CN109119059B - Double-negative-acoustic metamaterial structure based on Helmholtz resonator coupling - Google Patents
Double-negative-acoustic metamaterial structure based on Helmholtz resonator coupling Download PDFInfo
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- CN109119059B CN109119059B CN201811107467.0A CN201811107467A CN109119059B CN 109119059 B CN109119059 B CN 109119059B CN 201811107467 A CN201811107467 A CN 201811107467A CN 109119059 B CN109119059 B CN 109119059B
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- 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
- G10K11/172—Methods or devices for protecting against, or for damping, noise or other acoustic waves in general using resonance effects
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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
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Abstract
The invention relates to a double-negative-acoustic metamaterial structure based on Helmholtz resonator coupling, which comprises a plurality of double-negative-acoustic metamaterial units which are sequentially connected, wherein each double-negative-acoustic metamaterial unit comprises a waveguide with openings at the front end and the rear end and at least one pair of Helmholtz resonators which are connected on a waveguide pipe in parallel and coupled, and the Helmholtz resonators are hermetically connected with the waveguide to form a fluid communication space.
Description
Technical Field
The invention relates to the field of acoustic functional materials, in particular to a double-negative acoustic metamaterial structure based on Helmholtz resonator coupling.
Background
The acoustic functional material is a sub-wavelength structure which is artificially constructed, can realize the phenomena and functions which are not possessed by the traditional material, and effectively regulates and controls sound waves. Such as structures having a negative effective dynamic density or negative effective dynamic volume compressibility alone, have been implemented in a variety of designs. Related effects such as acoustic super-resolution focusing, acoustic stealth, and amplification of evanescent waves have also been implemented in laboratories. Meanwhile, the material with the negative effective mass density and the negative effective bulk compression coefficient can show a negative refractive index, realizes super-resolution convergence, and is called as an acoustic left-handed material. Acoustically functional materials with dual negative properties are implemented in the laboratory using a negative effective modulus perforated tube in combination with a negative effective density membrane material. However, this combination requires multi-cell connections and impedance matching and dissipation needs further improvement. The realization of a material with both negative effective density and negative effective bulk modulus of elasticity using negative effective density membrane coupling is done in the laboratory. Due to the structural seal, fluid loss or external fluid inflow caused by vibration is avoided, the double-negative acoustic metamaterial generated by the coupling effect of the single negative material is realized, less dissipation is realized, and the transmission performance is improved. Recently, by utilizing a multiple-volume scattering theory, symmetry of space and frequency of resonator distribution is broken, an acoustic metamaterial with effective mass density and effective volume compression coefficient being negative is realized, and a super-resolution prism is built based on the structure, however, bandwidth and high efficiency of double negative regions of the material need to be further improved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a double-negative acoustic metamaterial structure based on Helmholtz resonator coupling.
The purpose of the invention can be realized by the following technical scheme:
a double-negative-acoustic metamaterial structure based on Helmholtz resonator coupling comprises a plurality of double-negative-acoustic metamaterial units which are connected in sequence, wherein each double-negative-acoustic metamaterial unit comprises a waveguide with openings at the front end and the rear end and at least one pair of Helmholtz resonators which are connected in parallel on a waveguide pipe and coupled with the waveguide pipe, and the Helmholtz resonators are hermetically connected with the waveguide to form a fluid communication space;
the double-negative-acoustic metamaterial structure realizes negative effective mass density and negative effective volume compression coefficient through coupled Helmholtz resonators, enables the negative effective volume compression coefficient and the negative effective mass density to be overlapped in the same frequency band, and tunes the bandwidth of a double negative area and the position of the double negative area by changing the distance and the resonant frequency between the two coupled Helmholtz resonators on the double-negative-acoustic metamaterial unit.
The waveguide is a cylindrical one-dimensional waveguide, and the two Helmholtz resonators connected in parallel have the same basic resonance frequency.
The waveguide is a circular two-dimensional waveguide.
The Helmholtz resonator comprises a square cavity and a cylindrical neck connected with the waveguide.
The Helmholtz resonators connected in parallel have different basic resonance frequencies, and the eigen frequency of the double-negative-acoustic metamaterial structure is adjusted by arranging the Helmholtz resonators with different basic resonance frequencies.
When the double-negative acoustic metamaterial unit is in an intrinsic mode, the sound pressure field distribution of the two free interfaces has two different space symmetry forms, including in-phase distribution and anti-phase distribution.
The waveguide has adjustable length.
The Helmholtz resonators are symmetrically distributed on the same side or different sides of the central axis of the waveguide.
Compared with the prior art, the invention has the following advantages:
firstly, the structure is simple: the invention replaces the original structural form of adopting a single resonator and a film, and provides an acoustic functional material structure which can realize negative effective mass density and negative effective volume compression coefficient in a limited adjustable frequency band through a simple structure.
II, double negative characteristics: in terms of functions, negative effective mass density is coupled through a Helmholtz resonator, and the frequency bands of the two effective parameters are overlapped in the previous research, so that the Helmholtz resonator can realize negative effective volume compression coefficient, and single-broadband high-efficiency double-negative property and multi-band double-negative property can be realized by adjusting the distance and the resonance frequency between the two coupled Helmholtz resonators on the double-negative acoustic metamaterial unit.
Thirdly, high-efficiency characteristic: as for the existing double-negative unit structure, the unit adopts single-negative Helmholtz resonator metamaterial coupling to realize double negative, and has good impedance matching with surrounding media, so that the high-efficiency transmission of sound energy is realized, the energy loss is reduced, if the transmission of a double negative area in a figure 4a exceeds 90%, the transmission value is far higher than that of the double negative area realized by adopting a film material mode, and a high-efficiency solution is provided for the application of double negative materials.
Fourthly, explanation of double negative mechanism: the double negative mechanism adopts eigen mode expansion theory, well explains the principle that double negative is generated by overlapping monopole resonance and dipole resonance, is mutually verified with the eigenvalue simulation result, and also proves that the coupling structure can form two eigen modes of monopole resonance and dipole resonance, and the effective parameters of uniform theory quantitative analysis are overlapped in certain frequency bands, so that the requirement on the structure scale is looser.
Drawings
Fig. 1 is an equivalent circuit theoretical diagram of an acoustic metamaterial unit.
Fig. 2 (a) is a cross-sectional view of a double negative acoustic metamaterial unit.
Fig. 2b is a graph of transmission and reflection coefficient versus phase measurements.
Fig. 3 shows the distribution of the sound pressure field in the eigenmode, in which fig. (3a) shows the opposite phase distribution of the sound pressure field at 895.25Hz, and fig. (3b) shows the same phase distribution of the sound pressure field at 1185.3 Hz.
Fig. 4 shows the results of simulation, experimental and theoretical calculations of the transmission, reflection intensity and phase of the structure. Fig. 4a shows the transmission coefficient and phase results, fig. 4b shows the reflection coefficient and phase results, fig. 4c shows the experimental back-projection and theoretical calculation results for the effective parameters, and fig. 4d shows the expansion results of the interface response green function in eigenmodes.
Fig. 5 is a multiple Helmholtz resonator coupling case, where graph (5a) is the experimental and theoretical effective mass density and effective bulk compression coefficient, and graph (5b) is the experimental and theoretical transmission coefficient.
Fig. 6 shows the effective mass density and effective body compression factor extracted experimentally, simulated and theoretically.
Detailed Description
The invention provides an acoustic functional material, which realizes negative effective mass density through coupling of Helmholtz resonators and realizes that the negative effective volume compression coefficient and the negative effective mass density are overlapped in the same frequency band. The structure of the present invention is a resonant structure having a double negative property. The structure disclosed by the invention provides an acoustic device which can realize single-broadband high-efficiency double negative property and multi-band double negative property in airborne sound.
As shown in fig. 1, the double negative acoustic metamaterial structure realizes negative effective mass density and negative effective volume compression coefficient through coupled Helmholtz resonators, and enables the negative effective volume compression coefficient and the negative effective mass density to be overlapped in the same frequency band. The principle is as follows:
the equivalent acoustic impedance of a Helmholtz resonator is
Pipe orifice equivalent sound mass M of Helmholtz resonatorh＝ρoLeff/ShCavity equivalent acoustic capacity C of Helmholtz resonatorh＝V/ρ0c0，RhIs the acoustic resistance of a Helmholtz resonator, omega being the resonance angular frequency, rho0Is the density of air, c0Is the sound velocity in air, V is the cavity volume of the Helmholtz resonator, SnIs the cross-sectional area, L, of the Helmholtz resonator calibereffL + Δ l is the effective length of the helmholtz resonator orifice, and Δ l is the equivalent co-vibrating mass due to the acoustic radiation. Z0＝ρ0c0and/A is the distributed acoustic impedance of the waveguide, and A is the cross section of the waveguide. Ma＝ρ0The s/A is the coupling mass between two Helmholtz resonators, and s is the spacing between the resonators. To obtain a Fano-like transmission spectrum, the acoustic frequency should be close to the resonance frequency of the resonator, so | Zh|＜＜lZ0L. We can therefore give the effective acoustic impedance of the cell:
if the total transmission of Fano resonance is to be generated, the impedance matching of the cell to air must be satisfied, Z ═ Z0The double negative unit resonance condition can be deduced to be 2Z through the matching conditionh/Z0And + jks is 0, so as long as the condition ks < 1 is satisfied, the bandwidth of the double negative region and the position of the double negative region can be tuned by changing the distance s between the two coupled Helmholtz resonators on the double negative acoustic metamaterial unit or changing the resonance frequency omega.
The structure of the invention is as follows:
fig. 2 (a) shows a cross-sectional view of the structural unit. This figure shows a helmholtz resonator comprising two identical structures and a communicating cylindrical waveguide. The waveguide is connected with the Helmholtz resonators in a sealing mode, and the two Helmholtz resonators are symmetrically connected in parallel on the side face of the pipeline.
Example 1:
by way of non-limiting example, one preferred parameter of the functional structure of the invention is as follows: the inner radius of the cylindrical waveguide is 15mm (the thickness and the material of the outer wall are required to ensure the rigid hard boundary condition), and the length of the cylindrical waveguide is 100 mm. The neck of the helmholtz resonator is a cylindrical opening, the inner radius is 5mm, the height H is 8mm, and the interior of the cavity of the resonator is a cube with the size of 25mm × 25mm × 25 mm. The distance between the two Helmholtz resonators is 50mm, and the material can be any hard material. The transmission and reflection coefficients and phase measurements are shown in FIG. 2b and can be measured by a "Bruel and Kjaer type-4206" acoustic impedance tube. The front end provides plane waves for the loudspeaker, the rear end is made of sound absorption materials, and four microphones are distributed in the front and the rear of the impedance tube.
Although cylindrical waveguides and square cavity resonators are described in this example, different shapes of tubes and Helmholtz resonators may be used in the present invention. Meanwhile, Helmholtz resonators can also be of different resonance frequencies, and the waveguide can also be coupled with a plurality of resonators of the same or different basic resonance frequencies. Of course, the fundamental resonance frequency and distance of the helmholtz resonator and the length of the waveguide can be different, but cannot be adjusted at will, so that the coupling effect can be achieved sufficiently, and the eigenmode overlapping of the sound pressure opposite phases or in-phase motion at the two free ends of the structure can be realized.
Fig. 3 presents the distribution of the acoustic pressure field in the eigenmode of the structure of fig. 2, simulated from COMOSOL Multiphysics finite element software calculations. It can be seen that fig. 3a shows the reverse phase distribution of the sound pressure field at 895.25Hz, and fig. 3b shows the same phase distribution of the sound pressure field at 1185.3 Hz. Color Bar denotes the intensity distribution of the acoustic pressure field.
Fig. 4 presents the simulated, experimentally and theoretically calculated structural transmission, reflection intensity and phase. Fig. 4 (a) shows the transmission coefficient and phase, and fig. 4 (b) shows the reflection coefficient and phase. Fig. 4c shows the results of experimental back-stepping and theoretical calculations of the effective parameters, with the gray area representing the double negative band region (bandwidth of about 50 Hz). Theoretical calculation results are represented by solid lines, experimental results are represented by small circles, and simulation results are represented by small squares. Theoretical and experimental results show that at 859.25Hz, a transmission peak occurs, corresponding to a reflection minimum, at which the phase undergoes a pi transition. The transmission peak corresponds to a frequency which is exactly equal to the eigenfrequency of the Helmholtz resonator coupled system. It can be seen that the theoretical results agree quite well with the experimental results of the present invention.
Figure (4d) shows the result of the eigenmode expansion of the green function of the interface response,
in a symmetrical mode (in phase),
is in the anti-symmetric mode (anti-phase). As can be seen from FIG. 4d, at the 859.25Hz position
-a divergence of the light emitted by the light source,
zero crossing point, at which both the effective mass density and the effective mass compression factor are negative. When in use
At zero crossing around 916Hz, the double negative overlap ends and enters the region of the single negative effective body compression coefficient. The mode expansion theory is utilized to explain double negatives, a dipole (dipole) resonance mode is realized based on Helmholtz resonator coupling, negative effective mass density is introduced, and the superposition of a negative effective compression coefficient and the negative effective mass density is generated.
Example 2:
fig. 5 shows an example of the coupling of multiple Helmholtz resonators on the basis of the basic structure of fig. 2. The parameters of the waveguide and the Helmholtz resonator are the same as in fig. 1. By way of non-limiting example, the structure may be such that Helmholtz resonators are arranged in a non-helical winding, the number of Helmholtz resonators may be greater or less than 12, and the Helmholtz resonators may be non-cubic in shape. The number of Helmholtz resonators affects the bandwidth and transmission efficiency of the doubly negative region. Figure (5a) shows the experimental and theoretical effective mass density and effective bulk compression factor: the gray region is a double negative band region of about 200Hz, much larger than the 50Hz bandwidth provided by the double Helmholtz resonator system (as shown in figure (4 c)). Fig. 5b plots the experimental and theoretical transmission coefficients, and the grey areas show that the double negative areas achieve efficient acoustic energy transmission.
Example 3:
this example shows an example of the implementation of multiple band double negatives based on Helmholtz resonator coupling at different fundamental resonance frequencies. As a non-limiting example, a structure with multiple bands of double negative devices is shown in FIG. 6, in which three pairs of Helmholtz resonators are connected in parallel, and the fundamental resonance frequencies of the Helmholtz resonators are respectively H1＝1000Hz，H3＝1214Hz，H4752Hz, the waveguide parameters are unchanged. The coupling number of the Hemholtz resonators can be more than or less than 3 pairs, and the basic resonance frequencies of the Hemholtz resonators can be different from H1，H3，H4Fig. 6 shows the effective mass density and effective body compression coefficient extracted experimentally, in simulation and in theory, the dark gray region is a double negative region, and the light gray region is a conventional double positive region. It can be seen that the coupled system forms a 3-band double negative region, implementing a multi-band double negative region.
Claims (7)
1. A double-negative-acoustic metamaterial structure based on Helmholtz resonator coupling is characterized by comprising a plurality of double-negative-acoustic metamaterial units which are connected in sequence, wherein each double-negative-acoustic metamaterial unit comprises a waveguide with openings at the front end and the rear end and at least one pair of Helmholtz resonators which are connected to a waveguide pipe in parallel and coupled with the waveguide pipe in a sealing mode, the Helmholtz resonators are connected with the waveguide in a sealing mode to form a fluid communication space, and the length of the waveguide is adjustable;
the double-negative-acoustic metamaterial structure realizes negative effective mass density and negative effective volume compression coefficient through coupled Helmholtz resonators, enables the negative effective volume compression coefficient and the negative effective mass density to be overlapped in the same frequency band, and tunes the bandwidth of a double negative area and the position of the double negative area by changing the distance and the resonant frequency between the two coupled Helmholtz resonators on the double-negative-acoustic metamaterial unit.
2. The structure of claim 1, wherein the waveguide is a cylindrical one-dimensional waveguide, and the two parallel Helmholtz resonators have the same fundamental resonance frequency.
3. The Helmholtz resonator coupling-based double negative acoustic metamaterial structure as claimed in claim 1, wherein the waveguide is a circular two-dimensional waveguide.
4. The structure of claim 1, wherein the Helmholtz resonator comprises a square cavity and a cylindrical neck connected to the waveguide.
5. The structure of claim 1, wherein the Helmholtz resonators connected in parallel have different fundamental resonance frequencies, and the eigenfrequency of the structure of the double-negative acoustic metamaterial is adjusted by setting the Helmholtz resonators with different fundamental resonance frequencies.
6. The Helmholtz resonator coupling-based double negative acoustic metamaterial structure as claimed in claim 5, wherein the two free interface acoustic pressure field distributions have two different spatially symmetric forms including an in-phase distribution and an anti-phase distribution when the double negative acoustic metamaterial unit is in eigenmode.
7. The structure of the double-negative acoustic metamaterial structure based on the coupling of the Helmholtz resonators as claimed in claim 1, wherein the Helmholtz resonators are symmetrically distributed on the same side or different sides of the central axis of the waveguide.
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