Design method of gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator based on reduced multi-body system transfer matrix method

Abstract

The invention discloses a gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator design method based on a reduced multi-body system transfer matrix method. Based on an acoustic black hole principle and a dynamic vibration absorber working principle, a composite structure comprising a plurality of gradient embedded acoustic black holes and a dynamic vibration absorber is designed. Compared with a gradient embedded acoustic black hole structure with the same geometric size and material, the gradient embedded acoustic black hole and dynamic vibration absorber composite structure has better low-frequency broadband vibration isolation performance.

Description

Technical Field

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

[0002] Vibration isolation is an important means of vibration control. Generally speaking, for a single-degree-of-freedom system, only reducing its natural frequency can improve the vibration isolation effect. However, since parameters such as the springs and dampers of the structure cannot change according to external excitations, too large a stiffness will lead to a reduction in the vibration isolation frequency band, and too small a stiffness will affect the load-bearing capacity. On the other hand, damping suppresses vibration in the ineffective vibration isolation band and reduces the vibration isolation efficiency in the vibration isolation band range. It is difficult for classical vibration isolation techniques to coordinate such contradictions. In the field of vibration control, the acoustic black hole structure can be regarded as a broadband or multi-modal local vibration reducer, and vibration concentration and damping enhancement mainly occur near the local resonance frequency. Therefore, as an isolator, the acoustic black hole will naturally avoid introducing too much damping in the non-resonant / ineffective vibration isolation band, thereby avoiding the reduction of isolation efficiency in these frequency bands. However, due to the existence of a threshold frequency in the acoustic black hole structure, the low-frequency vibration isolation effect of small acoustic black hole structures is not good.

[0003] Considering that the energy absorption working principle of the dynamic vibration absorber element performs well in low-frequency vibration reduction and the characteristics of the acoustic black hole structure in broadband energy concentration, the low-frequency vibration isolation effect of the acoustic black hole structure can be improved without changing the size of the acoustic black hole structure by using the energy absorption principle of the dynamic vibration absorber element. The combined use of these two structures not only is expected to overcome the limitations of traditional passive isolators but also may achieve broadband vibration isolation at multiple frequencies in vibration control, thus becoming a more efficient and practical isolator design method. Summary of the Invention

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

[0005] The technical solution to achieve the purpose of the present invention is as follows: A design method of a gradient-embedded acoustic black hole and dynamic vibration absorber combined isolator includes the following steps:

[0006] (1) Based on the acoustic black hole principle, design an isolator with a gradient structure using multiple embedded acoustic black hole units;

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

[0008] (3) Calculate the vibration transmission rate of the gradient embedded acoustic black hole vibration isolator according to the displacement or force to be isolated by using the reduced multi-body system transfer matrix method; in step (3), the reduced multi-body system transfer matrix method is used to perform dynamic modeling on the gradient embedded acoustic black hole main structure, and the components included in each acoustic black hole unit all adopt the two-dimensional plane Euler Bernoulli uniform beam model, then this 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; substitute the parameters given in step (2) into the transfer matrix of the Euler Bernoulli beam to obtain the transfer matrices of each component, and then recursively calculate the reduced transfer matrices of each component and the column array related to the load function according to the topological structure of the multi-body system corresponding to the gradient embedded acoustic black hole vibration isolator; substitute the load and boundary conditions of the vibration isolator for inverse recursion, and the steady-state response of the vibration transmission rate of the gradient embedded acoustic black hole vibration isolator can be calculated.

[0009] (4) Determine the installation position and structural parameters of the dynamic vibration absorber for each resonance peak of the vibration transmission rate of the gradient embedded acoustic black hole vibration isolator respectively; 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 ; where, 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) Calculate the vibration transmission rate of the composite vibration isolator of the gradient embedded acoustic black hole and the dynamic vibration absorber by using the reduced multi-body system transfer matrix method. Use the reduced multi-body system transfer matrix method to perform dynamic modeling on the composite vibration isolator of the gradient embedded acoustic black hole and the dynamic vibration absorber. Each dynamic vibration absorber adopts the model of a spring-damper with an additional mass, then this composite vibration isolator can be simplified into a tree-shaped multi-body system composed of multiple components.

[0011] Substitute the parameters given in step (4) into the transfer matrix of the spring-damper with an additional mass to obtain the transfer matrices of each dynamic vibration absorber component, and then recursively calculate the reduced transfer matrix S of each component and the column array e related to the load function according to the topological structure of the multi-body system corresponding to the composite vibration isolator of the gradient embedded acoustic black hole and the dynamic vibration absorber; substitute the load and boundary conditions of the composite vibration isolator for inverse recursion, and the steady-state response of the vibration transmission rate of the composite vibration isolator of the gradient embedded acoustic black hole and the dynamic vibration absorber can be calculated.

[0012] Compared with the prior art, the present invention has the following remarkable advantages: (1) The gradient-embedded acoustic black hole and dynamic vibration absorber composite 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 frequency range to be isolated, and has high designability. Description of the Drawings

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

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

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

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

[0017] Figure 5 It is the comparison diagram of the frequency response of the vibration transfer rate before and after adding a dynamic vibration absorber to the gradient-embedded acoustic black hole isolator.

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

[0019] Figure 7 It is the experimental verification diagram of the gradient-embedded acoustic black hole and dynamic vibration absorber composite isolator. Detailed Embodiment

[0020] The present invention will be further described below in conjunction with the drawings of the specification and embodiments.

[0021] The technical solution adopted by the present invention is: designing an isolator with a gradient structure including multiple embedded acoustic black hole and dynamic vibration absorber composite units; determining the size parameters and material parameters of each part of the gradient-embedded acoustic black hole; calculating the vibration transfer rate of the gradient-embedded acoustic black hole; determining the installation position and structural parameters of the dynamic vibration absorber for each order resonance peak of the vibration transfer rate of the gradient-embedded acoustic black hole; calculating the vibration transfer rate of the gradient-embedded acoustic black hole and dynamic vibration absorber composite isolator.

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

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

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

[0025] (3) According to the displacement or force to be isolated, use the reduced multi-body system transfer matrix method to calculate the vibration transfer rate of the gradient embedded acoustic black hole vibration isolator;

[0026] (4) Determine the installation position and structural parameters of the dynamic vibration absorber for each resonance peak of the vibration transfer rate of the gradient embedded acoustic black hole vibration isolator respectively;

[0027] (5) Use the reduced multi-body system transfer matrix method to calculate the vibration transfer rate of the composite vibration isolator of the gradient embedded acoustic black hole and the dynamic vibration absorber.

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

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

[0030] In step (3), the reduced multi-body system transfer matrix method is used to perform dynamic modeling on the main structure of the gradient embedded acoustic black hole. The components included in each acoustic black hole unit all adopt the two-dimensional plane Euler-Bernoulli uniform beam model, then this vibration isolator can be regarded as a linear multi-body 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 component, and then recursively calculate the reduced transfer matrix S and the load function-related column array e of each component according to the topological structure of the multi-body system corresponding to the gradient embedded acoustic black hole vibration isolator. Substitute the load and boundary conditions of the vibration isolator for inverse recursion, and the steady-state response of the vibration transfer rate 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 additional 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 Among them, 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.

[0032] In step (5), the reduced multi-body system transfer matrix method is used to perform dynamic modeling on the gradient embedded acoustic black hole and dynamic vibration absorber composite isolator. Each dynamic vibration absorber adopts a spring damper model with additional mass, then this composite isolator can be simplified into a tree-shaped multi-body system composed of multiple components. Substitute the parameters given in step (4) into the transfer matrix of the spring damper with additional mass to obtain the transfer matrix of each dynamic vibration absorber component, and then recursively calculate the reduced transfer matrix and the relevant column matrix of the load function of each component according to the topological structure of the multi-body system corresponding to the gradient embedded acoustic black hole and dynamic vibration absorber composite isolator. Substitute the load and boundary conditions of the composite isolator for inverse recursion, and the steady-state response of the vibration transfer rate of the gradient embedded acoustic black hole and dynamic vibration absorber composite isolator can be calculated.

[0033] The following is further illustrated through the following simulation experiments in combination with the specification drawings.

[0034] A gradient-structured acoustic black hole isolator is designed using three acoustic black hole units with gradient-changing parameters.

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

[0036] The acoustic black hole isolator uses 45# steel. The material parameters and size parameters of each part are shown in Table 1.

[0037]

[0038] Table 1: Material and Size Parameters of the Three-Unit Gradient Embedded Acoustic Black Hole

[0039] Calculate the vibration transfer rate of the gradient embedded acoustic black hole isolator:

[0040] Use the reduced multi-body system transfer matrix method to perform dynamic modeling on the gradient embedded acoustic black hole isolator, and calculate its vibration transfer rate T = 20log 10 (|Y O / Y I |) of the steady-state response, where Y O and Y Iis the lateral displacement at the input and output ends of the system, and the vibration transmissibility of a uniform beam isolator with the same material and size as the internal acoustic black hole is used as a reference. The results are as Figure 2 .

[0041] Using the displacement response of the steady-state response of the vibration transmissibility of the gradient-embedded acoustic black hole isolator at each resonance peak frequency, the vibration energy accumulation points at each resonance peak frequency are found. Taking the second-order resonance peak frequency of the vibration transmissibility of the gradient-embedded acoustic black hole structure as an example, as Figure 3 shown is the displacement response diagram at the second-order resonance peak frequency, and the x-axis coordinate of the position where the maximum displacement is located can be obtained, that is, the position where the dynamic vibration absorber for the second-order resonance peak is to be installed. Select a suitable mass ratio μ and use and to calculate the damping ratio ξ and characteristic frequency ratio f of each dynamic vibration absorber. The parameters of each dynamic vibration absorber are shown in Table 2.

[0042]

[0043] Table 2: Parameters of the dynamic vibration absorber

[0044] After determining the installation position of the dynamic vibration absorber and the parameters of the mass ratio, damping ratio, and characteristic frequency ratio, the dynamic vibration absorber is attached to the gradient-embedded acoustic black hole structure to form a gradient-embedded acoustic black hole and dynamic vibration absorber composite isolator. The reduced multi-body system transfer matrix method is used to perform dynamic modeling on the gradient-embedded acoustic black hole and dynamic vibration absorber composite isolator, and its vibration transmissibility T = 20log 10 (|Y O / Y I |) of the steady-state response is calculated. The model simplification and recurrence process are as Figure 4 , and the vibration transmissibility of the gradient-embedded acoustic black hole isolator without the attached dynamic vibration absorber is used as a reference. The results are as Figure 5 . It can be seen that compared with the gradient-embedded acoustic black hole isolator without the attached dynamic vibration absorber, the gradient-embedded acoustic black hole and dynamic vibration absorber composite isolator can achieve a significant attenuation of vibration transmission in 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 resonance modes. The vibration energy is effectively captured and accumulated when passing through each acoustic black hole wedge segment from left to right. At the same time, the damped dynamic vibration absorber structure plays a role in energy absorption, and the energy accumulated by the acoustic black hole is effectively dissipated through damping, as Figure 6 .

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

Claims

1. A design method for a composite vibration isolator of a gradient embedded acoustic black hole and a dynamic vibration absorber based on a reduced multi-body system transfer matrix method, characterized in that: The following steps are involved: (1) Based on the acoustic black hole principle, a gradient structure vibration isolator is designed using multiple embedded acoustic black hole units; (2) Determine the dimensional parameters and material parameters of each part of the gradient embedded acoustic black hole isolator; (3) According to the displacement or force to be isolated, the vibration transmissibility of the gradient embedded acoustic black hole isolator is calculated using the reduced multi-body system transfer matrix method; In the step (3), the reduced multi-body system transfer matrix method is used to perform dynamic modeling on the main structure of the gradient embedded acoustic black hole. The components contained in each acoustic black hole unit adopt a two-dimensional plane Euler Bernoulli uniform beam model, so the gradient embedded acoustic black hole isolator can be regarded as a linear multi-body system composed of a two-dimensional plane Euler Bernoulli uniform beam; 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, and then the reduced transfer matrix and load function related array of each element are recursively deduced according to the topological structure of the multi-body system corresponding to the gradient embedded acoustic black hole isolator; the load and boundary conditions of the isolator are substituted for inverse recursion to calculate the steady-state response of the vibration transmissibility of the gradient embedded acoustic black hole isolator; (4) Determine the installation position and structural parameters of the dynamic vibration absorber according to each order resonance peak of the vibration transmissibility of the gradient embedded acoustic black hole 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, mass ratio μ = m2 / m1, characteristic frequency ratio f = ω2 / ω1, 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; (5) Using the reduced multi-body system transfer matrix method, the vibration transmissibility of the gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator is calculated; The reduced multi-body system transfer matrix method is used to conduct dynamic modeling of the composite vibration isolator with gradient embedded acoustic black hole and dynamic vibration absorber. Each dynamic vibration absorber adopts a spring-damper model with additional mass, so the composite vibration isolator can be simplified into a tree-shaped multi-body system composed of multiple elements. Substitute the parameters given in step (4) into the transfer matrix of the spring damper with additional mass to obtain the transfer matrix of each dynamic vibration absorber element, and then recursively deduce the reduced transfer matrix S and the load function related array e of each element according to the topological structure of the multi-body system corresponding to the gradient embedded acoustic black hole and the dynamic vibration absorber composite isolator; By substituting the load and boundary conditions of the composite vibration isolator for inverse recursion, the steady-state response of the vibration transmissibility of the composite vibration isolator with gradient embedded acoustic black hole and dynamic vibration absorber can be calculated.

2. The gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator design method based on the reduced multi-body system transfer matrix method according to claim 1 is characterized by: 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 a plurality of embedded acoustic black holes and dynamic vibration absorber units with gradient parameter changes.

3. The gradient embedded acoustic black hole and dynamic vibration absorber composite vibration isolator design method based on reduced multi-body system transfer matrix method according to claim 1 is characterized by: The size parameters of the vibration isolator in step (2) include the length L of the nth acoustic black hole unit n , uniform segment length L beam,n , wedge length L ABH,n , wedge segment curve power m, cut-off thickness H d,n , the length gradient of the wedge segment ΔL ABH , the length gradient of the uniform segment ΔL beam , thickness gradient of cut-off thickness ΔH d , and the total thickness H and total width D of the isolator; the material parameters include Young's modulus E, density ρ, and loss factor η.

Images