CN107170437B - Thin film sheet type acoustic metamaterial sound insulation device - Google Patents
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- CN107170437B CN107170437B CN201710248596.0A CN201710248596A CN107170437B CN 107170437 B CN107170437 B CN 107170437B CN 201710248596 A CN201710248596 A CN 201710248596A CN 107170437 B CN107170437 B CN 107170437B
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- G—PHYSICS
- G10—MUSICAL INSTRUMENTS; ACOUSTICS
- G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
- G10K11/00—Methods or devices for transmitting, conducting or directing sound in general; Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
- G10K11/16—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general
- G10K11/162—Selection of materials
- G10K11/168—Plural layers of different materials, e.g. sandwiches
Abstract
The invention discloses a thin film sheet type acoustic metamaterial sound-insulating device which is formed by superposing cellular structures with different thicknesses and different radiuses, wherein each cellular structure comprises a concentration mass block, a thin film and a frame, the periphery of the thin film is fixed on the frame, the concentration mass blocks are tightly adhered to the thin film, the thin film only needs to be flattened without applying tension, and the cellular structures are tightly and periodically arranged to form a plate-shaped sound-insulating device. The sound insulation device has good sound insulation effect, wide frequency band and high sound insulation amount, effectively breaks through the control of the mass law on the sound insulation amount, has strong adjustability, and can obtain the sound insulation device with the sound insulation amount below 2000Hz higher than the mass law by stacking different structures.
Description
Technical Field
The invention relates to the field of machinery and noise control, in particular to a thin film sheet type acoustic metamaterial sound insulation device.
Background
Acoustical metamaterials are artificially designed materials that have been extensively investigated over the past few years, primarily because they have promising applications and are hardly or impossible to find in nature, which have special properties that materials in nature do not have. They therefore open a door for improvement and even for putting into a completely new application. The acoustic material with a localized resonance band gap reported in 2000 was a precursor of the acoustic metamaterial, and was the earliest implemented acoustic metamaterial. The acoustic metamaterial has a negative mass density and elastic modulus. The thin film acoustic metamaterial is a novel acoustic metamaterial which is widely concerned in recent years and consists of a rigid frame, a tensioned rubber film and a mass block. The sound wave total reflection of characteristic frequency can be realized through effective dynamic negative mass, so that the effect of low-frequency sound insulation is achieved.
The main research objective of the present scholars is to reduce the frequency and widen the sound insulation frequency of the acoustic metamaterial, and the material and parameters are changed to make the thin film acoustic metamaterial have better sound insulation effect and wider working frequency. In addition, students can achieve better sound insulation effect according to the coupling of the film and other structures. However, there are three significant disadvantages to the current application of thin film acoustic metamaterials:
first, most of the thin film sheet acoustic metamaterials use rubber as a material, and the material has the disadvantages of unstable performance, easy aging, poor mechanical strength, basically no bearing capacity and relatively large limitation on practical engineering application.
Second, since the currently used thin film sheet materials are generally thin, the elastic modulus of the materials themselves is low, and the sheet stiffness is not sufficient to overcome the self-gravity to transmit vibration without applying tension, it is necessary to apply tension to the thin film in simulation and practical applications. However, to date, the additional systems and techniques required to control tension, whether by means of an applied electric field or magnetic field or by means of an air flow, are quite complex and control of tension is very inaccurate and stable. On the other hand, the thin-film acoustic metamaterial has very large dependence on tension, and small tension changes can cause large deviation or even disappearance of the sound insulation frequency band.
Finally, because the thin film sheet type acoustic metamaterial is based on the local resonance principle, the sound insulation frequency band designed at present is relatively narrow, even only acts at a certain single frequency, and most of sound waves needing to be isolated are sound waves with multiple frequencies and wide frequency superposition in both life and engineering application, so that the practical application is greatly limited.
Therefore, the film thin plate type acoustic metamaterial which has certain bearing capacity, good rigidity and weak tension dependence and even does not need to apply tension and is used for sound insulation of a wide frequency band is designed, and the film thin plate type acoustic metamaterial has very important significance for practical engineering application.
Disclosure of Invention
The invention aims to overcome the technical problems of difficult noise reduction, overlarge volume of a sound insulation device, single working frequency, larger tension dependence of a film and the like in the prior art, and provides a plate-shaped sound insulation device which is light, thin, wide in frequency, high in sound insulation, convenient to manufacture and free of tension, and the invention adopts the following technical scheme in order to achieve the purpose:
the film sheet type acoustic metamaterial sound-insulating device is characterized by being formed by superposing cell structures different in thickness and radius, wherein each cell structure comprises a concentrated mass block, a film and a frame, the periphery of the film is fixed on the frame, the concentrated mass blocks are tightly bonded with the film, the film is not required to be flattened and tension is not required to be applied, and the cell structures are tightly and periodically arranged to form the plate-shaped sound-insulating device.
Further, the thin film and the concentration mass block are stacked layer by layer to form a cellular structure with different layers, the upper surface and the lower surface of the concentration mass block are tightly adhered to the thin film, the layer number of the cellular structure is defined by the layer number of the thin film, the layer number of the thin film is determined according to the thickness and the radius of the thin film, and the larger the thickness of the thin film is, the smaller the radius is, and the smaller the layer number is.
Furthermore, the cell structure is a thin film with the radius of 20mm and the thickness of 0.2mm, and the number of layers is 3 to 6, preferably 4.
Furthermore, the cell structure is a thin film with the radius of 20mm and the thickness of 0.4mm, and the number of layers is 2-4.
Furthermore, the cell structure is a thin film with the radius of 15mm and the thickness of 0.2mm, and the number of layers is 2-6.
Furthermore, the sound insulation device is formed by superposing cell structures A and B with different layers, and an intermediate air layer is formed between the cell structures A and B.
Preferably, the cellular structure a has four layers, the cellular structure B has two layers, the thickness of the film in the cellular structure a is 0.2mm, each concentration mass block is 0.8g, the thickness of the film in the cellular structure B is 0.4mm, and each concentration mass block is 0.2 g.
Further, the film is circular, the concentrated mass block is cylindric, the concentrated mass block material is steel, the film material is nylon, the frame material is ABS plastics, the density, the elastic modulus and the poisson ratio of the mass block material, nylon film material, ABS plastics frame material are concentrated to steel are respectively: 7850kg/m3、205GPa、0.28；1150kg/m3、2GPa、0.4；1190kg/m3、2.2GPa、0.375。
Furthermore, the cellular structure has strong adjustability, the sound insulation frequency band can be accurately adjusted in a wide range by adjusting the radius and the thickness of the film and the size of the concentrated mass block, the adjusted sound insulation frequency band is determined according to the frequency of the sound waves to be isolated, two critical frequencies in the STL curve are predicted by a theoretical formula through a film sheet vibration theory, the size of the cellular structure is designed according to actual needs, and the sound insulation amount between different cellular structures is mutually compensated through the superposition of different cellular structures, wherein the formula is as follows:
compared with the prior art, the invention has the following beneficial technical effects:
the structure has good sound insulation effect, wide frequency band and high sound insulation amount, effectively breaks through the control of the mass law on the sound insulation amount, has strong adjustability, and can obtain the sound insulation device with the sound insulation amount below 2000Hz higher than the mass law by overlapping different structures.
Drawings
FIG. 1 is a schematic structural diagram of an embodiment of the present invention;
FIG. 2 is a schematic layout of an example experimental sample;
FIGS. 3(a) -3 (b) are graphs of sound transmission loss STL of four-layer cellular structures with two concentrated mass of 0.2g and 0.4g obtained by finite element and experiment respectively;
FIGS. 4(a) -4 (c) are graphs of acoustic transmission loss of film cellular structures of different concentrations of mass, different radii, and different thicknesses obtained by finite element calculations;
FIG. 5 is a schematic diagram of a stacked structure of two cell structures according to an embodiment of the present invention;
FIG. 6 is a graph showing the sound insulation of a stacked structure in which two kinds of cell structures are combined;
FIGS. 7(a) -7 (b) are schematic diagrams of equivalent models of cells;
FIG. 8 is a graph of cell equivalent density curves obtained in finite elements;
FIG. 9 is a graph of the average displacement of the film in the cell;
FIG. 10 is a graph showing the surface average vibration velocity of a cell film;
FIGS. 11(a) -11 (c) are graphs showing the influence of the number of layers of different-sized cellular structures on the sound insulation;
FIG. 12 is a schematic diagram of the theoretical mode shape of the thin film;
FIG. 13 is a cloud of displacements at f2 in the finite element.
Detailed Description
The invention will now be described in detail with reference to the accompanying figures 1-13 and specific examples, but without limiting the invention thereto.
The invention discloses a thin film sheet type acoustic metamaterial sound-insulating device which is a low-frequency broadband sound-insulating device with light weight and thin thickness. As shown in figure 1, the mass consists of a cylindrical steel concentrated mass 101, a nylon film 102 with the thickness of 0.2mm and an ABS plastic frame 103 with the thickness of 1-2 mm. The upper and lower surfaces of the concentrated mass block 101 are closely adhered to the nylon films 102 on the upper and lower sides thereof, the height of the concentrated mass block 101, i.e., the distance between the film layers, is fixed to 2mm, and the nylon films 102 are laminated in this way, and the periphery of the nylon films 102 is fixed to the frame 103 without applying tension. In this way, a cellular structure is formed, and the cellular structure is the smallest metamaterial unit for blocking low-frequency sound waves in the sound insulation device.
Further, in this way, the thin film 102 and the concentrated mass 101 are stacked one on another, so that a cell structure with different layers can be formed. The number of layers of the structure is defined by the number of layers of the film 102.
The smaller the radius of the film used for the cell structure, the larger the thickness, and the smaller the minimum value of the optimum number of layers. However, the effect is better when the number of layers is not larger, and when the number of layers reaches a certain value, the sound insulation performance is reduced or even disappears due to the coupling effect between layers.
Furthermore, the number of the thin films with the radius of 20mm and the thickness of 0.2mm in the cellular structure is 3 to 6, preferably 4, as shown in fig. 1, which is a schematic 4-layer cellular structure.
Furthermore, the cell structure is a thin film with the radius of 20mm and the thickness of 0.4mm, and the number of layers is 2-4.
Furthermore, the cell structure is a thin film with the radius of 15mm and the thickness of 0.2mm, and the number of layers is 2-6.
Fig. 11(a) to 11(c) show the influence curves of the number of layers of the cell structure of different sizes on the sound insulation amount.
Further, the frame 103 only plays a role in separating the cell structures in the sound insulation effect, so that the vibration among the cell structures is not influenced mutually, and the zero displacement boundary condition around the film is ensured. Typically, the cell structures are separated by a distance greater than 1 mm. The steel lumped mass 101 material has the following material parametersThe density, the elastic modulus and the poisson ratio of the material of the nylon film 102 and the material of the ABS plastic frame 103 are respectively as follows: 7850kg/m3,205GPa,0.28；1150kg/m3,2GPa,0.4；1190kg/m3,2.2GPa,0.375。
Furthermore, the plate-shaped sound insulation device formed by periodically arranging the cellular structures is very thin in material thickness and light in weight (different from the number of stacked layers, the total thickness of the structure shown in fig. 1 is 6.8mm, and the surface density rho is 2.02kg/m2) The sound insulation quantity is very high below 1000Hz, except for very narrow frequency band, the rest parts are much higher than the prediction of the same surface density mass law, the limit of the mass law on the sound insulation quantity is broken, and the material belongs to the material with light weight, thin thickness, wide frequency and high sound insulation quantity.
In order to analyze the sound insulation effect of the invention, the method of commercial finite element software COMSOL and standing wave tube experiment is respectively used for verification. The cross-sectional layout of the experimental sample is as shown in fig. 2, because the size of the standing wave tube is fixed to be 100mm, in order to ensure that the vibration between the adjacent cell structures does not influence each other, four completely identical four-layer cell structures are uniformly distributed in the range of 100mm in diameter, in fig. 2, R is 50mm, and R is 19 mm. The vibration conditions of the four cellular structures are completely consistent with the vibration of the single cellular structure and do not interfere with each other, and sound transmission loss STL curves of two cellular structures with concentrated masses of 0.2g and 0.4g are obtained through finite elements and experiments respectively, as shown in fig. 3(a) -3 (b). It can be seen that data and trends obtained by experiments and simulations are very close, frequency deviation corresponding to two valley values is within 10%, the two valley values and a sound insulation peak value are included, and sound insulation amount is higher than prediction of a quality law in a wide frequency band. Therefore, the finite element method can be used for replacing experimental measurement, and is quicker, more convenient and cost-saving.
Further, taking the example of 0.4g of each cell added with mass, the sound insulation mechanism is explained and two key frequency values are predicted by theory. Fig. 7(a) to 7(b) show equivalent models of a unit cell, in which (a) is a spring mass unit and (b) is a periodic cell array formed by connecting the units in (a) in series. For the motion of the nth cell in FIG. 7(b), the equation of motion can be derived
The steady state solution of the above equation under the excitation force with angular frequency ω and Bloch boundary conditions is:
where q is the Bloch wave vector. The dispersion relation of the system can thus be obtained:
obviously, the equivalent mass meff of the system can be obtained:
wherein the content of the first and second substances,
as can be seen from the formulas (4) and (5), the system is in omega0The negative mass is presented below. Based on this spring-mass periodic system, a metamaterial cellular structure can be constructed as shown in FIG. 1. 102 may be equivalent to the spring-mass system in fig. 7(a) and 101 may be equivalent to the connecting spring K in fig. 7 (b).
From the above, the cell structure should be constructed as the proposed spring-mass system, at ω0Below, i.e. below the first order natural frequency of the spring-mass system in fig. 7(a), a negative mass is present. The resulting cell equivalent density in the finite element is shown in fig. 8. It can be seen that at f1Below (169Hz), the system equivalent mass is negative, and the equivalence rationality is verified. When the system has a negative mass, the wave number becomes imaginary, and the sound wave forms a falling wave in the material, the amplitude of which decays exponentially, so that at f1A high sound insulation level can be obtained at (169Hz) or less.
The average displacement of the thin film in the unit cell is shown in fig. 9. At fpeakAt (555Hz), the average displacement of the membrane is zero, and the equivalent density of the system suddenly changes from a positive maximum value to a negative maximum value as shown in fig. 8, and the frequency at this moment happens to be completely consistent with the sound insulation peak value in fig. 3 (b). Since a larger value of the equivalent density indicates a larger inertia of the system, the more difficult the motion state is to be changed by an external force. At this time, the average displacement of the membrane is zero, which also indicates that the membrane is in a "quasi-static" state, and is a "rigid node" for the incident sound wave, and the sound wave cannot excite the vibration of the membrane, so that the membrane cannot conduct the sound wave to the other side.
The average vibration velocity of the cell membrane is shown in fig. 10. The average vibration velocity of the film side also corroborates the above analysis. It is clear from the figure that at the two sound insulation valleys, there are just two peaks of vibration speed, and the equivalent density of the film is substantially zero, which means that the film acts like "air" on the sound wave traveling road and has a very weak sound wave blocking effect. As shown in fig. 12 and 13, it can be seen from the displacement cloud in the finite element that these two frequencies are also the first two order resonant frequencies of the unit cell. In the resonant state, the structure couples with the acoustic wave to the greatest extent, transferring acoustic energy to the other side, so that the acoustic wave is substantially 100% transmitted. At fpeak, the average displacement and the average vibration speed of the film are both zero, and the equivalent density is maximum, which corresponds to the anti-resonance state between two resonance frequencies. The sound-proof peaks in fig. 3(a) -3 (b) are produced.
From the above analysis, it is known that f1 and f2 have an inseparable relationship with the vibration mode of the membrane, and f1 is the first-order natural frequency of the cell in the equivalent model fig. 7 (a). The mass of K is not taken into account in the derivation of the equivalent model, but the mass of the mass block in the material unit cell cannot be ignored, so that the mass of the concentrated mass block is equivalent to the mass of the thin film, and the natural frequency of the thin film is corrected on the basis of the equivalent mass block, so that two formulas (6) and (7) are obtained, wherein the formula (6) is a representation of the natural frequency of the thin film, and the formula (7) is further corrected on the basis of the equivalent model by considering the concentrated mass block. As shown in fig. 12 and 13, it can be found through the displacement cloud chart in the finite element that the vibration state of the film at f2 is consistent with the second-order mode of the film, so that the second-order frequency is further modified in consideration of the mass, the number of cell layers, and the like, and an approximate theoretical formula of f2 can be obtained.
Through the formulas (6), (7) and (8), two sound insulation valleys f can be predicted relatively accurately1,f2The values calculated by the theoretical formula and those obtained by finite element simulation are compared in tables 1 and 2.
Where E, ρ, σ, h, a, are the elastic modulus, density, poisson's ratio, thickness and radius of the film material, respectively. f'1Because f is considered to be a pair of concentrated masses1Further equivalents and modifications are made. Mu.snIs the root of equation (9).
J0(ka)I1(ka)+I0(ka)J1(ka)＝0 (9)
Wherein JiIs a Bessel function of the first kind, IiIs a first type of imaginary bezier function.
The definitions of two types of Bessel functions are:
wherein (x) is a gamma function;
where (x) is a gamma function.
It can be seen from the above formulas (6) to (8) that the positions of the two valleys in the STL curve can be easily adjusted by changing the thickness h and the radius a of the film. As shown in fig. 4(a) -4 (c).
TABLE 1 primitive cells f of different sizes and number of layers1Comparison of theoretical simulation
TABLE 2 primitive cells f of different sizes and number of layers2Comparison of theoretical simulation
Through the thin film sheet vibration theory, two frequencies which are key in the STL curve can be predicted by a theoretical formula, and the error is usually less than 10 percent so as to design the structure size of the unit cell according to different requirements in practical application.
Preferably, as shown in fig. 5, a four-layer cellular structure a with a film thickness of 0.2mm and 0.8g of each concentrated mass block and a two-layer cellular structure B with a film thickness of 0.4mm and 0.2g of each concentrated mass block are stacked, so that the sound insulation valley value of the B cellular structure near 500Hz can be compensated by the sound insulation peak value of the a cellular structure. The STL curve of the compounded cellular structure is basically the envelope curve of the STL curves of the original two cellular structures. In FIG. 5, 104 is cell structure A, 105 is cell structure B, and 106 is an intermediate air layer formed by separating A, B two cell structures by a frame.
The superposition mode can be determined according to the frequency of the sound waves to be isolated in practical application, and the sound insulation quantity between different cellular structures can be mutually compensated through superposition of the cellular structures with different thicknesses, and the result is shown in fig. 6.
The sound insulation device has strong adjustability, and the sound insulation frequency band can be conveniently, greatly and relatively accurately adjusted in a wide range by adjusting the radius and the thickness of the film and the size of the concentrated mass block. Through reasonable design, the cellular structures with different thicknesses and different radiuses are superposed, and the sound insulation material with the mass law prediction performance higher than that predicted by the mass law below 2000Hz can be obtained.
The above-described embodiments are only preferred embodiments of the present invention, and should not be construed as limiting the scope of the present invention, it should be noted that those skilled in the art can make various changes and modifications without departing from the spirit of the present invention, and these changes and modifications are all within the scope of the present invention.
Claims (8)
1. The film sheet type acoustic metamaterial sound insulation device is characterized by being formed by superposing cell structures with different thicknesses and different radiuses, each cell structure comprises a concentration mass block (101), a film (102) and a frame (103), the periphery of the film (102) is fixed on the frame (103), the concentration mass blocks (101) are tightly bonded with the film (102), the film (102) only needs to be flattened without applying tension, the frame (103) plays a role in separating the cell structures in sound insulation, vibration among the cell structures is guaranteed not to be influenced mutually, and zero displacement boundary conditions around the film (102) are guaranteed; the cellular structures are closely and periodically arranged to form a plate-shaped sound insulation device;
the thin film (102) and the concentrated mass block (101) are stacked layer by layer to form a cellular structure with different layers, the upper surface and the lower surface of the concentrated mass block (101) are tightly adhered to the thin film (102), the number of layers of the cellular structure is defined by the number of layers of the thin film (102), the number of layers of the thin film is determined according to the thickness and the radius of the thin film, and the larger the thickness of the thin film is, the smaller the radius is, and the smaller the number of layers is.
2. The thin film sheet type acoustic metamaterial sound insulating device according to claim 1, wherein the cellular structure includes thin films having a radius of 20mm and a thickness of 0.2mm, and the number of layers is 3 to 6.
3. The thin film sheet type acoustic metamaterial sound insulating device according to claim 1, wherein the cellular structure includes thin films having a radius of 20mm and a thickness of 0.4mm, and the number of layers is 2 to 4.
4. The thin film sheet type acoustic metamaterial sound insulating device according to claim 1, wherein: the cell structure is a thin film with the radius of 15mm and the thickness of 0.2mm, and the number of layers is 2-6.
5. The thin film sheet type acoustic metamaterial sound insulating device according to claim 2, wherein: the number of layers of the cellular structure is 4.
6. The sound-proof device of thin-film sheet type acoustic metamaterial according to claim 1, wherein the sound-proof device is formed by stacking cell structures A (104) and B (105) with different layers, and an intermediate air layer (106) is formed between the cell structures A (104) and B (105).
7. The thin film sheet type acoustic metamaterial sound insulating device according to claim 6, wherein the cellular structure A (104) is four layers, the cellular structure B (105) is two layers, the thickness of the thin film in the cellular structure A is 0.2mm, each concentrated mass is 0.8g, the thickness of the thin film in the cellular structure B is 0.4mm, and each concentrated mass is 0.2 g.
8. A thin-film sheet-type acoustic metamaterial sound isolator as claimed in claim 1, wherein the thin film (102) is circular, the lumped mass (101) is cylindrical, the material of the lumped mass (101) is steel, the material of the thin film (102) is nylon, the material of the frame (103) is ABS plastic, and the density, elastic modulus and poisson ratio of the steel lumped mass material, the nylon thin film material and the ABS plastic frame material are respectively: 7850kg/m3、205GPa、0.28；1150kg/m3、2GPa、0.4；1190kg/m3、2.2GPa、0.375。
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