Design and preparation method of acoustic black hole dynamic vibration absorber with density power law variation

Abstract

The application discloses a design and a preparation method of an acoustic black hole dynamic vibration absorber with density power law variation, designs and prepares a density power law acoustic black hole and a dynamic vibration absorber with deep subwavelength size based on the acoustic black hole principle; the density power law acoustic black hole unit is designed in a discrete manner so as to determine the size parameters and the material parameters of each part; the high-density tungsten particles uniformly dispersed in a polymer are used as raw materials to prepare the variable-density material required by the density power law acoustic black hole structure; the density power law acoustic black hole unit is prepared by using the prepared variable-density material according to the size parameters and the material parameters of each part of the density power law acoustic black hole structure, the acoustic black hole unit is connected to a main structure through a connector, and the density power law acoustic black hole dynamic vibration absorber is obtained. Compared with a traditional acoustic black hole dynamic vibration absorber with the same geometric length, the density power law acoustic black hole dynamic vibration absorber can realize low-frequency super-wideband damping enhancement and dynamic vibration absorption.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of vibration and noise reduction of acoustic black hole structure, in particular to a design and preparation method of a dynamic vibration absorber of acoustic black hole with power-law varying density. BACKGROUND

[0002] As a new technology, acoustic black hole can achieve broadband wave energy aggregation and damping enhancement effect with light structure due to its unprecedented wave manipulation characteristics. Traditional acoustic black hole is mainly based on power-law tailoring of geometric thickness. The current design and preparation of multi-material acoustic black hole mainly relies on 3D printing technology to manufacture small samples of acoustic black hole with power-law varying stiffness at constant density, and there is still a lack of general design and preparation method of density power-law acoustic black hole with varying density along the length direction of the structure and its dynamic absorber. SUMMARY

[0003] The purpose of the present application is to provide a design and preparation method of a dynamic vibration absorber of acoustic black hole with power-law varying density.

[0004] The technical solution for achieving the purpose of the present application is: a design and preparation method of a dynamic vibration absorber of acoustic black hole with power-law varying density, comprising the following steps:

[0005] (1) Based on the principle of acoustic black hole, a dynamic vibration absorber of acoustic black hole with power-law varying density is designed by using power-law variation of material density;

[0006] (2) The density power-law acoustic black hole unit is discretely designed to determine the size parameters and material parameters of each part;

[0007] (3) The variable density material required for the density power-law acoustic black hole structure is prepared by using high-density tungsten particles uniformly dispersed in the polymer as raw materials;

[0008] (4) According to the size parameters and material parameters of each part of the density power-law acoustic black hole structure, the density power-law acoustic black hole unit is prepared using the prepared variable density material, and the acoustic black hole unit is connected to the main structure through a connector to obtain a dynamic vibration absorber of acoustic black hole with power-law varying density.

[0009] Further, the dynamic vibration absorber in step (1) comprises a one-dimensional density power-law acoustic black hole unit and an equal-section beam as a connector between the acoustic black hole unit and the main structure.

[0010] Further, the density of the density power-law acoustic black hole structure is discretely divided into n sections in step (2), and the density of each section is ρ1-ρ n The length corresponding to the density of each section is l1-l n , which can be obtained by the following formula:

[0011] l i = l x,i+1 - l x,i , l x,i = ((h0 / (p i / p0) 0.5 - h tip ) / e) 0.5 , i e [1, n-1] (1)

[0012] e is the geometric shape factor; other dimensional parameters include uniform section length l xj , thickness h0, total length of density variation section l ABH , truncated thickness h tip , damping layer thickness h d , connector length l j , thickness h j ; other material parameters include the density of the uniform section of the power-law density acoustic black hole structure p0.

[0013] Further, the high-density tungsten particles uniformly dispersed in the PU polymer in step (3) are used as raw materials, wherein the PU polymer is composed of PU rubber and PU resin, so as to prepare the variable-density material required by the power-law density acoustic black hole structure; different materials are mixed according to the following mass ratio:

[0014]

[0015] wherein R1 = M T / M PU , R2 = M resin / M rubber , and the subscript “T” represents tungsten; wherein M resin and M rubber are the total mass of the PU resin and the PU rubber after being mixed with their curing agents, respectively; take the mass of the tungsten powder M T , and take the mass of the two PUs M resin and M rubber , so as to obtain composite material samples with different R1 proportions, i.e., composite material samples with different densities; then adjust the ratio R2 of the PU resin and the PU rubber, and mix the samples with the same R1 and different R2 again, so as to obtain samples with different densities and similar elastic moduli.

[0016] Further, the preparation of the density power law acoustic black hole unit in step (4) adopts a step-by-step solidification scheme; n+1 molds with increasing lengths are used, first, the first mold is used, the raw materials are mixed according to the corresponding ratio and poured into the mold, the first section of the acoustic black hole unit with a length of l1 and a density of v1 is solidified, that is, the first stage solidification is completed; after solidification is completed, the first section sample is demolded and taken out and placed in the second mold, at this time, the remaining length of the second mold is the length corresponding to the second section of the acoustic black hole unit with a density of v2; after the second stage solidification is completed, the above operation is repeated until the n section with a length of l n and a density of p n is solidified; finally, according to the above operation, the n+1 mold is used to complete the solidification of the last uniform section of the acoustic black hole unit with a length of l xj and a density of p0, and the whole solidification of the density power law acoustic black hole unit is completed.

[0017] Compared with the prior art, the present application has the following advantages: 1. The density power law ABH material is prepared based on the principle of composite material for the first time. 2. Compared with the traditional thickness power law ABH, the threshold frequency of the density power law ABH damping enhancement is greatly reduced. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a schematic diagram of a density power law acoustic black hole dynamic vibration absorber and a main structure combination system.

[0019] Figure 2 is a schematic diagram of a sample obtained by material preparation of the density power law acoustic black hole structure.

[0020] Figure 3 is a schematic diagram of step-by-step solidification preparation of the density power law acoustic black hole structure.

[0021] Figure 4 is a steady-state response curve diagram of a driving point on a main structure under point load conditions when the main structure is additionally provided with a density power law acoustic black hole dynamic vibration absorber.

[0022] Figure 5 is a modal loss factor diagram of the density power law acoustic black hole dynamic vibration absorber.

[0023] Figure 6 is a velocity admittance frequency response comparison curve diagram of a driving point on a main structure when the main structure is additionally provided with a density power law acoustic black hole dynamic vibration absorber and not additionally provided with the density power law acoustic black hole dynamic vibration absorber. DETAILED DESCRIPTION

[0024] The technical scheme adopted by the present application is: a density power law acoustic black hole dynamic vibration absorber with power law variation of material density along the length direction of the acoustic black hole structure is designed; the discretization design of the density power law acoustic black hole structure and the determination of the size parameters and material parameters of each part; the variable density material required for preparing the density power law acoustic black hole structure; the preparation scheme of the density power law acoustic black hole structure is determined.

[0025] The present application is further described below in combination with examples.

[0026] The specific process includes the following four steps:

[0027] (1) Based on the principle of acoustic black hole, a density power law acoustic black hole dynamic vibration absorber with power law variation of material density is designed;

[0028] (2) The discretization design is adopted for the density power law acoustic black hole structure to determine the size parameters and material parameters of each part;

[0029] (3) The variable density material required for preparing the density power law acoustic black hole structure is prepared by using the high-density tungsten particles uniformly dispersed in the polymer as raw materials.

[0030] (4) According to the size parameters and material parameters of each part of the density power law acoustic black hole structure, the prepared variable density material is used to prepare the density power law acoustic black hole unit, and the acoustic black hole unit is connected to the main structure through the connector to obtain the density power law acoustic black hole dynamic vibration absorber.

[0031] The dynamic vibration absorber in the step (1) comprises a one-dimensional density power law acoustic black hole unit, and an equal-section beam is used as the connector between the acoustic black hole units to constitute a density power law acoustic black hole structure dynamic vibration absorber.

[0032] In the step (2), the density variation section of the density power law acoustic black hole structure is discretized into 7 sections, and the density of each section is ρ1-ρ7, then the length l1-l7 corresponding to the density of each section can be obtained by the following formula:

[0033] l i =l x,i+1 -l x,i ,l x,i =((h0 / (ρ i / ρ0) 0.5 -h tip ) / ε) 0.5 ,i∈[1,6](1)

[0034] ε is a geometric shape factor; other size parameters include the uniform section length l xj of the acoustic black hole unit, the thickness h0, the total length l ABH of the density variation section, and the truncated thickness htip , damping layer thickness h d , connector length l j , thickness h j Other material parameters include density The uniform section of the density power law acoustic black hole has a density of p0.

[0035] The raw material of the density power law acoustic black hole in step (3) is high-density tungsten particles uniformly dispersed in a PU polymer, which is composed of a softer PU rubber and a harder PU resin. We mixed different materials according to the following mass ratio:

[0036]

[0037] where R1 = M T / M PU , R2 = M resin / M rubber , and subscript "T" represents tungsten. Here M resin and M rubber are the total masses of the PU resin and the PU rubber after mixing with their respective curing agents. Since the PU rubber and the PU resin have the same density, the density of the mixture is consistent when the mixing ratio between each of them and tungsten is the same. First, we mixed the tungsten particles with the PU resin and the PU rubber according to the R1 ratio. We took M T of tungsten powder, and the masses of the two PUs were M resin = M rubber = 0.5M PU = 0.5M T / R1. In this way, we obtained composite material samples of different R1 ratios and composite material samples of different densities. Then we adjusted the ratio R2 of the PU resin and the PU rubber and remixed the samples of different R2 ratios under the same R1 to obtain samples with different densities and similar elastic moduli. That is, we manipulated the density of the composite material without changing the modulus. The specific preparation steps of the density power law composite material are as follows:

[0038] 1) Weigh M W of tungsten powder, take R1 = 0.95, and obtain M PU = M W / R1.

[0039] 2) Take R2 = 0.52, and weigh M rubber = M PU / (R2 + 1) of PU rubber and M resin = R2 x M rubber of PU resin, respectively, where the corresponding masses of the PU rubber curing agent and the PU resin curing agent are weighed according to the different ratios.

[0040] 3) Mix the four polymers evenly according to a predetermined ratio.

[0041] 4) Mix the tungsten powder evenly into the prepared polymer mixture and stir quickly.

[0042] 5) Pour the mixture into a mold. Its size is the same as the DMA test sample size.

[0043] 6) After curing for about 12 hours, a composite material sample with a density of ρ can be obtained.

[0044] 7) After curing, measure the mass and volume of the sample, calculate its density, and use DMA to measure the remaining required parameters.

[0045] 8) Repeat steps 1-7 n times, each time changing only the value of R1 in step 1, denoted as R. 11 R 12 ...R 1n n = 7. This yields samples of different densities. The sample density is denoted as ρ. 11 ρ 12 ...ρ 1n The elastic modulus corresponding to each density value was measured using DMA and denoted as E. 11 E 12 ...E 1n .

[0046] 9) Repeat steps 1-8 m times, with R1 taking the value of R. 11 R 12 ...R 1n Only change the value of R2 in step 2, denoted as R. 21 R 22 ...R 2m m = 3. The density of the obtained sample is denoted as ρ. 21 ρ 31 ...ρ m1 , ρ 22 ρ 32 ...ρ m2 Wait until ρ 2n ρ 3n ...ρ mn The elastic modulus is denoted as E. 21 E 31 ...E m1 E 22 E 32 ...E m2 Wait until E 2n E 3n ...E mn As mentioned above, ρ resin =ρ rubber Therefore ρ 11 =ρ21 ... = ρ m1 , ρ 12 =ρ 22 ... = ρ m2 Similarly, we can obtain ρ 1n =ρ 2n ... = ρ mn Samples with equal density are grouped into a series, and the density of each series is reassigned as ρ1, ρ2, ..., ρ n .

[0047] 10) With R 11 To R 1n The x-axis represents the distance from ρ1 to ρ. n Using the vertical axis as the ordinate, the R1-ρ curve of the sample can be plotted.

[0048] 11) By testing samples with different R2 values ​​under the same R1, the common modulus range for samples of different densities is summarized, and the same Young's modulus E is taken within the error range. b Thus, densities from ρ1 to ρ can be obtained. n The modulus is E b n sample parameters.

[0049] In step (4), the density power-law acoustic black hole unit is prepared using a step-by-step curing scheme. Eight molds of progressively increasing length are used. First, the first mold is used, and the raw materials are mixed according to the corresponding ratio and poured into the mold to complete the first stage of curing of the acoustic black hole unit with length l1 and density ρ1, thus completing the first stage of curing. After curing, the first stage sample is demolded and placed in the second mold. The remaining length of the second mold is the length corresponding to the second stage of the acoustic black hole unit with density ρ2. After the second stage of curing is completed, the above operation is repeated until the nth stage with length l7 and density ρ7 is cured. Finally, following the above operation, the eighth mold is used to complete the final stage of curing of the acoustic black hole unit with length l. xj After the uniform segment with density ρ0 is solidified, the entire solidification of the density power-law acoustic black hole unit is completed.

[0050] The following simulation calculations and experiments, in conjunction with the accompanying drawings, further illustrate this point.

[0051] An acoustic black hole dynamic vibration absorber with a density power-law structure was designed by utilizing the material density variation along the length of the acoustic black hole structure. 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 l of the cantilever beam. z and thickness h z The cantilever beam is made of aluminum. A schematic diagram of the density power-law acoustic black hole dynamic vibration absorber combined with the main structure is shown below. Figure 1 .

[0052] Determination of the size parameters and material parameters of each part of the density power-law acoustic black hole dynamic absorber:

[0053] The target damping range of the density power-law acoustic black hole structure is 25 Hz-1200 Hz, i.e. the lower limit of the target damping frequency range f = 25 Hz. The coating on the acoustic black hole unit is a viscoelastic material.

[0054] The material parameters and size parameters of each part are shown in Table 1, and the remaining size parameters do not require special design.

[0055]

[0056]

[0057] Table 1: Material and size parameters of the density power-law acoustic black hole

[0058] The schematic diagram of the raw material sample of the density power-law acoustic black hole structure is shown in Figure 2 , and the schematic diagram of the step-by-step solidification preparation of the density power-law acoustic black hole structure is shown in Figure 3 After the density power-law acoustic black hole structure is prepared, in order to verify the low-frequency broadband damping effect of the density power-law acoustic black hole dynamic absorber, the density power-law acoustic black hole dynamic absorber is installed at a position of 60% L of the main structure, and the free end of the cantilever beam is subjected to a unit harmonic load, as shown in Figure 1 The steady-state response of the mobility of the driving point on the main structure is calculated by simulation calculation with and without the density power-law acoustic black hole dynamic absorber:

[0059] The linear bifurcated multi-body system transfer matrix method is used for dynamic modeling of the combined system, and the Euler-Bernoulli beam model is used for each part of the combined system, and the combined system is simplified as a multi-element bifurcated multi-body system. The transfer matrix of each element is obtained by substituting the given parameters into the transfer matrix of the Euler-Bernoulli beam, and the total transfer matrix is obtained by "assembling" the transfer matrix of each element according to the topological structure of the bifurcated multi-body system corresponding to the combined system. The boundary conditions and point loads of the combined system are substituted into the total transfer equation, and the steady-state response of the driving point on the main structure with the density power-law acoustic black hole dynamic absorber is calculated. When the main structure is not attached with a dynamic absorber, only the size parameters of the dynamic absorber in the given parameters are set to 0, and the steady-state response of the driving point on the main structure under the same boundary conditions and load conditions without the dynamic absorber is obtained. The velocity mobility (Mobility = 20 log jωY / F) steady-state response of the driving point of the cantilever beam with two types of acoustic black hole dynamic absorbers is calculated, and the driving point mobility frequency response of the same cantilever beam without the dynamic absorber is taken as the reference, and the results are shown in Figure 4The calculation results demonstrate that with the introduction of density power-law ABH-DVA, the resonance peaks of the main beam at all orders are significantly suppressed within the target frequency range.

[0060] 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 density power-law acoustic black hole dynamic vibration absorber. Figure 5 The modal loss factors of the density power-law acoustic black hole dynamic vibration absorber were compared with those of the corresponding traditional thickness power-law acoustic black hole dynamic vibration absorber. It is evident that the threshold frequency for enhanced damping of the density power-law ABH is significantly lower than that of the traditional thickness power-law ABH.

[0061] The above design results and calculations have also been verified by experiments, such as... Figure 6 As shown in Table 1, the velocity admittance frequency response of the driving point on the main structure was obtained experimentally with and without the density power-law acoustic black hole dynamic vibration absorber. The dimensional parameters involved in the experiment are shown in Table 1. The experimental results prove the correctness of the density power-law ABH-DVA design, fabrication method, and simulation calculation results. Within the target frequency range, the vibration reduction effect of the designed density power-law ABH-DVA is significant and reliable.

Claims

1. A method for designing and fabricating a density power-law-dependent acoustic black hole dynamic vibration absorber, characterized in that, Includes the following steps: (1) Based on the principle of acoustic black holes, a power-law change acoustic black hole dynamic vibration absorber with density power-law change is designed. (2) Discretization design is adopted for density power-law acoustic black hole units to determine the size and material parameters of each part; (3) By using high-density tungsten particles uniformly dispersed in polymer as raw materials, variable density materials required for density power-law acoustic black hole structures are prepared. In step (3), high-density tungsten particles uniformly dispersed in PU polymer are used as raw materials. The PU polymer is composed of PU rubber and PU resin, thereby preparing the variable density material required for the density power law acoustic black hole structure. Mix the different materials according to the following mass ratio: In the formula, R1 = M T / M PU R2 = M resin / M rubber The subscript "T" indicates tungsten; where M resin With M rubber The total mass of PU resin and PU rubber after being mixed with their respective curing agents; take mass M. T Tungsten powder, with a mass of M for both types of PU. resin M rubber This allows us to obtain composite material samples with different R1 ratios, which in turn yield composite material samples with different densities. Then, by adjusting the ratio R2 of PU resin and PU rubber, we can remix samples with different R2 ratios under the same R1 ratio to obtain samples with different densities but similar elastic moduli. (4) Based on the size and material parameters of each part of the density power law acoustic black hole structure, a density power law acoustic black hole unit is prepared using the prepared variable density material. The acoustic black hole unit is connected to the main structure through a connector to obtain a density power law changing acoustic black hole dynamic vibration absorber.

2. The design and fabrication method of the acoustic black hole dynamic vibration absorber with density power law variation according to claim 1, characterized in that: The dynamic vibration absorber described in step (1) includes a one-dimensional density power-law acoustic black hole unit and a beam with a constant cross-section that serves as a connector between the acoustic black hole unit and the main structure.

3. The design and fabrication method of the acoustic black hole dynamic vibration absorber with density power law variation according to claim 1, characterized in that: In step (2), the density variation segment of the density power-law acoustic black hole structure is discretized into n segments, each with a density of ρ1-ρ2. n The length corresponding to each density segment is l1-l n It can be obtained from the following formula: l i =l x,i+1 -l x,i ,l x,i =((h0 / (ρ) i / ρ0) 0.5 -h tip ) / ε) 0.5 ,i∈[1,n-1](1)ε is the geometric shape factor; other size parameters include the uniform segment length l of the acoustic black hole unit. xj Thickness h0, total length l of density variation section ABH Cut-off thickness h tip Damping layer thickness h d Connector length l j Thickness h j Other material parameters include the density power-law acoustic black hole structure with a uniform segment density of ρ0.

4. The design and fabrication method of the acoustic black hole dynamic vibration absorber with density power law variation according to claim 1, characterized in that: In step (4), the density power-law acoustic black hole unit is prepared using a step-by-step curing scheme. Using n+1 molds with progressively increasing lengths, the first mold is used. The raw materials are mixed according to the corresponding proportions and poured into the mold to complete the curing of the first segment of the acoustic black hole unit with length l1 and density ρ1, thus completing the first stage of curing. After curing, the first segment sample is demolded and placed into the second mold. The remaining length in the second mold is the length corresponding to the second segment of the acoustic black hole unit with density ρ2. After the second stage of curing is completed, the above operation is repeated until a segment of length l is completed. n Density is ρ n The nth segment is cured; finally, following the above steps, the (n+1)th mold is used to complete the final segment of the acoustic black hole unit with a length of l. xj After the uniform segment with density ρ0 is solidified, the entire solidification of the density power-law acoustic black hole unit is completed.

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