A design method for gradient reinforced acoustic black hole isolator

Abstract

The present invention discloses a design method of a gradient reinforced acoustic black hole isolator. Based on the acoustic black hole principle, an acoustic black hole isolator including multiple gradient reinforced acoustic black hole units is designed. Compared with a periodic acoustic black hole isolator of the same mass and material, it is found that the gradient reinforced acoustic black hole isolator has better static stiffness and vibration isolation performance.

Description

Technical Field

[0001] The invention belongs to the field of vibration reduction and noise reduction of acoustic black hole structures, and specifically, is a design method for a novel acoustic black hole vibration isolator with a gradient reinforced structure. Background Art

[0002] Vibration isolation is one of the main technologies in the field of vibration control, and plays a key role in precision manufacturing, aerospace, shipbuilding, civil engineering and other fields. Traditional vibration isolators can often only work in low-frequency narrow segments or high-frequency broadbands, and cannot meet the actual vibration isolation requirements of interference frequencies that vary within a low-frequency broadband range. On the other hand, considering the load-bearing requirements in the actual working environment, the vibration isolator must also maintain an effective vibration reduction effect under a larger load environment. How to achieve low-frequency broadband vibration reduction under relatively high structural stiffness and strength is still a difficult problem facing the engineering community. In the past 20 years, due to its compact, lightweight and high energy concentration characteristics, the acoustic black hole structure has been widely studied and paid attention to in the field of vibration reduction. Existing research has proved that the acoustic black hole structure has excellent broadband energy aggregation and loss characteristics, and is an effective broadband vibration absorber at medium and high frequencies. However, the existing acoustic black hole vibration isolators still have the defects of insufficient structural stiffness and strength, and limited low-frequency broadband vibration isolation capabilities, which restricts their progress towards engineering applications. At present, there is still a lack of acoustic black hole vibration isolators with both load-bearing and vibration isolation performance. Design methods. Summary of the invention

[0003] The purpose of the present invention is to provide a design method for a gradient reinforced acoustic black hole isolator.

[0004] The technical solution to achieve the purpose of the present invention is: a gradient reinforced acoustic black hole isolator design method, comprising the following steps:

[0005] (1) Based on the acoustic black hole principle, a gradient structure vibration isolator is designed using multiple embedded double-leaf reinforced acoustic black hole units;

[0006] (2) Determine the size parameters and material parameters of each part of the gradient reinforced acoustic black hole isolator;

[0007] (3) According to the displacement or force to be isolated, the vibration transmissibility of the gradient reinforced acoustic black hole isolator is calculated using the multi-body system transfer matrix method;

[0008] (4) The equivalent flexibility coefficient of the gradient-reinforced acoustic black hole isolator is calculated using the multi-body system transfer matrix method.

[0009] Compared with the prior art, the present invention has the following significant advantages: (1) The gradient-reinforced acoustic black hole isolator has better low-frequency broadband vibration isolation performance. (2) The gradient-reinforced acoustic black hole isolator has higher static stiffness than the traditional non-gradient structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a schematic diagram of a gradient reinforced acoustic black hole isolator.

[0011] Figure 2 It is the frequency response diagram of vibration transmissibility of gradient reinforced acoustic black hole isolator.

[0012] Figure 3 It is the spatial distribution diagram of vibration displacement of gradient reinforced acoustic black hole isolator at different frequencies.

[0013] Figure 4 This is a comparison chart of the vibration isolation transmissibility between the gradient reinforced acoustic black hole isolator and the periodically reinforced acoustic black hole isolator. Figure 4 (a) in the equation is 3 units. Figure 4 Unit (b) 5 in Figure 4 (c) in the equation is 7 units.

[0014] Figure 5 This is a comparison chart of the static stiffness of the gradient-reinforced acoustic black hole isolator and the periodically-reinforced acoustic black hole isolator.

[0015] Figure 6 This is a test verification diagram of the vibration isolation performance of the gradient reinforced acoustic black hole isolator. DETAILED DESCRIPTION

[0016] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0017] The technical solution adopted by the present invention is: designing an acoustic black hole vibration isolator with a gradient reinforced structure comprising multiple acoustic black hole units; determining the size parameters and material parameters of each part of the gradient reinforced acoustic black hole vibration isolator; calculating the vibration transmissibility of the gradient reinforced acoustic black hole vibration isolator; and calculating the equivalent flexibility coefficient of the gradient reinforced acoustic black hole vibration isolator.

[0018] The specific process includes the following 4 steps:

[0019] (1) Based on the acoustic black hole principle, a gradient structure vibration isolator is designed using multiple embedded double-blade reinforced acoustic black hole units, such as Figure 1 shown.

[0020] (2) Determine the size parameters and material parameters of each part of the acoustic black hole isolator;

[0021] (3) According to the displacement or force to be isolated, the vibration transmissibility of the gradient reinforced acoustic black hole isolator is calculated using the multi-body system transfer matrix method;

[0022] (4) Using the multi-body system transfer matrix method, the equivalent flexibility coefficient of the gradient-reinforced acoustic black hole isolator is calculated;

[0023] In the step (1), the vibration isolator base can be a uniform beam structure with a rectangular cross section or a cylindrical uniform beam structure with a circular cross section. The base contains a plurality of double-leaf reinforced acoustic black hole units with gradient parameter changes.

[0024] The isolator size parameters in step (2) include the length L of the nth acoustic black hole unit n , wedge length L ABH,n , the length of the tendon L J,n , cut-off thickness H d,n , and the length gradient ΔL of the wedge segment, the length of the uniform segment d and the total thickness H of the isolator; the material parameters include Young's modulus E, density ρ, and loss factor η.

[0025] In the step (3), the linear multi-body system transfer matrix method is used to perform dynamic modeling on the gradient-reinforced acoustic black hole isolator. The components contained in each acoustic black hole unit adopt the two-dimensional plane Euler Bernoulli uniform beam and non-uniform beam and massless rigid sheet model. Then, the isolator can be regarded as a linear multi-body system composed of a two-dimensional plane Euler Bernoulli uniform beam, a non-uniform beam and a massless rigid sheet. Substitute the parameters given in step (2) into the transfer matrix of the Euler Bernoulli beam and the rigid sheet to obtain the transfer matrix of each element, and then "assemble" the transfer matrix of each element according to the topological structure of the multi-body system corresponding to the gradient-reinforced acoustic black hole isolator to obtain the total transfer matrix. Substitute the load and boundary conditions of the isolator into the total transfer equation to calculate the steady-state response of the vibration transmissibility of the gradient-reinforced acoustic black hole isolator.

[0026] In step (4), the equivalent compliance factor (ECF) is used as a parameter for evaluating the static stiffness of the acoustic black hole structure.

[0027]

[0028] where y ABH and y are the displacements generated by the unit force applied to the free end of the base beam structure containing the acoustic black hole, i.e., the gradient reinforced acoustic black hole structure and the base beam structure without the acoustic black hole, respectively. The larger the ECF, the greater the displacement generated by the structure with the acoustic black hole compared to the structure without the acoustic black hole, indicating that the acoustic black hole has a greater impact on the static stiffness of the structure; conversely, the smaller the ECF, the smaller the displacement generated by the structure with the acoustic black hole compared to the structure without the acoustic black hole, indicating that the acoustic black hole has a smaller impact on the static stiffness of the structure.

[0029] The following simulation experiment is used to further illustrate the invention in conjunction with the accompanying drawings.

[0030] An acoustic black hole isolator with a gradient structure is designed using three acoustic black hole units with gradient changes in parameters, namely Figure 1 Where n=3.

[0031] Determine the size parameters and material parameters of each part of the acoustic black hole isolator:

[0032] The acoustic black hole isolator is made of stainless steel. The material parameters and size parameters of each part are shown in Table 1.

[0033]

[0034]

[0035] Table 1: Material and size parameters of the three-unit gradient-reinforced acoustic black hole

[0036] Calculate the vibration transmissibility of the gradient-reinforced acoustic black hole isolator:

[0037] The linear multi-body system transfer matrix method is used to model the dynamics of the gradient reinforced acoustic black hole isolator and calculate its vibration transmissibility T = 20log 10 (|Y O / Y I |) steady-state response, where Y O and Y I is the lateral displacement of the input and output ends of the system, and the vibration transmissibility of a uniform beam isolator of the same material and size without an acoustic black hole inside is taken as a reference. The results are shown in Figure 2 . It can be seen that compared with the uniform beam, the gradient reinforced beam can achieve significant attenuation of vibration transmission in almost the entire frequency band except for very low frequencies. This is because the designed acoustic black hole acts as a low-frequency broadband trap, including rich low-frequency broadband local resonance modes. The vibration energy is effectively captured and concentrated when passing through each acoustic black hole wedge segment from left to right, especially when passing through the first wedge segment, so that the vibration at the output end is effectively attenuated, such as Figure 3 In addition, in order to further verify the superiority of the vibration isolation performance of the vibration isolator, the vibration isolation transmissibility of the gradient reinforced acoustic black hole vibration isolator and the periodic reinforced acoustic black hole vibration isolator were compared. Figure 4 , both have the same material and mass. It can be seen that the gradient reinforced acoustic black hole isolator has a wider low-frequency vibration isolation band than the periodic reinforced acoustic black hole isolator. Except for very low frequencies, it can achieve almost full-band vibration attenuation, while the periodic structure can only achieve a large vibration attenuation in its stopband frequency range, and its passband frequency vibration transmission is still very high.

[0038] Calculate the equivalent flexibility coefficient of the gradient-reinforced acoustic black hole isolator:

[0039] The gradient-reinforced acoustic black hole isolator with unit force excitation applied to one end is modeled using the linear multi-body system transfer matrix method, and the periodic reinforced beams and gradient reinforced beams of different units are selected to calculate their equivalent flexibility coefficients. Figure 5 That is, the equivalent flexibility coefficient of the gradient reinforced beam is smaller than that of the periodically reinforced beam when the number of units is the same, that is, the static stiffness of the gradient reinforced beam is greater than that of the periodically reinforced beam.

[0040] The above design results have also been verified by experiments. Figure 6 As shown, the vibration transmissibility frequency response of the isolator base structure with embedded gradient reinforced acoustic black hole and without internal acoustic black hole structure was obtained by experimental means. The dimensional parameters and material parameters involved in the experiment are shown in Table 2.

[0041]

[0042] Table 2: Dimensions and material parameters of the gradient reinforced acoustic black hole isolator in the test

Claims

1. A gradient reinforced acoustic black hole isolator design 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 double-leaf reinforced acoustic black hole units; (2) Determine the size parameters and material parameters of each part of the gradient reinforced acoustic black hole isolator; (3) According to the displacement or force to be isolated, the vibration transmissibility of the gradient-stiffened acoustic black hole isolator is calculated using the multi-body system transfer matrix method; the gradient-stiffened acoustic black hole isolator is dynamically modeled using the linear multi-body system transfer matrix method, and the components contained in each acoustic black hole unit are all two-dimensional plane Euler Bernoulli uniform beam and non-uniform beam and massless rigid thin plate models. The isolator is then regarded as a linear multi-body system composed of a two-dimensional plane Euler Bernoulli uniform beam, a non-uniform beam and a massless rigid thin plate; the parameters given in step (2) are substituted into the transfer matrix of the Euler Bernoulli beam and the rigid thin plate to obtain the transfer matrix of each component, and then the transfer matrix of each component is "assembled" according to the topological structure of the multi-body system corresponding to the gradient-stiffened acoustic black hole isolator to obtain the total transfer matrix; the load and boundary conditions of the isolator are substituted into the total transfer equation to calculate the steady-state response of the vibration transmissibility of the gradient-stiffened acoustic black hole isolator; (4) Using the multi-body system transfer matrix method, the equivalent flexibility coefficient of the gradient reinforced acoustic black hole isolator is calculated; the equivalent flexibility coefficient ECF is used as a parameter to evaluate the static stiffness of the acoustic black hole structure. Among them, y ABH and y are the displacements generated by applying a unit force at the free end of the base beam structure containing an acoustic black hole, i.e., the gradient reinforced acoustic black hole structure, and the base beam structure without an acoustic black hole.

2. The gradient reinforced acoustic black hole isolator design method according to claim 1, characterized in that: In 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 double-leaf reinforced acoustic black hole units with gradient parameter changes.

3. The gradient reinforced acoustic black hole isolator design method according to claim 1, characterized in that: The size parameters of the vibration isolator in step (2) include the length L of the nth acoustic black hole unit n , wedge length L ABH,n , the length of the tendon L J,n , cut-off thickness H d,n , the length gradient ΔL of the wedge segment, the length of the uniform segment d and the total thickness H of the isolator; the material parameters include Young's modulus E, density ρ, and loss factor η.

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