unit is made of a viscoelastic material. The material and geometric parameters of each part are shown in Table 1; the remaining geometric parameters do not require special design.

[0034]

[0035] Table 1: Material and geometric parameters of acoustic black holes with Young's power-law modulus variations

[0036] Calculate the modal loss factor of an acoustic black hole dynamic vibration absorber with power-law variation of Young's modulus:

[0037] A dynamic model of an acoustic black hole dynamic vibration absorber with a power-law variation in Young's modulus is performed using the linear bifurcation multibody system transfer matrix method, and its modal loss factor is calculated. To verify the low-frequency broadband vibration reduction effect of the acoustic black hole dynamic vibration absorber with a power-law variation in Young's modulus, under fixed-free boundary conditions, the following steps are taken: Figure 2 The acoustic black hole dynamic vibration absorber with conventional geometric thickness power-law variation, exhibiting the same mass, length, and width, serves as a control; its thickness variation function is: , The coefficient is denoted by ; its uniform segment density and height are respectively . and The cut-off thickness is The material and geometric parameters are shown in Table 2, and the remaining parameters are the same as in Table 1. The modal loss factors of the two acoustic black hole dynamic vibration absorbers were compared, such as... Figure 3 .

[0038]

[0039] Table 2: Material and geometric parameters of acoustic black holes with conventional power-law variations in geometric thickness

[0040] Taking a cantilever beam structure as an example, the acoustic black hole dynamic vibration absorber with Young's modulus power law variation is installed at the location of the main structure. At this point, the free end of the cantilever beam is subjected to a unit harmonic load, such as Figure 4 The vibration reduction performance of the acoustic black hole dynamic vibration absorber obtained by the design method of this invention is verified by simulating the steady-state admittance response of the driving point on the main structure with and without the addition of an acoustic black hole dynamic vibration absorber with power-law variation of Young's modulus.

[0041] The linear bifurcated multibody system transfer matrix method is used to dynamically model the combined system. Each part of the combined system adopts an Euler Bernoulli beam model, simplifying the combined system into a multi-element bifurcated multibody system. Substituting the given parameters into the Euler Bernoulli beam transfer matrix yields the transfer matrix of each element. Based on the topology of the corresponding bifurcated multibody system, the transfer matrices of each element are "assembled" to obtain the overall transfer matrix. Substituting the boundary conditions and point loads of the combined system into the overall transfer equation allows for the calculation of the steady-state response of the driving point on the main structure when an acoustic black hole dynamic vibration absorber with power-law variations in density and Young's modulus is added. When the main structure is without an added dynamic vibration absorber, simply setting the relevant dynamic vibration absorber geometric parameters to 0 yields the steady-state response of the driving point on the main structure without the added dynamic vibration absorber under the same boundary conditions and loads. The velocity admittance of the cantilever beam driving point after adding an acoustic black hole dynamic vibration absorber with power-law variations in Young's modulus is calculated. Steady-state response, with the drive point admittance frequency response of the same cantilever beam without an additional dynamic vibration absorber as a reference, the results are as follows: Figure 5 The calculation results demonstrate that with the introduction of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation, the resonance peaks of the main beam at all orders above the target frequency are significantly suppressed. The geometric parameters involved in the experiment are shown in Table 1.

Claims

1. A design method for a modulus power-law acoustic black hole dynamic vibration absorber, characterized in that, Includes the following steps: (1) Based on the principle of acoustic black holes, a structural model of an acoustic black hole dynamic vibration absorber with power-law variation of Young's modulus is constructed by utilizing the power-law variation of Young's modulus of the material. (2) Determine the geometric and material parameters of each part of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation; (3) Using the multibody system transfer matrix method, calculate the modal loss factor of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation; (4) The main structure adopts a beam structure. Determine the geometric parameters and material parameters of the main structure; (5) Determine the installation position of the dynamic vibration absorber on the main structure and use it as an additional vibration damping device on the main structure.

2. The design method for a modulus power-law acoustic black hole dynamic vibration absorber according to claim 1, characterized in that: The dynamic vibration absorber in step (1) includes a one-dimensional acoustic black hole element whose Young's modulus varies along the length of the structure, wherein the formula for the variation of Young's modulus is: ,in , and For coefficients, The thickness of a uniform segment of an acoustic black hole exhibiting a power-law variation in Young's modulus. It is a positive integer greater than or equal to 2; the beam with uniform cross-section is used as the connector between the acoustic black hole unit and the main structure, forming a dynamic vibration absorber for an acoustic black hole structure with a power law variation of Young's modulus.

3. The design method for a modulus power-law acoustic black hole dynamic vibration absorber according to claim 1, characterized in that: The geometric parameters in step (2) include the length of the uniform segment of the acoustic black hole unit. ,thickness Length of material change section Damping layer thickness Connector length ,high Material parameters include the Young's modulus of the uniform section. ,density Loss factor Young's modulus of viscoelastic damping layer ,density Loss factor The connector is made of aluminum, and its Young's modulus is... ,density Loss factor Overall width of the structure .

4. The design method for a modulus power-law acoustic black hole dynamic vibration absorber according to claim 1, characterized in that: In step (3), the linear bifurcation multibody system transfer matrix method is used to perform dynamic modeling of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation. The acoustic black hole unit and the connector adopt the Euler Bernoulli beam model, which simplifies it into a multi-element bifurcation multibody system. Substitute the parameters given in step (2) into the transfer matrix of the Euler Bernoulli beam to obtain the transfer matrix of each element. Then, according to the topology of the bifurcated multibody system corresponding to the acoustic black hole dynamic vibration absorber with Young's modulus power law variation, "assemble" the transfer matrices of each element to obtain the total transfer matrix. Substituting the boundary conditions into the total transfer matrix yields the corresponding characteristic equation. Solving the characteristic equation using the recursive eigenvalue search algorithm yields the modal loss factor of the acoustic black hole dynamic vibration absorber with Young's modulus power law variation.

5. The design method for a modulus power-law acoustic black hole dynamic vibration absorber according to claim 1, characterized in that: In step (4), the main structure is a beam structure with arbitrary boundary conditions, and the length of the beam is given. and thickness The cantilever beam is made of aluminum, and its Young's modulus is... The density is The loss factor is .

6. The design method for a modulus power-law acoustic black hole dynamic vibration absorber according to claim 1, characterized in that: In step (5), the acoustic black hole dynamic vibration absorber is used as an additional vibration reduction device on the main structure, and the installation position is selected near the maximum displacement or velocity response of the main structure within the target vibration reduction frequency range.

Images