CN110277083B - Low-frequency sound absorption metamaterial - Google Patents

Low-frequency sound absorption metamaterial Download PDF

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CN110277083B
CN110277083B CN201810218618.3A CN201810218618A CN110277083B CN 110277083 B CN110277083 B CN 110277083B CN 201810218618 A CN201810218618 A CN 201810218618A CN 110277083 B CN110277083 B CN 110277083B
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周萧明
廖允鸿
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
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Abstract

The invention relates to a low-frequency sound absorption metamaterial, and belongs to the technical field of sound absorption metamaterials. The sound absorption metamaterial is mainly based on a circuit control theory of piezoelectric materials, the piezoelectric film and the piezoelectric stack are independently regulated and controlled through the piezoelectric film circuit and the piezoelectric stack circuit, the matching condition of acoustic resistance and acoustic reactance can be greatly improved under the condition of not changing the geometric configuration and the size of the sound absorption metamaterial, the sound absorption intensity, the sound absorption frequency and the sound absorption bandwidth of the sound absorption metamaterial are regulated and controlled, the sound absorption frequency range is wider for sound waves below 300Hz, and the sound absorption frequency can be regulated within the wider range. The sound absorption metamaterial has the advantages of small structure thickness, small volume and high sound absorption efficiency, and breaks through the limitations of the traditional method and the common metamaterial in low-frequency (less than or equal to 300Hz) sound absorption.

Description

Low-frequency sound absorption metamaterial
Technical Field
The invention particularly relates to an ultrathin light metamaterial with a good sound absorption effect on sound waves within 300Hz, and belongs to the technical field of sound absorption metamaterials.
Background
The noise pollution is wide in the life of people, such as the fields of urban construction, transportation, industrial production, aerospace and the like, great harm is caused to the physical and mental health of people, and particularly, the low-frequency noise is a difficult point to process. The traditional sound absorption means mainly comprise porous media (such as sponge, foam, fibrofelt and the like) and perforated and micro-perforated plates, sound absorption is carried out based on damping dissipation and heat conduction mechanisms, a good sound absorption effect is achieved on the noise of a medium-high frequency band, the loss of low-frequency sound waves is very weak, certain sound absorption performance needs to be achieved by using structures or materials with the same wavelength size, and the defects of large size, low efficiency and the like exist.
In recent years, metamaterial has attracted wide attention of people due to special dynamic properties (negative density and negative modulus) and strong wave control functions (cloak, unidirectional transmission and superlens), and a new idea is provided for low-frequency sound absorption. Aiming at low-frequency noise, people design various types of sound absorption metamaterials according to different principles, and perfect absorption is realized through a structure with a sub-wavelength scale. For example, attaching a pre-stressed membrane in front of the back cavity and attaching a mass to the membrane allows perfect sound absorption around the selected frequency, with the required thickness being much smaller than the wavelength (Mei, J., et al, Dark Acoustic Materials as super absorbers for low-frequency sound. Based on the principle of space folding, a 1/4 wavelength sound tube is bent and coiled in a plane, so that full absorption can be realized near the resonant frequency, and the thickness required by the structure is greatly reduced (Cai, X., et al, Ultrathin low-frequency sound absorbing board base on planar resonator or planar resonator Helmholtz transmitters, 2014.105(12): p.121901; Li, Y.and B.M.Association, Acoustic measurement-based panel resonator with low wavelength sound absorbing board applied Physics Letters,2016.108(6): p.063502; Chen, C., A. 2017.110, A.low-frequency sound absorbing board with low wavelength applied Physics Letters, 903.903.903.52). Or coupling two or more resonators to adjust the total acoustic impedance by Hybrid resonance of the resonators to match the background dielectric impedance when the metamaterial resonates, thereby achieving total absorption (Yang, M., et al., subway h total acoustic impedance with a depenerator. applied Physics Letters,2015.107(10): p.104104; Li, J., et al., A sound absorbing method with a multiplied resonator. applied Physics Letters,2016.109(9): p.091908; Fu, C., Hybrid resonator for multiple frequency measurement and reflection in large applications. arrays. 2017.110). In addition, Coherent absorption in the optical domain is introduced into the Acoustic domain, two sound waves with the same amplitude and opposite propagation directions are incident on a monopole or dipole oscillator, and the phase difference is adjusted to be 0 or pi to satisfy the condition of total absorption (Wei, P., et al, symmetric and anti-symmetric Coherent Acoustic absorption for optical waves, applied Physics Letters,2014.104(12): p.121902; Meng, C., et al, Acoustic Coherent detectors as Sensitive Nuclear detectors, scientific Reports, 2017.7). The metamaterials have good sound absorption performance at low frequency, are light in weight and small in size, but have a very narrow sound absorption frequency band and are very inconvenient to adjust, and once the metamaterial is manufactured, the working frequency is basically fixed, so that the metamaterial is greatly limited in practical application.
The piezoelectric material has the advantages of light weight, small volume, convenience for circuit regulation and control and the like, and is widely applied to the problem of sound absorption, such as pasting a piezoelectric sheet on a thin plate to combine with back cavity sound absorption, adding a piezoelectric film on a perforated plate or manufacturing the perforated plate by using the piezoelectric material, combining the piezoelectric film with a porous material to enhance sound absorption and the like. The sound absorption efficiency and the adjustability of the sound absorption means based on the piezoelectric materials are greatly improved through the regulation and control of an external circuit, however, the working frequency band is still narrow, and the real wide and low-frequency sound absorption is still difficult to realize. In order to achieve broadband sound absorption, the concept of acoustic "black holes" has been proposed, using metamaterials to induce incident sound waves of different angles of incidence into an inner core filled with damping material for dissipation (Li, r. -q., et al, a hybrid and an acoustic organic absorbent composite with a damping material) (Applied Physics Letters,2011.99(19): p.193507; sample, a, d.torred, and J.S n-type-Dehesia, an acoustic hybrid absorbent and a magnetic substrate, Applied Physics Letters,2012.100(14): p.144103; Zheng, l.y., a new type of sound, a hybrid and an acoustic absorbent, application, p.22, p.7. acoustic absorbent, p.22. acoustic absorbent, p.7. acoustic absorbent, p.3. acoustic absorbent, p.7. acoustic absorbent, p.3. acoustic absorbent, p.7. acoustic absorbent, p.3. acoustic absorbent, p.7. acoustic absorbent, p.3. acoustic absorbent, p.7. acoustic absorbent, p.3. acoustic absorbent, p.3. acoustic absorbent, p.2. acoustic absorbent, acoustic absorbent; or widening the sound absorption band by using the coupling among Multiple structures (Romero-Garc i a, V., et al., Use of complex frequency plate to design broad and sub-wave length absorbers. the Journal of the acoustic Society of America,2016.139(6): p.3395-3403; Tang, Y., et al., Hybrid acoustic methodology superior for broad and band-low frequency Sound instruments, 2017.7: p.43340; Yang, J.S. Lee, and Y.Y.Kim, Multiple bands in arrays for broad and band-like sound absorbers, P.P. 2017.50. Journal of P.P.3); and designing a configuration of Broadband impedance matching by combining an optimization algorithm and an acoustic impedance matching theory (Jim nez, N., et al, Broadband and quality perfect impedance using a modulated multi-layer impedance material. AIP Advances,2016.6(12): p.121605; Liu, T., J.Zhu, and L.Cheng, A Broadband and acoustic impedance based on a localized inductive impedance bridging method. the Journal of the acoustic impedance of America,2016.139(4): p.2182-2182; Yang, M., et al, optical impedance-impedance matching structures. materials Horizons, 7). However, these structures have a relatively good absorption effect mainly for sound waves above a certain cut-off frequency, and some of them have a relatively large thickness, so that it is still difficult to treat low-frequency sound waves, especially low-frequency noise below 300Hz, and a new wide low-frequency sound absorption mechanism is also urgently needed.
Disclosure of Invention
Aiming at the problems of large structure thickness, narrow sound absorption frequency and poor sound absorption effect of sound waves below 300Hz of the existing sound absorption material, the invention aims to provide the low-frequency sound absorption metamaterial, which is mainly based on the circuit control theory of piezoelectric materials, and the piezoelectric film and the piezoelectric stack are independently regulated and controlled by an external circuit, so that the matching condition of acoustic resistance and acoustic reactance can be greatly improved, the sound absorption performance of the metamaterial is improved, the geometric configuration and the size of the metamaterial do not need to be changed, and the metamaterial has good absorption effect on the sound waves below 300 Hz.
The purpose of the invention is realized by the following technical scheme.
A low-frequency sound absorption metamaterial comprises a back cavity, a composite film, a piezoelectric film circuit, a piezoelectric stack and a piezoelectric stack circuit;
the back cavity is a cavity structure with one open end and the thickness h c2 cm-10 cm, preferablySelecting 3-5 cm;
the composite film is a composite structure formed by sequentially laminating a piezoelectric film, a metal film and the piezoelectric film; the piezoelectric film is of a circular ring structure, a boss structure is processed in the center of the metal film, and the piezoelectric film is nested on the boss structure of the metal film; the piezoelectric film is made of PZT-5 series piezoelectric ceramic materials, preferably PZT-5H or PZT-5J, and the metal film is made of aluminum, copper, iron, aluminum alloy and the like, preferably aluminum;
a negative capacitor I and a resistor are connected in series in the piezoelectric film circuit;
the piezoelectric stack is composed of NsPiezoelectric sheets of the same sheet geometry are laminated in succession, the radius R of the sheets being1The polarization direction of the two adjacent piezoelectric sheets is opposite; the piezoelectric sheet is made of PMN-PT series piezoelectric ceramic materials, preferably PMN-0.33 PT;
a negative capacitor II and a negative inductance are connected in series in the piezoelectric stack circuit;
the composite film is fixedly connected with the open end of the back cavity, so that the back cavity forms a closed cavity; the piezoelectric stack is arranged in the back cavity, one end of the piezoelectric stack is fixedly connected with the back cavity, and the other end of the piezoelectric stack is fixedly connected with a boss structure of the metal film in the composite film; one layer of piezoelectric film in the composite film is connected with one piezoelectric film circuit, the other layer of piezoelectric film is connected with the other piezoelectric film circuit, and the two layers of piezoelectric films and the two piezoelectric film circuits are grounded; piezoelectric stack circuit one end all is connected with every piezoelectric patches in the piezoelectric stack, and the other end ground connection, every piezoelectric patches in the piezoelectric stack all ground connection moreover.
In addition, when the negative inductance in the piezoelectric stack circuit is not zero, a wide low-frequency sound absorption metamaterial is obtained; when the negative inductance is zero, the adjustable narrow low-frequency sound absorption metamaterial is obtained.
Has the advantages that:
in the metamaterial, the negative capacitor and the resistor which are connected in series are introduced into the piezoelectric film circuit, and the total acoustic resistance and the acoustic reactance are regulated (the sound absorption strength is improved), so that the acoustic impedance of the metamaterial is better matched with that of air, and necessary conditions are provided for sound absorption of the metamaterial; the piezoelectric stack circuit is introduced with the series negative capacitor and the series negative inductance, so that the piezoelectric stack has the characteristics of negative rigidity and dispersion rigidity, and the total acoustic resistance and acoustic reactance are regulated (the peak frequency and the bandwidth of sound absorption are regulated and controlled), which are key factors for realizing low-frequency adjustable sound absorption and wide-low-frequency sound absorption; in addition, based on the circuit control theory of the piezoelectric material, the acoustic resistance and the acoustic reactance of the metamaterial can be changed under the condition of not changing the geometric configuration and the size of the metamaterial through the design of the piezoelectric film circuit and the voltage stack circuit, the sound absorption intensity, the sound absorption frequency and the sound absorption bandwidth of the metamaterial are regulated and controlled, and the regulation is convenient. The metamaterial has the advantages of small structural thickness and small volume, improves the absorption efficiency, and breaks through the limitations of the traditional method and the common metamaterial in low-frequency (less than or equal to 300Hz) sound absorption.
Drawings
Fig. 1 is a schematic structural diagram of a wide and low frequency sound absorption metamaterial according to embodiment 1.
Fig. 2 is a diagram of a theoretical region based on the radius of the piezoelectric sheet, the inner and outer radii of the piezoelectric film, and the radius of the metal film when theoretical calculation is performed.
Fig. 3 is a sound absorption frequency spectrum graph obtained by theoretical calculation and simulation calculation of the sound absorption metamaterial in example 1.
Fig. 4 is a sound absorption frequency spectrum graph obtained by theoretical calculation and simulation calculation of the sound absorption metamaterial in example 2.
Fig. 5 is a sound absorption frequency spectrum graph obtained by theoretical calculation and simulation calculation of the sound absorption metamaterial in example 3.
Fig. 6 is a sound absorption spectrum graph obtained by theoretical calculation and simulation calculation of the sound absorption metamaterial in the comparative example 1.
The piezoelectric film comprises a back cavity 1, a piezoelectric film 2, a metal film 3, a negative capacitor I, a negative capacitor 5, a resistor 6, a piezoelectric sheet 7, a negative capacitor II, and a negative inductance 8.
Detailed Description
The invention is further illustrated by the following figures and detailed description, wherein the process is conventional unless otherwise specified, and the starting materials are commercially available from a public disclosure without further specification.
In the following examples, the theoretical calculation of the sound absorption coefficient is as follows:
the low-frequency sound absorption metamaterial is an axisymmetric model based on the radius (R) of a piezoelectric sheet 61) Inner radius and outer radius (R) of piezoelectric film 22And R3) Radius (R) of metal film 34) For reference, the cross-section of the composite film is divided into four regions, the central region being equal to the cross-sectional area of the piezoelectric stack, as shown in fig. 2. Considering that the four regions are all homogeneous media, the respective densities, thicknesses, Young's moduli and Poisson ratios are respectively rho1,h1,E1,υ1,ρ2,h2,E2,υ2,ρ3,h3,E3,υ3And ρ4,h4,E4,υ4(ii) a The lower end of the piezoelectric stack is fixed, the upper end of the piezoelectric stack is connected with the center of the composite film, the piezoelectric stack is regarded as an equivalent spring, and the stiffness coefficient is KsThe acting force exerted on the composite film by the piezoelectric stack is F. Under the action of acoustic load, the upper end of the piezoelectric stack and the center of the composite film move integrally: f ═ Ksw1，w1Is the displacement of the composite film in region 1. The acting force exerted on the composite film by the piezoelectric stack is considered as being satisfied when the load is uniformly distributed:
Figure BDA0001599155930000071
the equivalent load strength for each point in region 1 is therefore:
Figure BDA0001599155930000072
when only the acoustic load acts, each region satisfies the wave equation
Figure BDA0001599155930000073
Wherein the content of the first and second substances,
Figure BDA0001599155930000074
for bending stiffness, w (r) is the out-of-plane displacement at radius r, E is the composite filmAnd upsilon is the poisson ratio of the composite film, ρ is the density of the composite film, h is the thickness of the composite film, ω -2 π f is the angular frequency, f is the acoustic frequency, and Δ P is the sound pressure difference between the two sides of the composite film. The general solution of equation (1) can be written as follows
Figure BDA0001599155930000075
Wherein the content of the first and second substances,
Figure BDA0001599155930000076
J0(kr),Y0(kr),I0(kr),K0(kr) being a first, second and first second modified Bessel function, a1,a2,a3,a4Is an unknown vibration coefficient. For four areas on the composite film, the control equation and the related solution are in the form of the following according to the load and the boundary condition to which the four areas are subjected:
region 1
Since the composite film in the area is simultaneously subjected to the sound pressure load and the load of the piezoelectric stack, the control equation is expressed as
Figure BDA0001599155930000077
After simplification, the product can be obtained
Figure BDA0001599155930000078
Wherein the content of the first and second substances,
Figure BDA0001599155930000079
the solution of which can be expressed as
Figure BDA0001599155930000081
Region 2
Figure BDA0001599155930000082
Wherein the content of the first and second substances,
Figure BDA0001599155930000083
the solution of which can be expressed as
Figure BDA0001599155930000084
Region 3
Figure BDA0001599155930000085
Wherein the content of the first and second substances,
Figure BDA0001599155930000086
the solution of which can be expressed as
Figure BDA0001599155930000087
Region 4
Figure BDA0001599155930000088
Wherein the content of the first and second substances,
Figure BDA0001599155930000089
the solution of which can be expressed as
Figure BDA00015991559300000810
Wherein the content of the first and second substances,
Figure BDA00015991559300000811
for 14 unknown vibration coefficients, the solution can be made by the continuity condition,the process is as follows
Region 1 and region 2 have a radius R1There are continuity conditions:
continuous displacement
w1(R1)＝w2(R1) (12) slope continuity
Figure BDA0001599155930000091
Continuous shear force
Figure BDA0001599155930000092
Continuous bending moment
Figure BDA0001599155930000093
Region 2 and region 3 at radius R2There are continuity conditions:
continuous displacement
w2(R2)＝w3(R2) (16) slope continuity
Figure BDA0001599155930000094
Continuous shear force
Figure BDA0001599155930000095
Continuous bending moment
Figure BDA0001599155930000096
Region 3 and region 4 have a radius R3There are continuity conditions:
continuous displacement
w3(R3)＝w4(R3) (20) slope continuity
Figure BDA0001599155930000097
Continuous shear force
Figure BDA0001599155930000101
Continuous bending moment
Figure BDA0001599155930000102
For region 4, at radius R4When the boundary is fixed, its displacement and slope are zero, then there is
w4(R4)＝0(24)
Figure BDA0001599155930000103
Through simultaneous equations (12) - (25), the corresponding 14 unknown coefficients can be solved, and then the acoustic impedance of the composite film can be obtained, and the expression is as follows
Figure BDA0001599155930000104
Wherein the content of the first and second substances,
Figure BDA0001599155930000105
the cross-sectional area of the cavity (i.e. the total area of the composite film),
Figure BDA0001599155930000106
is the area of the region 1 and,
Figure BDA0001599155930000107
is the area of the region 2 and,
Figure BDA0001599155930000108
is the area of the region 3 and,
Figure BDA0001599155930000109
is the area of region 4. Since the vibration of the composite film is small and plane waves are on both sides, Δ P remains equal across the entire cross section. Where w is the average displacement of the composite film and can be expressed as
Figure BDA00015991559300001010
After the acoustic impedance of the composite film is obtained, for the back cavity 1, the acoustic impedance is expressed as follows, taking into consideration that the inside of the cavity is an acoustic hard boundary
Figure BDA00015991559300001011
Where ρ is0,c0,k0Is the density, sound velocity and wave vector h of the air when sound waves propagate in the aircIs the cavity thickness. The total acoustic impedance can be expressed as
Figure BDA0001599155930000111
In the formula, RtAnd XtRespectively, the total dimensionless acoustic resistance and acoustic reactance, and the acoustic absorption coefficient can be obtained
Figure BDA0001599155930000112
In the above calculations, regions 1, 2, 3, 4 are all considered to be homogeneous media, and the equivalent spring rate KsThe default is known. The area 3 is actually composed of three layers of films, the equivalent spring stiffness of the piezoelectric stack is unknown, so corresponding equivalent parameters need to be solved and can be substitutedThe above process is calculated. The material of the region 3 is divided into two parts, consisting of a metal film 3 and a piezoelectric film 2. In the case of very thin thicknesses, the main parameters that have an effect on the vibration of the composite film are density and bending stiffness. Equivalence for density satisfies conservation of mass
ρeff＝Vaρa+Vmρm(31)
Wherein, VaAnd VmDenotes the volume fraction, ρ, of the metal film 3 and the piezoelectric film 2aAnd ρmIs the density of the metal film 3 and the piezoelectric film 2. The overall bending stiffness of region 3 comprises two parts: the bending stiffness of the metal film 3 and the piezoelectric film 2 was solved in the following manner
Figure BDA0001599155930000113
Figure BDA0001599155930000114
At hm＝haCan be obtained in the case of
Figure BDA0001599155930000115
Figure BDA0001599155930000116
When calculating the above-listed equivalent parameters, Em、υmThe young's modulus and poisson's ratio of the piezoelectric film 2 in an external circuit are respectively expressed, and the solution is further performed. For equivalent parameters of the two-dimensional piezoelectric sheet, the thickness of the piezoelectric film is very thin, so that a plane stress model is considered, and the material parameters meet isotropy in a plane. The plane of the piezoelectric sheet 6 is 1-2 planes, the thickness direction is 3 directions, and the constitutive relation can be expressed as follows
Figure BDA0001599155930000121
Wherein S is1、S2、S6To be strained, T1、T2、T6In order to be the stress,
Figure BDA0001599155930000122
is the short circuit flexibility factor of the piezoelectric film 2,
Figure BDA0001599155930000123
the electric displacement, the piezoelectric constant, the dielectric constant, and the electric field intensity of the piezoelectric film 2. When the area of the annular piezoelectric sheet 6 is as
Figure BDA0001599155930000124
Thickness of hmThe impedance of the external circuit is ZmThe current in the circuit can be represented as
Figure BDA0001599155930000125
Wherein the content of the first and second substances,
Figure BDA0001599155930000126
combining equations (36) and (37), after simplification, one can obtain
Figure BDA0001599155930000127
Wherein the content of the first and second substances,
Figure BDA0001599155930000128
is the self-capacitance of the piezoelectric film 2, and can be expressed as
Figure BDA0001599155930000129
Under the condition of plane stress, the constitutive relation of the isotropic material satisfies
Figure BDA00015991559300001210
Wherein E is Young's modulus, upsilon is Poisson's ratio, and G is shear modulus, and the expressions (38) and (40) are corresponded to each other to obtain
Figure BDA0001599155930000131
Figure BDA0001599155930000132
So far the equivalent parameters of region 3 have been found. For a piezo-electric stack, from NsA sheet of piezoelectric material having a total thickness of hsThe upper end is connected with the composite film, the lower end is fixed, and the section of the piezoelectric sheet 6 has a radius R1The circle of (c). The parameters and the geometric shapes of each piezoelectric sheet 6 in the piezoelectric stack are the same, the polarization directions of adjacent piezoelectric sheets 6 are opposite, and the piezoelectric stack is connected with an external circuit Z through couplingsTo adjust the amplitude and frequency dispersion characteristics of the equivalent rigidity, and the external circuit thereof is provided with a negative inductance LsAnd a negative capacitance CsAre connected in series. Under the action of acoustic load, when the composite film vibrates, the piezoelectric material deforms in the thickness direction (3 direction), and since the total dimension of the piezoelectric stack in the thickness direction is larger than the cross-sectional dimension of the piezoelectric stack, the constitutive equation of the material can be written as
Figure BDA0001599155930000133
Figure BDA0001599155930000134
Wherein S is3,T3,
Figure BDA0001599155930000135
And E3Respectively strain, stress, electric displacement and electric field in the thickness direction of the piezoelectric stack,
Figure BDA0001599155930000136
the piezoelectric constant, the short circuit flexibility coefficient and the dielectric constant of the piezoelectric stack are respectively. According to the elasticity control theory of piezoelectric materials, after sound waves act on the composite film, the equivalent modulus of the piezoelectric stack can be expressed as
Figure BDA0001599155930000137
Wherein the content of the first and second substances,
Figure BDA0001599155930000138
the electromechanical coupling coefficient, the short circuit Young modulus, the piezoelectric stack capacitance and the external circuit impedance of the piezoelectric stack are respectively. After obtaining the equivalent modulus of the piezoelectric material, the equivalent spring rate thereof can be expressed as
Figure BDA0001599155930000139
To this end, the equivalent stiffness KsAnd 3, the related parameters of the material in the area are obtained, and the sound absorption conditions under different circuit parameters can be theoretically calculated by bringing the parameters into the previous analysis process.
Example 1
As shown in fig. 1, a wide and low frequency sound absorption metamaterial includes a back cavity 1, a composite film, a piezoelectric film circuit, a piezoelectric stack and a piezoelectric stack circuit;
the back cavity 1 is a cavity structure with one open end and the thickness hcIs 3 cm;
the composite film is a composite structure formed by sequentially bonding a piezoelectric film 2, a metal film 3 and the piezoelectric film 2 together; the piezoelectric film 2 is of a circular ring structure, a boss structure is machined in the center of the metal film 3, and the piezoelectric film 2 is nested on the boss structure of the metal film 3; the piezoelectric film 2 is made of PZT-5H piezoelectric ceramic material, and the other material isThe metal film 3 is an aluminum film; in addition, R in FIG. 21＝1mm、R2＝20mm、R340mm and R4The thickness of the piezoelectric film 2 inside and outside the cavity of the back cavity 1 is 0.2mm, the thickness of the metal film 3 in the regions 1 and 2 is 0.6mm, and the thickness of the metal film 3 in the regions 3 and 4 is 0.2 mm;
a negative capacitor I4 and a resistor 5 are connected in series in the piezoelectric film circuit; wherein, the negative capacitance I4 is-400 nF, and the resistance 5 is 55 omega;
the piezoelectric stack is formed by sequentially bonding 8 piezoelectric sheets 6 with the same geometric shape, wherein the radius R of each piezoelectric sheet 61Smaller than the inner radius of the piezoelectric film 2, and the polarization directions of two adjacent piezoelectric sheets 6 are opposite; in addition, the piezoelectric sheet 6 is made of PMN-0.33PT, has the thickness of 1.25mm and the radius of 1 mm;
a negative capacitor II 7 and a negative inductor 8 are connected in series in the piezoelectric stack circuit; wherein the negative capacitance II 7 is-1.4489 nF, and the negative inductance 8 is-1.2H;
the composite film is fixedly connected with the open end of the back cavity 1, so that the back cavity 1 forms a closed cavity; the piezoelectric stack is arranged in the back cavity 1, one end of the piezoelectric stack is fixedly connected with the back cavity 1, and the other end of the piezoelectric stack is fixedly connected with the center of the composite film; one layer of piezoelectric film 2 positioned outside the back cavity 1 is connected with one piezoelectric film circuit, the other layer of piezoelectric film 2 positioned in the back cavity 1 is connected with the other piezoelectric film circuit, and the two layers of piezoelectric films 2 and the two piezoelectric film circuits are grounded; piezoelectric stack circuit one end all is connected with every piezoelectric patches 6 in the piezoelectric stack, and the other end ground connection, every piezoelectric patches 6 in the piezoelectric stack all ground connection moreover.
The normal incidence sound wave within 300Hz is applied to the wide and low frequency sound absorption metamaterial, the sound absorption effect is evaluated through two ways of theoretical calculation and simulation in finite element software Comsol, and the results of the theoretical calculation and the simulation are shown in detail in FIG. 3. Theoretical calculation shows that the absorption rate of the sound absorption metamaterial reaches more than 0.8 within the range of 72Hz to 260Hz, as shown by a curve A in figure 3; as can be known from simulation, the sound absorption metamaterial reaches the absorption rate of more than 0.8 within the range of 86Hz to 257Hz, as shown by a curve B in figure 3. The whole trend of the sound absorption result of the theoretical calculation and the finite element simulation is the same, the goodness of fit is high, and the accurate and reliable absorption result of the wide and low frequency sound absorption metamaterial is demonstrated; the sound absorption rate is more than 0.8 within the range of about 80Hz to 260Hz, and the sound absorption effect of wide and low frequency is good.
Example 2
On the basis of the embodiment 1, the negative capacitance I4 is modified to be 350nF, the resistance 5 is modified to be 180 omega, the negative capacitance II 7 is modified to be 1.4503nF, and the negative inductance 8 is modified to be 1.4H, and other structural compositions and parameter settings of the wide and low frequency sound absorption metamaterial in the embodiment are the same as those of the wide and low frequency sound absorption metamaterial in the embodiment 1.
The normal incidence sound wave within 300Hz is applied to the wide and low frequency sound absorption metamaterial, the sound absorption effect is evaluated through two ways of theoretical calculation and simulation in finite element software Comsol, and the results of the theoretical calculation and the simulation are shown in FIG. 4 in detail. Theoretical calculation shows that the absorption rate of the sound absorption metamaterial reaches more than 0.9 within the range of 91Hz to 250Hz, as shown by a curve A in figure 4; as can be seen from simulation, the sound absorption metamaterial reaches the absorption rate of more than 0.9 in the range of 112Hz to 236Hz, as shown by a curve B in FIG. 4. The whole trend of the sound absorption result of the theoretical calculation and the finite element simulation is the same, the goodness of fit is high, and the accurate and reliable absorption result of the wide and low frequency sound absorption metamaterial is demonstrated; has sound absorption rate of more than 0.9 in the range of about 100 Hz-230 Hz, and has good wide and low frequency sound absorption effect.
Example 3
On the basis of the embodiment 1, the negative capacitance I4 is modified to be 400nF, the resistance 5 is modified to be 55 omega, the negative capacitance II 7 is modified to be 1.4496nF, and the negative inductance is modified to be 0H, and other structural compositions and parameter settings of the narrow-adjustable low-frequency sound absorption metamaterial in the embodiment are the same as those of the wide low-frequency sound absorption metamaterial in the embodiment 1.
The sound absorption effect of the tunable narrow low-frequency sound absorption metamaterial is evaluated by applying normal incidence sound waves within 300Hz and by two ways of theoretical calculation and simulation in finite element software Comsol, and the results of the theoretical calculation and the simulation are shown in detail in FIG. 5. According to theoretical calculation, the absorptivity of the sound absorption metamaterial at 81Hz is 0.88, as shown by a curve I-A in figure 5; as can be seen from simulation, the absorptivity of the sound absorption metamaterial at 76Hz is 0.86, as shown by a curve I-B in FIG. 5.
After the negative capacitor II 7 in the piezoelectric stack circuit is respectively modified to-1.4525 nF and-1.4554 nF, other conditions are not changed, theoretical calculation and simulation are carried out, and the results are shown in II-A, II-B, III-A and III-B in FIG. 5 in detail. Theoretical calculation shows that after the negative capacitance II 7 is modified to-1.4525 nF, the absorptivity of the sound absorption metamaterial at 191Hz is 0.94, as shown by a curve II-A in FIG. 5; after the negative capacitance II 7 was modified to-1.4554 nF, the absorption rate of the sound absorption metamaterial at 246Hz was 0.98, as shown by the curve III-A in FIG. 5. According to simulation, after the negative capacitance II 7 is modified to-1.4525 nF, the absorptivity of the sound absorption metamaterial at 191Hz is 0.92, as shown by a curve II-B in FIG. 5; after the negative capacitance II 7 was modified to-1.4554 nF, the absorption rate of the sound absorption metamaterial at 246Hz was 0.95, as shown by the curve III-B in FIG. 5.
The theoretical calculation and simulation results in fig. 5 have high goodness of fit, which shows that the absorption result is accurate and reliable; according to the related results, by changing the parameters of the negative capacitor II 7, the adjustable narrow low-frequency sound absorption metamaterial can adjust and control the sound absorption frequency within the range of 50Hz to 300Hz on the premise of ensuring high absorption rate, and the geometric configuration and the size do not need to be changed.
Comparative example 1
The other structural compositions and parameter settings of the low-frequency sound absorption metamaterial are the same as those of the wide low-frequency sound absorption metamaterial in the embodiment 1 except that the piezoelectric stack and the piezoelectric stack circuit are not arranged.
The sound absorption effect of the low-frequency sound absorption metamaterial in the comparative example is evaluated by applying normal incidence sound waves within 300Hz and simulating in finite element software Comsol, and the results of theoretical calculation and simulation are shown in detail in FIG. 6. Theoretical calculation shows that the absorptivity of the super sound absorption metamaterial at 291Hz is 0.99, as shown in a curve A in figure 6. As can be seen from simulation, the absorptivity of the super sound absorption metamaterial at 291Hz is 0.98, as shown in a curve B in FIG. 6.
According to the calculation result of the comparative example 1, when the piezoelectric stack and the piezoelectric stack circuit are not arranged in the figure 1, only narrow-frequency absorption can be realized; although the frequency of the sound absorption peak value can be changed by changing the value of the negative capacitance I4, the adjustable frequency range is very small, and the frequency of the sound absorption peak cannot be reduced to the range below 200Hz in the case, namely, the existing low-frequency sound absorption metamaterial has the problems of narrow sound absorption frequency band and poor adjustability.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (8)

1. A low frequency sound absorption metamaterial is characterized in that: the metamaterial comprises a back cavity (1), a composite film, a piezoelectric film circuit, a piezoelectric stack and a piezoelectric stack circuit;
the back cavity (1) is a cavity structure with one open end;
the composite film is a composite structure formed by sequentially laminating a piezoelectric film (2), a metal film (3) and the piezoelectric film (2); the piezoelectric film (2) is of a circular ring structure, a boss structure is machined in the center of the metal film (3), and the piezoelectric film (2) is nested on the boss structure of the metal film (3);
a negative capacitor I (4) and a resistor (5) are connected in series in the piezoelectric film circuit;
the piezoelectric stack is composed of NsThe piezoelectric film is formed by sequentially laminating piezoelectric sheets (6) with the same sheet geometric shape, the radius of each piezoelectric sheet (6) is smaller than the inner radius of the piezoelectric film (2), and the polarization directions of two adjacent piezoelectric sheets (6) are opposite;
a negative capacitor II (7) and a negative inductor (8) are connected in series in the piezoelectric stack circuit;
the composite film is fixedly connected with the open end of the back cavity (1) to ensure that the back cavity (1) forms a closed cavity; the piezoelectric stack is arranged in the back cavity (1), one end of the piezoelectric stack is fixedly connected with the back cavity (1), and the other end of the piezoelectric stack is fixedly connected with a boss structure of the metal film (3) in the composite film; one layer of piezoelectric film (2) in the composite film is connected with one piezoelectric film circuit, the other layer of piezoelectric film (2) is connected with the other piezoelectric film circuit, and the two layers of piezoelectric films (2) and the two piezoelectric film circuits are grounded; piezoelectric stack circuit one end all is connected with every piezoelectric patches (6) in the piezoelectric stack, and the other end ground connection, and every piezoelectric patches (6) in the piezoelectric stack all ground connection moreover.
2. The low frequency sound absorbing metamaterial according to claim 1, wherein: the thickness of the back cavity (1) is 2 cm-10 cm.
3. The low frequency sound absorbing metamaterial according to claim 1, wherein: the thickness of the back cavity (1) is 3 cm-5 cm.
4. The low frequency sound absorbing metamaterial according to claim 1, wherein: the piezoelectric film (2) is made of PZT-5 series piezoelectric ceramic materials.
5. The low frequency sound absorbing metamaterial according to claim 4, wherein: the piezoelectric film (2) is made of PZT-5H or PZT-5J.
6. The low frequency sound absorbing metamaterial according to claim 1, wherein: the metal film (3) is made of aluminum, copper, iron or aluminum alloy.
7. The low frequency sound absorbing metamaterial according to claim 1, wherein: the piezoelectric sheet (6) is made of PMN-PT series piezoelectric ceramic materials.
8. The low frequency sound absorbing metamaterial according to claim 7, wherein: the piezoelectric sheet (6) is made of PMN-0.33 PT.
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