CN109754777A - A multi-cellular cooperatively coupled acoustic metamaterial structure design method - Google Patents

Abstract

The invention discloses a multi-cellular cooperatively coupled acoustic metamaterial structure design method, which is divided into two types: a structural design method with insufficient localized stiffness and a structural design method with sufficient localized stiffness; The structural design method uses a partition frame with a localized stiffness lower than the stiffness of the thin plate to separate the local resonance cells, so that a strong coupling resonance behavior occurs between the single cells, and a multi-cell composite structure with a lumped coupling resonance effect is formed. ; Structural design method with sufficient localized stiffness, using a partition frame with localized stiffness higher than sheet stiffness, so that the resonance between individual cells does not affect each other within the design frequency band, and then through multiple sheet widths, sheet thicknesses or The cells with the gradient distribution of the weight structure parameters of the additional mass are combined into a multi-cell combined structure. The invention can be applied to various vehicles and various architectural decorations, and provides a brand-new noise reduction scheme for creating a low-noise environment.

Description

A multi-cellular cooperatively coupled acoustic metamaterial structure design method

technical field

The invention belongs to the technical field of acoustic metamaterials, and in particular relates to a multi-cell collaboratively coupled acoustic metamaterial structure design method for realizing low-frequency broadband ultra-strong acoustic attenuation.

Background technique

Existing sound insulation structures are generally bulky and thick homogeneous plates, which are difficult to meet the actual noise reduction requirements in fields with high requirements for light weight. In addition, the sound insulation performance of these homogeneous sound insulation structures obeys the change law of the law of mass, and the sound insulation effect is good in high frequency bands, but the sound insulation performance in low frequency bands is very poor. This severely restricts the design of vehicle sound insulation components and hall sound insulation structures, and poses technical challenges to low-frequency sound insulation. Acoustic metamaterials developed in recent years have provided new solutions for low-frequency sound absorption, sound insulation and vibration reduction, especially thin-film structures, which can achieve low-frequency sound absorption and sound insulation through ultra-thin and ultra-light structures. However, since these designs all rely on the local resonance properties of the structure, only narrow-band acoustic attenuation can be achieved. Although the multi-layer structure can obtain broadband sound insulation performance, the thickness increases exponentially, which is not conducive to practical engineering applications. Considering that in many practical applications, the noise is broadband, therefore, it is very necessary to design low-frequency broadband sound absorption and sound insulation structures.

In 2000, the research team of Professor Shen Ping of Hong Kong University of Science and Technology published a paper in Science, proposing a local resonant phononic crystal with dynamic equivalent negative mass density, breaking the constraint between the lattice size and the wavelength of the acoustic wave. Low frequency vibration and noise control provides new ideas. After that, the researchers proposed a large number of local resonance phononic crystal structures and proposed the concept of acoustic metamaterials. In terms of sound insulation, in 2008, Yang Zhiyu et al. proposed a two-dimensional thin-film acoustic metamaterial with dynamic equivalent negative mass density, which was obtained in a low-frequency narrow band with an ultra-thin and lightweight structure with a thickness as low as millimeters. Excellent sound insulation properties. Then they achieved low-frequency broadband sound insulation by stacking multiple layers. In terms of sound absorption, in 2012, Mei Jun and others designed a thin-film dark acoustic metamaterial with low-frequency broadband super sound absorption properties. Thin-film acoustic metamaterials have attracted the attention of a large number of researchers due to their relatively small structural thickness and areal density.

Although thin-film and thin-plate acoustic metamaterials also belong to local resonance acoustic metamaterials in terms of physical properties. However, considering its advantages of small thickness and low areal density, it is expected to be the best choice for solving the problem of low-frequency vibration and noise reduction in engineering practice, so it is introduced separately here, and it is determined as the research focus of this paper. Thin-plate acoustic metamaterials are generally arranged on a continuous thin plate with periodic holes or columns. The thickness of the plate, the size and shape of the holes and columns are adjustable. Membrane-type acoustic metamaterials are different from thin-plate-type structures. Generally, a frame is used to separate a single cell, and a mass block is arranged on the membrane. Since the membrane is not stiff enough to overcome its own gravity, tension is required to propagate the vibrations. Therefore, in membrane-type acoustic metamaterials, not only the unit size and shape of the membrane can be adjusted, but also the membrane tension. In addition, the resonant frequency and acoustic properties of the unit can be adjusted by changing the shape, weight, number, and position of the mass.

The study of thin plate and film-like structures has a long history. As early as 1957, Cohen et al. studied a circular film with a fixed boundary with a mass, revealing the vibration characteristics of this structure and the influence of the resonance frequency. factor. In 1964, Romilly gave an analytical solution for the vibration frequency and mode shape of a boundary-fixed thin-film structure in a rigid cylindrical tube, and obtained the resonance frequency, anti-resonance frequency and transmittance of the structure under the condition of plane wave incidence. The study also showed that thin-plate structures have similar properties, including double-layer structures. In 1984, Kriegsmann et al. studied the acoustic scattering behavior of thin films and explored the interaction of fluids with thin films, showing that fluids reduce the resonant frequency of thin films. In 1985, Ahluwalia used the matched asymptotic expansion method to study the scattering properties of monochromatic plane acoustic waves by thin films and sheets in the long-wave limit. In 1995, Norris et al. studied the acousto-structure interaction between thin films and acoustic waves, deeply analyzed the variation of the diffraction coefficient with frequency, and proposed the quasi-resonance phenomenon. In 2006, Amabili et al. studied the vibration characteristics of a rectangular thin plate structure with a mass block under simply supported and fixed boundary conditions, and analyzed the influence of the mass's moment of inertia on the vibration frequency. In 2007, Bonello et al. studied the propagation law of Lamb waves in thin plates under the long-wave limit, and explored the effect of surface coatings on thin plates.

In 2008, Professor Zhiyu Yang of Hong Kong University of Science and Technology and others proposed a thin-film acoustic metamaterial based on the theory of local resonance. The lightweight structure with a thickness as low as micron level successfully obtained excellent sound insulation ability in low frequency band, which is a low-frequency noise reduction. Offers a whole new solution. Since the earliest proposed thin-film metamaterials can only obtain good sound insulation in a very narrow frequency band near the anti-resonance frequency, in subsequent studies, the use of thin-film acoustic metamaterials to obtain sound attenuation in a wider frequency band is a common problem. topic of general interest. Yang Zhiyu et al. obtained high sound attenuation in the broadband of 50Hz to 1500Hz by means of multi-layer superposition. Naify et al. successively obtained multiple resonance sound insulation peaks through the annular mass block and the planar cell array, and studied the influence of the unqualified frame on the sound insulation, indicating that the unqualified frame will cause the overall effect of the structure and increase the effective sound insulation frequency band width. Zhang et al. also studied and obtained multiple sound insulation peaks by using different mass blocks through connected cells, and the research by Naify et al. belongs to the in-plane multi-element coupling behavior. In 2014, Chen et al. successively used the thin-plate model and the thin-film model to study the energy dissipation mechanism of thin-film acoustic metamaterials through theoretical derivation.

In addition to thin-film acoustic metamaterials for sound insulation, in 2012, the research group of Prof. Shen Ping from Hong Kong University of Science and Technology also proposed a thin-film dark acoustic metamaterial with broadband and super sound-absorbing properties at low frequencies, which improved the thin-film type. Solutions for acoustic metamaterials in low-frequency noise control. In this study, a rectangular membrane structure was used, and each cell was arranged with two symmetrical semi-circular iron-sheet masses separated by a rigid plastic frame. Under the excitation of sound waves, the two semi-circular iron pieces flap like two wings of a bird, thereby realizing energy loss. A very important factor in this study is that a back cavity needs to be arranged behind the membrane structure. In 2014, the team used an elastic film structure with a back cavity, and successfully achieved perfect sound absorption in the low frequency band through a vertical incident standing wave tube experiment. At the same time, the structure also has the characteristic of tunable phase, that is to say, this work simultaneously realizes the acoustic metasurface from the experimental level. In addition, another work of theirs also designed a bilayer elastic film structure with dual negative parameters at the same time, revealing the coupled resonance behavior between the two films in a single cell.

Thin-plate-like structures are common structural forms for composing two-dimensional periodic structures, and have received extensive attention from researchers in the study of phononic crystals and acoustic metamaterials. In the early studies of Bragg scattering phononic crystals, researchers have done a lot of research on plate-like structures, such as perforated plates and pillars embedded in another material. In terms of local resonance, in 2007, Wu et al. studied the thin plate-like structure earlier, and obtained a local resonance acoustic forbidden band of Lamb wave mode by filling the periodic holes of the thin plate with soft rubber material. On the other hand, in 2008, Wu et al. and Pennec et al. independently reported structures with periodic columns arranged on thin plates, and analyzed the influence factors of Lamb wave mode conversion and band gap in thin plate-like structures. In this configuration, the heavier cylinders arranged on the thin plate are equivalent to forming a "solid-state Helmholtz resonator", which can obtain a vibrational bandgap in the low frequency range below the Bragg bandgap. On the basis of the thin plate with column structure, Oudich et al. proposed a double-layer column structure, and analyzed the vibration mode and band gap mechanism of the cell. The band gap obtained by these structures is still above kHz, which is difficult to meet the needs of controlling low-frequency vibration and noise. In general, Lamb propagation and mode conversion in thin-plate-like structures have become a research hotspot, and many local resonance thin-plate-like structures and derived structures have been proposed by researchers. Among them, low-frequency vibration reduction and noise reduction is an important branch of this research, which has attracted the general attention of many researchers in the fields of mechanics and engineering.

Abundant surface waves are generated in thin plate-like structures, therefore, they have very important research value and wide potential applications. As early as 1998, Tanaka et al. studied surface acoustic waves generated in two-dimensional elastic periodic structures. In 2004, Wang Gang et al. of the National University of Defense Technology studied the two-component local resonance structure in which soft rubber columns are periodically arranged in an epoxy resin matrix. In 2006, the research group of Professor Cheng Jianchun of Nanjing University studied the low-order Lamb wave band gap of one-dimensional thin plate composite structure, and the forbidden band frequency is in the MHz frequency band. In 2008, Chen et al. studied surface waves and mode conversion mechanisms in thin-plate structures. The bandgap frequencies obtained by the above structures are relatively high, and it is difficult to use them in low-frequency vibration reduction and noise reduction. Professor Zuo Shuguang of Tongji University and others explored the application of thin plate with column structure in the vibration reduction of body roof. Numerical simulation shows that the low frequency vibration of the roof is attenuated by more than 30dB. The research team of Professor Wu Jiuhui of Xi'an Jiaotong University successively proposed the structure and sandwich structure with helical beams and convolutional beams in the plate, and obtained a wider band gap in the low frequency band.

To sum up, the thickness of thin-film acoustic metamaterials can be as low as micrometers, and the areal density is also very low. So far, it is the most promising alternative for solving low-frequency vibration and noise problems in engineering practice. However, for practical engineering applications, it has been repeatedly emphasized that there are the following two problems: First, the stiffness of the elastic film is very low, the acoustic and mechanical properties are unstable, and it strongly depends on the film tension, which is difficult to quantify. control; secondly, the membranes that generally constitute elastic membrane acoustic metamaterials are often made of superelastic silicone rubber materials, which are very easy to age even if they are not under load, and the silicone membranes in elastic membrane acoustic metamaterials must withstand tension, which greatly reduces material life. These faced problems greatly limit its application range. In fact, the use of a material with a higher modulus of elasticity can also have the effect of eliminating the tension dependence, that is, using a rigid sheet that does not require tension. However, the elastic modulus of the rigid sheet is much larger than that of the elastic film, and its natural frequency is naturally much higher, so it is difficult to design the local resonance low-frequency vibration and noise reduction structure. To this end, the present invention provides a multi-cell synergistic coupling acoustic metamaterial structure design method through a novel integrated unit structure design concept and a thin plate structure as the basic object, which can be further divided into a structural design method with insufficient localized stiffness and a localized structural design method. There are two methods for designing structures with sufficient domain stiffness. The structure designed by this method can overcome a series of shortcomings in the thin film structure that hinder practical engineering applications, and provide a technical solution for the design of an acoustic structure with a lightweight, ultra-thin low-frequency broadband sound wave with super attenuation.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a multi-cell synergistic coupling acoustic metamaterial structure design method for guiding the design of low-frequency broadband super sound absorption or sound insulation structure, in order to achieve ultra-light and ultra-thin structure, to achieve super low-frequency broadband acoustic wave Attenuation effect.

The present invention adopts following technical scheme to realize:

A multi-cellular synergistic coupling acoustic metamaterial structure design method, which is divided into two types: a structural design method with insufficient localized stiffness and a structural design method with sufficient localized stiffness; wherein,

The structural design method with insufficient localized stiffness uses a partition frame with a localized stiffness lower than the stiffness of the thin plate to separate the local resonance cells, so that a strong coupling resonance behavior occurs between the single cells, and a lumped coupling resonance effect is formed. The multicellular composite structure of ;

The structural design method with sufficient localized stiffness adopts the partition frame whose localized stiffness is higher than that of the thin plate, so that the resonance between single cells does not affect each other in the design frequency band, and then through multiple thin plate widths, thin plate thicknesses or additional The cells of the mass weight structure parameter gradient distribution are combined into a multi-cell combined structure.

A further improvement of the present invention is that the structural design method with insufficient localized stiffness specifically includes the following steps:

1) Select the unit cell structure form of the film or sheet structure;

2) on the basis of step 1), using ethylene-vinyl acetate copolymer as a framework, a supercellular structure composed of a plurality of cells is designed;

3) According to actual needs, further adjust and optimize the lattice constants, sheet thickness, additional mass weight, frame edge width and frame thickness structural parameters of a single cell and frame.

A further improvement of the present invention is that it also includes adding a back cavity to the cell, and the structure can achieve a low-frequency broadband super sound absorption effect.

A further improvement of the present invention is that the structural design method with sufficient localized rigidity specifically includes the following steps:

1) Select the unit cell structure form of the film, thin plate or resonant cavity structure;

2) According to the principle of cell resonance frequency gradient distribution, select the lattice constant, thickness, additional mass weight structure parameters of the film and sheet, or the cavity size of the resonance cavity structure, and carry out the multi-cellular structure design of parameter gradient distribution;

3) Using a hard material with a localized stiffness higher than that of films and sheets as a partition frame, a plurality of cells with the designed parameter gradient distribution are combined into a supercell;

4) According to actual needs, further adjust and optimize the lattice constant of a single cell, the thickness of the thin film and the thin plate, the weight structure parameters of the additional mass, or the cavity size of the resonant cavity structure.

A further improvement of the present invention is that it also includes adding a back cavity to the single-layer board structure used as sound insulation, and the structure can achieve a low-frequency broadband super sound absorption effect.

The present invention has following beneficial technical effect:

1. The present invention cleverly converts the negative effect of the overall effect into a positive effect that is beneficial to the improvement of sound insulation performance by introducing a flexible frame structure with insufficient localized rigidity and utilizing the strong coupling interaction between the flexible frame and the cell. , the structure designed by this design method has excellent sound insulation performance, even without the mass block, the average sound insulation within 1600Hz exceeds 20dB;

2. In the design method of the present invention, the flexible frame part acts as an irregular mass block, thereby greatly improving the sound insulation of the entire multi-cellular structure;

3. When an iron mass block is added to each cell in the structure designed by the invention, the sound insulation performance can be further improved, and the average sound insulation within 1600 Hz is close to 32dB, which truly realizes the low-frequency broadband super sound insulation;

4. The present invention also introduces modal displacement to quickly evaluate the design scheme. In the structure designed by the present invention, by selecting the elastic parameters of the thin plate with gradient distribution in each cell, it can achieve broadband and super sound insulation. The calculation results show that within 2000Hz The average sound insulation is about 40dB, and the minimum sound insulation is as high as 23dB;

5. In the structure designed by the present invention, by selecting the mass block parameters of the gradient distribution and adopting the mechanism with a back cavity, the low-frequency broadband sound absorption effect with an average sound absorption coefficient exceeding 0.8 within 800 Hz can be achieved, and the minimum sound absorption coefficient is not low. at 0.5.

6. In the structure designed by the present invention, in addition to realizing multiple sound insulation and sound absorption peaks, the amplitude at the valley value has also been greatly improved;

7. In the structure designed by the present invention, three mass blocks with different thicknesses are used, which are 1-layer, 3-layer and 5-layer iron sheets respectively. Through experiments, the broadband sound insulation effect of the multi-cell collaborative coupling design can be verified. In addition to the appearance of two sound insulation peaks, the sound insulation at the valley value is also greatly improved. In the measurement frequency band within 1600Hz, the minimum sound insulation is higher than 24dB, and the average sound insulation is close to 30dB.

To sum up, according to the above characteristics of the multi-cell synergistic coupling acoustic metamaterial structure design method for realizing low-frequency broadband super sound attenuation provided by the present invention, on the one hand, the overall effect, which plays a role in traditional sound insulation, is successfully achieved. On the other hand, by using the synergistic coupling resonance between cells with gradient distribution of multiple structural parameters, not only can multiple sound insulation be obtained It can realize the effect of broadband super sound attenuation, and also greatly improve the sound insulation amount or the amplitude of the sound absorption coefficient at the valley value, and truly realize the super attenuation performance of low frequency broadband sound waves. Since the essence of this acoustic metamaterial design method is the modulation of the localized stiffness between cells to obtain the lumped coupled resonance effect, or the modulation of the parameters between cells to obtain the cell structure parameters of the gradient distribution, so Applicable to the design of almost all types of local resonance artificial microstructures. The invention can provide a core technical basis for the design of sound insulation interior parts of automobiles, trains, planes, ships and other equipment, or the design of sound insulation and sound absorption structures in buildings.

Description of drawings

Figure 1a shows a thin-plate multi-cell synergistically coupled acoustic metamaterial structure using a flexible polyester frame; Figure 1b shows a thin-plate multi-cell synergistically coupled acoustic metamaterial structure using a rigid plastic frame; Figure 1c shows each cell with a Thin-plate multi-cell synergistically coupled acoustic metamaterial structure of cylindrical iron mass;

Figure 2 shows the comparison of the measurement results of the sound insulation of different frames without the mass block structure and the measurement results of the uniform plate with similar areal density and the prediction results of the mass density law;

Figure 3 shows the measurement results of sound insulation of different frame belt mass block structures and the comparison with the prediction results of the mass density law;

Fig. 4a is a schematic diagram of the multi-cellular cooperative coupling structure; Fig. 4b is the modal displacement calculation result of the multi-cellular cooperative coupling structure with parameter gradient distribution;

Figure 5a is the calculation result of the sound insulation and reflection coefficient of the multi-cellular cooperative coupling structure with parameter gradient distribution; Figure 5b is the calculation result of the thickness direction displacement of the sheet of the multi-cellular cooperative coupling structure with parameter gradient distribution; Figure 5c is the multi-cellular cooperative coupling structure with parameter gradient distribution The calculation result of the strain energy density of the structural sheet; Fig. 5d shows the calculation result of the sound absorption coefficient of the multi-cellular synergistic coupling structure with the parameter gradient distribution;

Figure 6a is a schematic diagram of the experimental sample of the multi-cell synergistic coupling structure; Figure 6b is the measurement result of the sound insulation of the multi-cell synergistic coupling structure with parameter gradient distribution and uniform distribution.

Detailed ways

The present invention will be described in further detail below in conjunction with the accompanying drawings.

(1) Design scheme of flexible frame multi-cell synergistic coupling structure

Looking at all local resonance structures, the overall effect caused by the insufficient localized stiffness of the partition unit will attenuate or even completely disappear the structure's ability to control mechanical waves. Therefore, the overall effect has become a major negative for the design of local resonance structures. factor. By adopting the flexible frame multi-cell cooperatively coupled acoustic metamaterial structure design method provided by the present invention, a type of ultra-light, ultra-thin, and rigid sheet-type acoustic metamaterial structure with lumped coupling resonance effect is designed. This type of structure consists of two elastic lightweight polyester (or plastic) frames sandwiched by a rigid nylon sheet with a thickness of 0.2mm. Compared with the previously reported elastic film-type acoustic metamaterial structures, theoretically, the tension dependence of the film is completely eliminated after the rigid sheet is used. Here, a rigid nylon sheet with greater stiffness is used, and then a larger size integrated unit sample is designed. For rigid thin-plate structures, it is advantageous to use a structure with a larger plane size, and there is no need for too many auxiliary structures with sufficiently large localized stiffness to ensure the sound attenuation capability of the structure. Such auxiliary structures often contribute the most to the surface density. , thereby greatly reducing the areal density of the overall structure. In addition, by using a frame with insufficient localized stiffness to act as both localized stiffness and additional mass, coupled bending resonance of the frame and the thin plate can be achieved. Coupling resonance can not only reduce the resonant frequency of the overall sample and move the effective sound insulation band to low frequencies, but also effectively transform the overall resonance effect, which is originally unfavorable for low frequency sound insulation, into a positive factor that can improve sound insulation.

First, the corresponding metamaterial samples were fabricated and tested for sound insulation by using the B&K-4206T standing wave tube test system. The diameter of the samples was 100 mm. As shown in Figure 1a and Figure 1b, the designed structural specimen of polyester frame sandwiched with nylon sheet has an areal density of about 1.4kg/m ² and adopts a square lattice form. For the type A cells in the figure 1. The lattice constant is 24mm, the thickness of the rigid nylon sheet 2 is 0.2mm, and the thickness of the polyester frame 3 is 1.5mm. The Young's modulus, Poisson's ratio and density of nylon sheet 2 are 4GPa, 0.28 and 1150kg/m ³ ; those of polyester are 0.2GPa, 0.45 and 936kg/m ³ ; and those of plastic are 206GPa, 0.33 and 7850kg, respectively /m ³ . At the same time, for the B-type supercell 4 in the figure, a sample using a plastic frame 5 without a mass was also fabricated, as shown in Figure 1b. The sample was excited by a broadband plane acoustic wave in a standing wave tube with a frequency range of 4-1600 Hz with a step size of 4 Hz.

In addition to the structure without the mass block, samples with polyester and plastic frames, respectively, with a cylindrical iron sheet mass block 6 were also fabricated and tested for sound insulation, as shown in Figure 1c. Between the frame 7 and the film 8, the film 8 and the mass 6 are bonded together by high-strength glue, the polyester frame 3 is made by hand with a knife, and the plastic frame 5 is made by 3D printing. It can be seen from Figure 1a that the entire sample can also be regarded as an integrated unit, which consists of a B-type supercell 4 composed of 4 A-type cells 1 in the center and 8 A-type cells 1 next to it. In this case, the B-type supercell 4 can be regarded as a master cell, and the 8 A-type supercells 1 next to it can be regarded as slave cells. This is actually an overall effect. When the localized stiffness of the frame is large enough, the overall effect will not be excited, and the low-order vibration mode of the whole sample is determined by the eigenfrequency of the A-type cells; and when the frame is localized When the stiffness is insufficient, the frame and the membrane will be coupled, and the low-order vibration mode of the entire structure will be determined by the coupled resonance mode of the membrane and the frame. The structural form of the master cell-slave cell integrated unit is equivalent to the utilization of the overall effect, which can not only move the resonant frequency of the sample to the low frequency, but also use the frame as part of the effect of additional mass, which can improve the sound insulation performance.

The sound insulation of two groups of metamaterial samples with different frame materials and a uniform polyester sheet sample (control group) obtained from the test is shown in Figure 2. In the figure, the frequencies indicated by the black arrows are 234Hz, 580Hz and 1140Hz in turn; the frequencies indicated by the blue arrows are 400Hz and 963Hz respectively; the black solid line represents the sound insulation of the polyester frame specimen, and the blue solid line is the plastic frame test piece The sound insulation of the piece, the red solid line represents the sound insulation of a uniform polyester sheet with a thickness of 1.5mm. In the figure, the sound insulation data predicted by the law of mass density when the areal density is 1.4kg/m ² is also given, which is indicated by the magenta dotted line. By comparing the sound insulation test data of samples made of polyester and plastic frames, it can be found that in the frequency band below 1140Hz, the sound insulation amplitude of the polyester frame structure specimen is much higher than that of the uniform polyester sheet specimen. The maximum gain reaches 28dB at 580Hz, and the average gain is also as high as nearly 20dB. Even if only the frequency band after the first sound insulation valley (the critical frequency of stiffness control region and damping control region in sound insulation theory) is considered, that is, the frequency band above 234Hz, the maximum sound insulation amount achieved at 580Hz is as high as 39dB. Since the sound insulation is a logarithmic value, a sound insulation of 40dB means that the amplitude of the transmitted sound pressure is only 1% of the incident sound pressure, and the attenuation amplitude is as high as 99%.

Here, the acoustic peak of the structure is also caused by the anti-resonance of the structure, which is consistent with the earliest reported thin-film acoustic metamaterials, so the acoustic attenuation is mainly caused by reflection. In the frequency range below 1000Hz, the average sound insulation of this metamaterial is close to 25dB, which is equivalent to less than 6% of the transmitted sound pressure, and the attenuation amplitude exceeds 94%. In addition, in addition to the stiffness control area, the frequency bandwidth of the sound insulation exceeding 30dB has also reached nearly 200Hz, which fully reflects the outstanding broadband sound insulation capability. Compared with the previous elastic thin-film acoustic metamaterial structures, this rigid sheet-type acoustic metamaterial can achieve higher sound insulation through a single-layer structure, and even no additional mass is required. Except for the approximately 1/4 area covered by the frame, the remaining 3/4 area of the specimen is only 0.2mm thick, as thin as a piece of ordinary paper! Since the rigidity of the nylon sheet is large enough, no initial tension is required, so the sound insulation performance is stable enough.

By comparing the sound insulation test data of the structure composed of the frame of two different materials, the harder plastic and the softer polyester in Figure 2, it is shown that due to the coupling interaction between the frame and the nylon sheet, the overall stiffness ratio of the polyester frame specimen is higher than that of the frame. The plastic frame specimen is small, and the coupling resonance frequency is correspondingly lower. This results in the frequency of the first sound insulation valley of the polyester frame specimen (solid black line) appearing ahead of that of the plastic frame specimen (solid blue line) at about 234 Hz and the latter at about 234 Hz. About 400Hz, and the sound insulation of the polyester frame specimen at the sound insulation valley is about 6dB higher than that of the plastic frame specimen. Similarly, the frequency of the sound insulation peak of the polyester frame specimen is also ahead of that of the plastic frame specimen, the former appears at about 580 Hz, and the latter appears at about 963 Hz, and the sound insulation of the polyester frame specimen is at the sound insulation peak. It is about 5dB higher than the plastic frame specimen. Since the rigidity of the polyester frame is much smaller than that of the nylon sheet, the coupling resonance energy dissipation effect occurs at the connection parts, resulting in the sound insulation of the polyester frame specimens is higher than that of the plastic frame specimens, regardless of the sound insulation valley or the sound insulation peak. The reason why the sound insulation of the polyester frame structure is higher than that of the plastic frame structure at the first-order peaks and valleys is that the energy dissipation of this metamaterial is realized by the coupled bending vibration of the frame and the thin plate, and the frame In addition to the role of providing stiffness, more importantly, through the coupling with the thin plate, a certain additional mass is applied to the thin plate. Since the stiffness of the polyester frame is much smaller than that of the plastic, the additional mass imposed by the polyester frame on the thin plate is larger, and the low-order vibration mode of the whole sample is dominated by the thin plate, so the sound insulation of the polyester frame specimen is always higher than that of the plastic frame. The height of the test piece.

Although the bulk effect is present in all samples, only a well-designed acoustic metamaterial structure can substantially improve the sound-attenuating capability of the structure through this bulk effect. The coupled resonance effect is absent in previously proposed elastic membrane-type acoustic metamaterials, because in those structures, the stiffness of the elastic membrane is many orders of magnitude smaller than that of the frame, and the localized stiffness of the frame is sufficiently high that there is no difference between the cells. There are coupled resonance modes. That is, for the lumped coupling resonance effect to occur, the condition that needs to be satisfied is that the bending stiffness of the frame is lower than or close to that of the thin plate.

In the research of elastic thin-film acoustic metamaterials, the resonance frequency of the structure is often adjusted by adding mass blocks, and it can also increase the sound insulation and sound absorption coefficient. Here, mass blocks were added to the two frame structures respectively, and the samples were tested. The test results are shown in Figure 3. In the figure, the black solid line represents the sound insulation of the tested polyester frame specimen, and the red solid line represents the sound insulation of the tested plastic frame specimen. The areal density of the two structures after adding the mass block is about 3kg/m ² , and the magenta dotted line in the figure shows the prediction result of the mass density law corresponding to the areal density. Comparing the sound insulation of the two frame structures, it can be seen that in the low frequency broadband below 1250Hz, the average sound insulation amplitude of the polyester frame specimen is about 10dB higher than that of the plastic frame specimen, and the maximum gain is as high as 15dB. In addition, in the entire test frequency band, the sound insulation of the polyester frame structure is higher than the prediction result of the mass density law, and in the frequency band above 200Hz (except the stiffness control area), the sound insulation of the polyester frame structure has been maintained above 25dB , the average sound insulation is more than 32dB, showing outstanding broadband sound attenuation ability. In terms of the overall thickness and areal density of the structure, compared with the 5-layer superimposed elastic thin-film acoustic metamaterial proposed by Prof. Zhiyu Yang et al., the areal density is reduced by 5 times and the overall thickness is reduced by 20 times. Low frequency broadband sound attenuation.

To sum up, the thin plate-like structure designed by the flexible frame multi-cell synergistic coupling acoustic metamaterial design method has the following advantages: (1) The mechanical properties of the structure (high strength, long life, not easy to damage) and acoustic properties (wideband (2) The thickness is very small and the surface density is also very low, which can meet the lightweight requirements of aircraft and various vehicles; (3) In very wide In the low frequency range, it has a very high sound insulation ability, which meets the requirements of broadband low frequency sound insulation; (4) The negative impact of the overall effect is eliminated, and the difficulty of tension adjustment is also avoided because it does not require tension; (5) Structure Simple, convenient for mass production and manufacture, and low cost. The lumped coupled resonance effect provided by the present invention not only interprets the role of the frame and the additional mass from a new perspective, but also demonstrates that the design of acoustic metamaterials can be extended to the design of multi-cell combined units, not limited to the design of single cells , which can greatly enrich the design theory of acoustic metamaterials.

(2) Design scheme of rigid frame multi-cell synergistic coupling structure

Using the structure design method of the rigid frame multi-cell synergistically coupled acoustic metamaterial provided by the present invention, a composite structure including 9 thin-plate cells as shown in FIG. 4a is designed. This structure belongs to a multi-cell array structure, including 9 (arranged by 3×3) square thin plate cells. In each cell, a cylindrical mass 6 is attached to the center of the thin plate 8, and the thin plate 8 is arranged on both sides of the surrounding A frame 7. The side length of each cell sheet is 20mm, the thickness is 5mm, the radius of the mass block is 5mm, and the thickness is 1.25mm. The side length of the entire composite supercell structure is 80mm, the thickness is 3mm, and the side width of the frame is 5mm. First, modal analysis was performed on the designed composite supercellular structure by commercial software. In the analysis model, the thin plate was made of silicone rubber with an elastic modulus of 2MPa, a Poisson's ratio of 0.49, and a density of 1000kg/m ³ . The iron sheet is used as the additional mass, and its elastic modulus is 206GPa, Poisson's ratio is 0.33, and the density is 7850kg/m ³ . In order to adjust the resonant frequency of each unit to different pre-designed frequency positions to achieve broadband sound attenuation, the mass density of each mass block is continuously changed from 3000kg/ ^m3 in 1# at intervals of 1000kg/ ^m3 to 11000kg/m ³ in 9# (the number of each unit is shown in Fig. 4a). In addition, in order to effectively separate different cells, a rigid nylon material was used as the frame, the elastic modulus of which was 50GPa, the Poisson's ratio was 0.28, and the density was 1200kg/m ³ .

The first 20 order natural frequencies are calculated under the fixed condition of the outermost boundary of the frame, and Fig. 4b plots the normalized modal displacement in the thickness direction of each cell sheet at 120 Hz. It can be seen from the figure that the density of each cell mass block is different, which is equivalent to the use of different additional masses, and the peaks of the modal displacement of each cell appear at different frequencies. The higher the density of the mass, the lower the frequency of the corresponding peak. In addition, the peak displacements of each cell are close, and in the peak frequency range of the first 8 cells, the modal displacement amplitudes of the remaining cells are close to 0. However, in the range lower than the peak frequency of the ninth cell, the first cell also produces a certain displacement component, showing a certain coupling effect. Since the acoustic transmission characteristics of local resonance structures are strongly dependent on the eigenmodes of the structure, the calculated modal displacement results can be used to reveal the acoustic attenuation mechanism of these structures, which is in contrast to the previous modes used in vibration response solutions. The state superposition method is somewhat similar.

In order to further analyze the cooperative coupling behavior of the multi-cell array structure, two structures are designed by using the multi-cell cooperative coupling acoustic metamaterial design method provided by the present invention, respectively for improving the broadband sound insulation performance and absorption coefficient in the low frequency range. Compared with the structure for sound insulation, the structure for sound absorption adds a back cavity with a depth of 20mm enclosed by a rigid reflective wall. In addition, in order to better demonstrate the synergistic coupling effect and provide additional parameter adjustment methods, plates with gradient distribution of elastic modulus are used in each different unit of the structure for sound insulation, so as to obtain different peaks of sound insulation; In the structure for sound absorption, additional mass blocks of gradient distribution are used to achieve different absorption peaks. In the structure for sound insulation, the elastic modulus of the plates in cells 1# to 9# increased linearly from 20MPa to 340MPa with an interval of 40MPa. Meanwhile, the corresponding parameters of the mass remained the same in all 9 cells, and its elastic modulus, Poisson's ratio and mass density were 206 GPa, 0.33 and 7850 kg/m ³ , respectively. Other geometric and material parameters of the structure for sound insulation and all parameters of the structure for sound absorption are the same as those used in the modal analysis in Figure 4.

The sound insulation and reflection coefficient of the structure used for sound insulation are shown in Fig. 5a, the average strain energy density is shown in Fig. 5b, and the out-of-plane displacement in the z direction is shown in Fig. 5c. The curve in Figure 5a clearly shows that there are 9 distinct troughs in sound insulation and reflection coefficient, corresponding to 8 distinct sound insulation peaks, and the maximum sound insulation is close to 60dB. More importantly, it exhibits excellent sound attenuation performance in the entire calculated frequency range below 2000Hz, with an average sound insulation of more than 40dB, and due to strong reflections, the minimum sound insulation amplitude is increased to about 30dB. By comparing Figures 5b-c, it can be seen that each trough in Figure 5a corresponds exactly to a peak of the average strain energy density and the out-of-plane displacement profile from a positive peak to a negative peak. Since the average strain energy density and out-of-plane displacement amplitudes at the first peak are much larger than those at other peaks, the sound insulation at the first valley reaches a minimum. Furthermore, in Fig. 5d, the structure used for sound absorption exhibits several dense peaks and valleys in the range of 100–300 Hz. Most importantly, the minimum sound absorption coefficient reaches about 0.5, with an excellent broadband sound absorption effect of about 0.99 in the range of 400-700 Hz, and the average sound absorption coefficient is higher than 0.8 in the frequency band below 800 Hz. It is precisely because of the cooperatively coupled resonance behavior between the cells that the sound insulation in Fig. 5a and the sound absorption coefficient in Fig. 5d oscillate significantly in some frequency bands. In the sound insulation curve, this oscillation appears in the range of about 300 to 1700 Hz, including 9 distinct valleys and 8 peaks; while in the sound absorption coefficient curve, this oscillation frequency band appears in the frequency range of about 100 to 300 Hz Inside, it also shows several distinct troughs and peaks. While these peaks and troughs are relatively independent and can be determined primarily by one cell, the presence of other peaks does contribute to an increase in amplitude. Also, since the amplitudes at these valleys are not very small, relatively strong sound attenuation is achieved in the broadband range.

The physical mechanisms behind the cooperative coupling behavior in this multicellular structure are discussed below. Previous studies have shown that if the localized stiffness of the frame is large enough to completely separate the elements and the corresponding parameters of each element are consistent with those of the other elements, then the acoustic transmission characteristics of a planar element array structure will be consistent with that of a single-cell structure. of. In this case, there is no cooperative coupling behavior between cells. However, in the structure designed by the design method provided by the present invention, in order to achieve the effect that each cell has a different resonance frequency, a gradient distribution of material or structural parameters is used to obtain the synergistic coupling resonance behavior between the cells. In this integrated unit structure, the vibrational properties of the overall supercell structure are determined by the linear superposition of the vibrational properties of all units. Specifically, the sound insulation performance of the entire structure is determined by the average displacement of the flat plates of all units in the direction of sound propagation. Similarly, the sound absorption performance of the whole structure is determined by the strain energy density of the plate, which is a linear superposition of the sheet strain energy densities of all elements. The reason why each cell can produce a significant trough in the sound insulation curve or a peak in the sound absorption coefficient curve is that the low-order vibration displacement of a single cell is relatively large. By precisely designing the natural frequency of each unit, it has a certain interval, so that under the action of the incident sound wave, in a wide frequency band, there are always some units that can produce very strong resonance. At each peak of the sound insulation curve, the strong anti-resonance of some cells combines with the relatively weak anti-resonance of the incident sound wave and other cells to obtain a sound insulation peak with strong sound attenuation. Similarly, sharp absorption peaks are achieved because the resonances of some cells are much stronger than those of other cells at this frequency. In addition, at each trough of the sound insulation curve, when the cell with lower natural frequency deviates from the anti-resonance frequency, the cell with higher natural frequency starts to anti-resonate, and the superposition of vibrations of all cells ensures that the sound Reflection can be maintained at a relatively high level. Similarly, at each trough of the sound absorption coefficient curve, as the element with the lower natural frequency deviates from the resonant frequency, the element with the higher natural frequency starts to resonate, and the superposition of the vibrations of all the elements keeps the sound absorption coefficient at relatively high level. Compared with the previous design scheme, this synergistic coupling resonance effect is beneficial to ensure that the sound insulation or absorption coefficient of the structure is maintained at a high level in a wide frequency range, and the amplitude of the sound insulation or absorption coefficient is at a trough. Attenuation is effectively improved, followed by a wide-band strong sound attenuation in the low-frequency range. It is precisely because the magnitude of sound insulation or sound absorption coefficient is contributed by multiple cells that it can be maintained at a relatively high level through the cooperative coupling behavior between multiple cells in a specific frequency range.

In order to verify the above multi-cell synergistic coupling design method experimentally, two multi-cell structures were designed and processed, one of which is shown in Figure 6a, and its sound insulation was measured by B&K 4206T impedance tube system. It should be noted that in Figure 5a, 8 obvious sound insulation peaks in the frequency band below 2000 Hz are achieved by calculation, which proves the excellent sound insulation performance of the synergistic coupling structure. However, in this calculation, different cells adopt sheets of different elastic moduli, which are difficult to manufacture in practice. Therefore, a simpler structure was designed and machined here instead of directly machining the corresponding sample. Here are multiple sound isolation peaks experimentally achieved by using different masses. Since the frequency separation that can be obtained by changing the mass is relatively small, only 3 types of mass parameters are used in this structure. Furthermore, to demonstrate the difference between structures with and without synergistic coupling effects, a structure using the same mass was also designed and fabricated. Both structures consist of rigid nylon sheets with a thickness and diameter of 0.2mm and 100mm, respectively. The sheet is sandwiched by two 4 mm thick photocurable resin frames, and other geometric parameters are shown in Fig. 6a. The difference between the two structures is that a steel additional mass with a diameter of 10 mm and a thickness of 0.5 mm is arranged on each cell of the control structure. In the experimental group structure, cells 1#, 2# and 3# are each arranged with 5 layers of mass blocks; cells 4#, 5# and 6# are each arranged with 3 layers of mass blocks; cells 7#, 8# and 9# Each cell is arranged with one layer of mass blocks. In the control structure, there is no synergistic coupling effect between cells, so the acoustic transmission properties of the whole structure are similar to that of a single cell structure. In contrast, in the experimental group structure, 3 different types of masses (1, 3 and 5 layers of masses, respectively) were used, resulting in 3 distinct sound insulation valleys. The measured sound insulation curve is shown in Figure 6b. It can be seen that the sound insulation curve of the experimental group structure produces three obvious troughs (respectively 168Hz, 276Hz and 376Hz) and two peaks (respectively 204Hz and 320Hz). In contrast, the sound insulation curve of the control structure only produced a distinct trough at 416 Hz. In addition, in the whole measurement frequency band (50 to 1600 Hz), the sound insulation amplitude of the experimental group structure is always higher than 24dB, and the average value reaches 29.8dB, which indicates that it has excellent broadband sound insulation ability in the low frequency band. Since there is no synergistic coupling resonance effect between cells in the structure of the control group, an obvious trough of sound insulation is generated at 416 Hz, and its amplitude is only 14 dB, and the average sound insulation in the measurement frequency band is significantly lower than that of the experimental group. By comparing the sound insulation of the structure of the control group and the structure of the experimental group, it is clearly demonstrated experimentally and theoretically that broadband sound attenuation in the low frequency range can be achieved due to the synergistic coupling resonance effect.

As can be seen from the above data, the technical effect achieved by the present invention:

1. The present invention cleverly converts the negative effect of the overall effect into a positive effect that is beneficial to the improvement of sound insulation performance by introducing a flexible frame structure with insufficient localized rigidity and utilizing the strong coupling interaction between the flexible frame and the cell. , the structure designed by this design method has excellent sound insulation performance, even without the mass block, the average sound insulation within 1600Hz exceeds 20dB;

2. In the design method of the present invention, the flexible frame part acts as an irregular mass block, thereby greatly improving the sound insulation of the entire multi-cellular structure;

3. When an iron mass block is added to each cell in the structure designed by the invention, the sound insulation performance can be further improved, and the average sound insulation within 1600 Hz is close to 32dB, which truly realizes the low-frequency broadband super sound insulation;

4. The present invention also introduces modal displacement to quickly evaluate the design scheme. In the structure designed by the present invention, by selecting the elastic parameters of the thin plate with gradient distribution in each cell, it can achieve broadband and super sound insulation. The calculation results show that within 2000Hz The average sound insulation is about 40dB, and the minimum sound insulation is as high as 23dB;

5. In the structure designed by the present invention, by selecting the mass block parameters of the gradient distribution and adopting the mechanism with a back cavity, the low-frequency broadband sound absorption effect with an average sound absorption coefficient exceeding 0.8 within 800 Hz can be achieved, and the minimum sound absorption coefficient is not low. at 0.5.

6. In the structure designed by the present invention, in addition to realizing multiple sound insulation and sound absorption peaks, the amplitude at the valley value has also been greatly improved;

7. In the structure designed by the present invention, three mass blocks with different thicknesses are used, which are 1-layer, 3-layer and 5-layer iron sheets respectively. Through experiments, the broadband sound insulation effect of the multi-cell collaborative coupling design can be verified. In addition to the appearance of two sound insulation peaks, the sound insulation at the valley value is also greatly improved. In the measurement frequency band within 1600Hz, the minimum sound insulation is higher than 24dB, and the average sound insulation is close to 30dB.

Claims (5)

1. a multi-cellular synergistic coupling acoustic metamaterial structure design method is characterized in that, the method is divided into two kinds of structural design methods with insufficient localized rigidity and structural design methods with sufficient localized rigidity; wherein, The structural design method with insufficient localized stiffness uses a partition frame with a localized stiffness lower than the stiffness of the thin plate to separate the local resonance cells, so that a strong coupling resonance behavior occurs between the single cells, and a lumped coupling resonance effect is formed. The multicellular composite structure of ; The structural design method with sufficient localized stiffness adopts the partition frame whose localized stiffness is higher than that of the thin plate, so that the resonance between single cells does not affect each other in the design frequency band, and then through multiple thin plate widths, thin plate thicknesses or additional The cells of the mass weight structure parameter gradient distribution are combined into a multi-cell combined structure. 2. The method for designing a multi-cellular cooperatively coupled acoustic metamaterial structure according to claim 1, wherein the method for designing a structure with insufficient localized stiffness specifically comprises the following steps: 1) Select the unit cell structure form of the film or sheet structure; 2) on the basis of step 1), using ethylene-vinyl acetate copolymer as a framework, a supercellular structure composed of a plurality of cells is designed; 3) According to actual needs, further adjust and optimize the lattice constants, sheet thickness, additional mass weight, frame edge width and frame thickness structural parameters of a single cell and frame. 3 . The method for designing a multi-cell synergistically coupled acoustic metamaterial structure according to claim 2 , further comprising adding a back cavity to the cell, the structure being able to achieve a low-frequency broadband super sound absorption effect. 4 . 4. The multi-cellular cooperatively coupled acoustic metamaterial structural design method according to claim 3, wherein the structural design method with sufficient localized rigidity specifically comprises the following steps: 1) Select the unit cell structure form of the film, thin plate or resonant cavity structure; 2) According to the principle of cell resonance frequency gradient distribution, select the lattice constant, thickness, additional mass weight structure parameters of the film and sheet, or the cavity size of the resonance cavity structure, and carry out the multi-cellular structure design of parameter gradient distribution; 3) Using a hard material with a localized stiffness higher than that of films and sheets as a partition frame, a plurality of cells with the designed parameter gradient distribution are combined into a supercell; 4) According to actual needs, further adjust and optimize the lattice constant of a single cell, the thickness of the thin film and the thin plate, the weight structure parameters of the additional mass, or the cavity size of the resonant cavity structure. 5. The method for designing a multi-cell synergistic coupling acoustic metamaterial structure according to claim 4, further comprising adding a back cavity to the single-layer plate structure used as sound insulation, and the structure can realize low-frequency broadband super strong Sound absorption effect.