Design Method of Gradient Embedded Acoustic Black Hole and Dynamic Vibration Absorber Composite Vibration Isolator Based on Reduced Multibody System Transfer Matrix Method

Abstract

This invention discloses a design method for a gradient-embedded acoustic black hole and dynamic vibration absorber composite vibration isolator based on the reduced multibody system transfer matrix method. Based on the principles of acoustic black holes and dynamic vibration absorbers, a composite structure incorporating multiple gradient-embedded acoustic black holes and dynamic vibration absorbers is designed. Comparison with a gradient-embedded acoustic black hole structure of the same geometry and materials reveals that the gradient-embedded acoustic black hole and dynamic vibration absorber composite structure exhibits better low-frequency broadband vibration isolation performance.

Description

Technical Field

[0001] This invention belongs to the field of vibration reduction and noise reduction of acoustic black hole structures. Specifically, it is a novel acoustic black hole vibration isolator design method that combines a gradient embedded acoustic black hole with a dynamic vibration absorber. Background Technology

[0002] Vibration isolation is an important means of vibration control. Generally, for a single-degree-of-freedom system, simply reducing its natural frequency can improve the vibration isolation effect. However, since parameters such as springs and dampers in the structure cannot change according to external excitation, excessive stiffness leads to a reduction in the isolation frequency band, while insufficient stiffness affects the load-bearing capacity. On the other hand, damping suppresses vibration in the ineffective isolation band, but reduces the isolation efficiency within the isolation band itself. Classical vibration isolation techniques struggle to reconcile these contradictions. In the field of vibration control, acoustic black hole structures can be considered broadband or multimodal local vibration dampers, where vibration concentration and damping enhancement mainly occur near the local resonant frequency. Therefore, as a vibration isolator, an acoustic black hole naturally avoids introducing excessive damping in the non-resonant / ineffective isolation band, thus preventing a reduction in isolation efficiency in these bands. However, due to the existence of a threshold frequency in acoustic black hole structures, the low-frequency vibration isolation effect of small acoustic black hole structures is poor.

[0003] Considering the excellent performance of dynamic vibration absorber elements in low-frequency vibration reduction due to their energy absorption principle, and the broadband energy concentration characteristics of acoustic black hole structures, the low-frequency vibration isolation effect of acoustic black hole structures can be improved by utilizing the energy absorption principle of dynamic vibration absorber elements without changing the dimensions of the acoustic black hole structure. A composite system combining these two structures not only holds promise for overcoming the limitations of traditional passive vibration isolators but may also achieve broadband vibration isolation across multiple frequencies, thus becoming a more efficient and practical vibration isolator design method. Summary of the Invention

[0004] The purpose of this invention is to provide a novel acoustic black hole vibration isolator design method that combines a gradient-embedded acoustic black hole with a dynamic vibration absorber.

[0005] The technical solution to achieve the purpose of this invention is: a design method for a gradient-embedded acoustic black hole and dynamic vibration absorber composite vibration isolator, comprising the following steps:

[0006] (1) Based on the principle of acoustic black holes, a gradient structure vibration isolator is designed using multiple embedded acoustic black hole units;

[0007] (2) Determine the dimensional and material parameters of each part of the gradient-embedded acoustic black hole vibration isolator;

[0008] (3) Based on the displacement or force to be isolated, the vibration transmissivity of the gradient embedded acoustic black hole vibration isolator is calculated using the reduced multibody system transfer matrix method. In step (3), the main structure of the gradient embedded acoustic black hole is modeled dynamically using the reduced multibody system transfer matrix method. The components contained in each acoustic black hole unit adopt a two-dimensional plane Euler-Bernoulli uniform beam model. The gradient embedded acoustic black hole vibration isolator can be regarded as a linear multibody system composed of two-dimensional plane Euler-Bernoulli uniform beams. 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, based on the topology of the multibody system corresponding to the gradient embedded acoustic black hole vibration isolator, the reduced transfer matrix and load function related matrix of each element are recursively derived. Substitute the load and boundary conditions of the vibration isolator into the recursive calculation to obtain the steady-state response of the vibration transmissivity of the gradient embedded acoustic black hole vibration isolator.

[0009] (4) Determine the installation position and structural parameters of the dynamic vibration absorber for each order resonance peak of the vibration transmissibility of the gradient embedded acoustic black hole vibration isolator; the parameters of the dynamic vibration absorber include the mass ratio μ, damping ratio ξ, frequency ratio f and installation position L of the nth dynamic vibration absorber. DVA,n Wherein, the mass ratio μ = m2 / m1, the characteristic frequency ratio f = ω2 / ω1, the damping ratio ξ = c2 / 2m2ω1, m1 is the mass of the main vibration system, ω1 is the characteristic frequency of the main vibration system, m2 is the mass of the dynamic vibration absorber, ω2 is the characteristic frequency of the dynamic vibration absorber, and c2 is the damping of the dynamic vibration absorber.

[0010] (5) The vibration transmissivity of the gradient-embedded acoustic black hole and dynamic vibration absorber composite vibration isolator is calculated using the reduced multibody system transfer matrix method. The dynamic vibration absorber composite vibration isolator is modeled dynamically using the reduced multibody system transfer matrix method. Each dynamic vibration absorber adopts a spring damper model with added mass. Then, the composite vibration isolator can be simplified into a tree-shaped multibody system composed of multiple elements.

[0011] Substitute the parameters given in step (4) into the transfer matrix of the spring damper with added mass to obtain the transfer matrix of each dynamic vibration absorber element. Then, based on the topology of the multibody system corresponding to the gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator, recursively derive the reduced transfer matrix S and load function related matrix e of each element. Substitute the load and boundary conditions of the composite vibration isolator into the recursive calculation to obtain the steady-state response of the vibration transmissivity of the gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator.

[0012] Compared with the prior art, the present invention has the following significant advantages: (1) The gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator has better low-frequency broadband vibration isolation performance; (2) The gradient embedded acoustic black hole and dynamic vibration absorber composite structure can be flexibly adjusted according to the required vibration isolation frequency range, and has high designability. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of a composite vibration isolator consisting of a gradient-embedded acoustic black hole and a dynamic vibration absorber.

[0014] Figure 2 It is a frequency response diagram of the vibration transmissivity of a gradient-embedded acoustic black hole structure.

[0015] Figure 3 This is the displacement response diagram at the second-order resonance peak frequency of the vibration transmissivity of the gradient-embedded acoustic black hole structure.

[0016] Figure 4 This is a model topology diagram of a gradient-embedded acoustic black hole and dynamic vibration absorber composite vibration isolator, and a recursive process diagram using the reduced transfer matrix method. Figure 3 In the diagram, (a) is the model topology diagram and (b) is the recursive process diagram of the reduced transfer matrix method.

[0017] Figure 5 This is a comparison of the frequency response of vibration transmissibility before and after the addition of a dynamic vibration absorber to the gradient-embedded acoustic black hole vibration isolator.

[0018] Figure 6 This is a spatial distribution diagram of vibration displacement at different frequencies of a composite vibration isolator consisting of a gradient-embedded acoustic black hole and a dynamic vibration absorber.

[0019] Figure 7 This is an experimental verification diagram of a composite vibration isolator consisting of a gradient-embedded acoustic black hole and a dynamic vibration absorber. Detailed Implementation

[0020] The present invention will now be further described with reference to the accompanying drawings and embodiments.

[0021] The technical solution adopted in this invention is as follows: designing a vibration isolator with a gradient structure comprising multiple embedded acoustic black hole and dynamic vibration absorber composite units; determining the dimensional and material parameters of each part of the gradient embedded acoustic black hole; calculating the vibration transmissibility of the gradient embedded acoustic black hole; determining the installation position and structural parameters of the dynamic vibration absorber based on the resonance peaks of each order of the vibration transmissibility of the gradient embedded acoustic black hole; and calculating the vibration transmissibility of the composite vibration isolator of the gradient embedded acoustic black hole and dynamic vibration absorber.

[0022] The specific process includes the following 5 steps:

[0023] (1) Based on the principle of acoustic black holes, a gradient structure vibration isolator is designed using multiple embedded acoustic black hole units, such as... Figure 1 As shown;

[0024] (2) Determine the dimensional and material parameters of each part of the gradient-embedded acoustic black hole vibration isolator;

[0025] (3) Based on the displacement or force to be isolated, the vibration transmissibility of the gradient embedded acoustic black hole vibration isolator is calculated using the reduced multibody system transfer matrix method.

[0026] (4) Determine the installation position and structural parameters of the dynamic vibration absorber for each order resonance peak of the vibration transmissivity of the gradient embedded acoustic black hole vibration isolator.

[0027] (5) The vibration transmission rate of the gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator is calculated by using the reduced multibody system transfer matrix method.

[0028] In step (1), the vibration isolator substrate can be a uniform beam with a rectangular cross-section or a cylindrical uniform beam structure with a circular cross-section. The substrate contains multiple embedded acoustic black holes and dynamic vibration absorber units with varying parameters.

[0029] The vibration isolator size parameters in step (2) include the length L of the nth acoustic black hole unit. n Length L of uniform segment beam,n Length L of the wedge segment ABH,n wedge segment curve power m, cut-off thickness H d,n and the length gradient ΔL of the wedge segment ABH The length gradient ΔL of the uniform segment beam Thickness gradient ΔH of the cut-off thickness d The total thickness H and total width D of the vibration isolator; material parameters include Young's modulus E, density ρ, and loss factor η.

[0030] In step (3), the reduced multibody system transfer matrix method is used to perform dynamic modeling of the gradient-embedded acoustic black hole main structure. The components contained in each acoustic black hole unit adopt a two-dimensional planar Euler-Bernoulli uniform beam model. Therefore, the vibration isolator can be regarded as a linear multibody system composed of two-dimensional planar Euler-Bernoulli uniform beams. Substituting the parameters given in step (2) into the transfer matrix of the Euler-Bernoulli beam, the transfer matrix of each element is obtained. Then, based on the topology of the multibody system corresponding to the gradient-embedded acoustic black hole vibration isolator, the reduced transfer matrix S and the load function correlation matrix e of each element are recursively derived. Substituting the load and boundary conditions of the vibration isolator into the recursive calculation, the steady-state response of the vibration transmissivity of the gradient-embedded acoustic black hole vibration isolator can be calculated.

[0031] In step (4), a dynamic vibration absorber model is constructed using a spring damper with added mass. The parameters of the dynamic vibration absorber include the mass ratio μ, damping ratio ξ, frequency ratio f, and installation position L of the nth dynamic vibration absorber. DVA,n Wherein, the mass ratio μ = m2 / m1, the characteristic frequency ratio f = ω2 / ω1, and the damping ratio ξ = c2 / 2m2ω1, m1 is the mass of the main vibration system, ω1 is the characteristic frequency of the main vibration system, m2 is the mass of the dynamic vibration absorber, ω2 is the characteristic frequency of the dynamic vibration absorber, and c2 is the damping of the dynamic vibration absorber.

[0032] In step (5), the reduced multibody system transfer matrix method is used to perform dynamic modeling of the gradient-embedded acoustic black hole and dynamic vibration absorber composite vibration isolator. Each dynamic vibration absorber adopts a spring-damper model with added mass, so the composite vibration isolator can be simplified into a tree-shaped multibody system composed of multiple elements. Substituting the parameters given in step (4) into the transfer matrix of the spring-damper with added mass, the transfer matrix of each dynamic vibration absorber element is obtained. Then, based on the topology of the multibody system corresponding to the gradient-embedded acoustic black hole and dynamic vibration absorber composite vibration isolator, the reduced transfer matrix and load function related matrix of each element are recursively derived. Substituting the load and boundary conditions of the composite vibration isolator into the recursive calculation, the steady-state response of the vibration transmissivity of the gradient-embedded acoustic black hole and dynamic vibration absorber composite vibration isolator can be calculated.

[0033] The following simulation experiment, in conjunction with the accompanying drawings, further illustrates this point.

[0034] An acoustic black hole vibration isolator with a gradient structure was designed using an acoustic black hole element with three gradient parameters.

[0035] Determine the dimensional and material parameters of each part of the acoustic black hole vibration isolator:

[0036] The acoustic black hole vibration isolator is made of 45# steel. The material and dimensional parameters of each part are shown in Table 1.

[0037]

[0038] Table 1: Material and size parameters of a three-unit gradient-embedded acoustic black hole

[0039] Calculate the vibration transmissivity of the gradient-embedded acoustic black hole vibration isolator:

[0040] Dynamic modeling of a gradient-embedded acoustic black hole vibration isolator was performed using the reduced multibody system transfer matrix method, and its vibration transmissibility T = 20log 10 (|Y O / Y I The steady-state response of |), where Y O and Y IThe lateral displacements at the system input and output are taken as a reference, with the vibration transmissibility of a uniform beam isolator of the same material and size without an internal acoustic black hole as a reference. The results are as follows: Figure 2 .

[0041] By utilizing the steady-state response of the vibration transmissivity of a gradient-embedded acoustic black hole vibration isolator at various resonance peak frequencies, the locations of vibration energy accumulation at each resonance peak frequency are identified. Taking the second-order resonance peak frequency of the vibration transmissivity of the gradient-embedded acoustic black hole structure as an example, such as... Figure 3 The diagram shows the displacement response at the second resonance peak frequency. The x-axis coordinate of the location of the maximum displacement can be obtained, which is the installation position of the dynamic vibration absorber targeting the second resonance peak. Selecting a suitable mass ratio μ and utilizing... and The damping ratio ξ and characteristic frequency ratio f of each dynamic vibration absorber were calculated, and the parameters of each dynamic vibration absorber are shown in Table 2.

[0042]

[0043] Table 2: Parameters of Dynamic Vibration Absorber

[0044] After determining the installation location, mass ratio, damping ratio, and characteristic frequency ratio parameters of the dynamic vibration absorber, it is attached to the gradient-embedded acoustic black hole structure to form a composite vibration isolator of the gradient-embedded acoustic black hole and the dynamic vibration absorber. The dynamic model of the composite vibration isolator of the gradient-embedded acoustic black hole and the dynamic vibration absorber is then performed using the reduced multibody system transfer matrix method, and its vibration transmissibility T = 20log 10 (|Y O / Y I The steady-state response of |) is simplified and the recursive process is as follows: Figure 4 And using the vibration transmissibility of a gradient-embedded acoustic black hole isolator without an attached dynamic vibration absorber as a reference, the results are as follows: Figure 5 As can be seen, compared to the gradient-embedded acoustic black hole vibration isolator without an attached dynamic vibration absorber, the composite vibration isolator of the gradient-embedded acoustic black hole and dynamic vibration absorber can achieve significant attenuation of vibration transmission across almost the entire frequency band. This is because the designed acoustic black hole acts as a low-frequency broadband notch filter, including rich low-frequency broadband local resonant modes. Vibration energy is effectively captured and concentrated as it passes through the various wedge-shaped segments of the acoustic black hole from left to right. Simultaneously, the damped dynamic vibration absorber structure plays a role in energy absorption, and the energy concentrated by the acoustic black hole is effectively dissipated through damping. Figure 6 .

[0045] The above design results have also been verified by experiments, such as... Figure 7 As shown, the vibration transmissivity frequency response of the composite vibration isolator of gradient embedded acoustic black hole and dynamic vibration absorber was obtained by experimental means.

Claims

1. A design method of a gradient-embedded acoustic black hole and dynamic vibration absorber compound vibration isolator based on a reduced multi-body system transfer matrix method, characterized in that, The method comprises the following steps: (1) designing a gradient structure vibration isolator by using multiple embedded acoustic black hole units based on the principle of acoustic black hole; (2) determining the size parameters and material parameters of each part of the gradient embedded acoustic black hole vibration isolator; (3) calculating the vibration transmissibility of the gradient embedded acoustic black hole vibration isolator by using the reduced multi-body system transfer matrix method according to the displacement or force to be isolated; In the step (3), the gradient embedded acoustic black hole main structure is modeled by using the reduced multi-body system transfer matrix method, the components included in each acoustic black hole unit are modeled by using the two-dimensional plane Euler-Bernoulli uniform beam model, and the gradient embedded acoustic black hole vibration isolator can be regarded as a linear multi-body system composed of two-dimensional plane Euler-Bernoulli uniform beams; the transfer matrix of each element is obtained by substituting the parameters given in the step (2) into the transfer matrix of the Euler-Bernoulli beam, and then the reduced transfer matrix and the load function related matrix of each element are recursively calculated according to the topological structure of the multi-body system corresponding to the gradient embedded acoustic black hole vibration isolator; the steady-state response of the vibration transmissibility of the gradient embedded acoustic black hole vibration isolator can be calculated by substituting the load and boundary conditions of the vibration isolator into the inverse recursion. (4) determining the installation position and structure parameters of the dynamic vibration absorber for each order resonance peak of the vibration transmissibility of the gradient embedded acoustic black hole vibration isolator; The parameters of the dynamic absorber include a mass ratio μ, a damping ratio ξ, a frequency ratio f and a mounting position L of the nth dynamic absorber DVA,n ; wherein the mass ratio μ = m2 / m1, the characteristic frequency ratio f = ω2 / ω1, the damping ratio ξ = c2 / 2m2ω1, m1 is the mass of the main vibration system, ω1 is the characteristic frequency of the main vibration system, m2 is the mass of the dynamic absorber, ω2 is the characteristic frequency of the dynamic absorber, and c2 is the damping of the dynamic absorber. (5) calculating the vibration transmissibility of the gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator by using the reduced multi-body system transfer matrix method; The gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator is modeled by using the reduced multi-body system transfer matrix method, each dynamic vibration absorber is modeled by using the spring damper model with additional mass, and the composite vibration isolator can be simplified as a tree-shaped multi-body system composed of multiple elements. The transfer matrix of each dynamic vibration absorber element is obtained by substituting the parameters given in the step (4) into the transfer matrix of the spring damper with additional mass, and then the reduced transfer matrix S and the load function related matrix e of each element are recursively calculated according to the topological structure of the multi-body system corresponding to the gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator. The steady-state response of the vibration transmissibility of the gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator can be calculated by substituting the load and boundary conditions of the composite vibration isolator into the inverse recursion.

2. The reduced multi-body system transfer matrix method based design method of gradient-embedded acoustic black hole and dynamic vibration absorber compound vibration isolator according to claim 1, wherein: In the step (1), the vibration isolator base is a uniform beam structure with a rectangular cross section or a cylindrical uniform beam structure with a circular cross section; the vibration isolator base contains multiple parameter gradient change embedded acoustic black holes and dynamic vibration absorber units.

3. The reduced multi-body system transfer matrix method based design approach for a gradient-embedded acoustic black hole and dynamic vibration absorber compound vibration isolator of claim 1, wherein: The size parameters of the isolator in step (2) include the length L of the nth acoustic black hole unit n , the length L of the uniform section beam,n , the length L of the wedge section ABH,n , the power m of the wedge section curve, the thickness H of the truncation d,n , the length gradient AL of the wedge section ABH , the length gradient AL of the uniform section beam , the thickness gradient AH of the truncation d , and the total thickness H and the total width D of the isolator; the material parameters include the Young's modulus E, the density p, and the loss factor η.

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