# Acoustic Metamaterial and Wave Control

### Negative refraction of chiral thin plate elastic metamaterial

When elastic metamaterial has negative effective mass and negative effective modulus simultaneously, there will be negative refraction behavior. Through the design of thin plate's cell, it will have negative effective modulus came from the rotational resonation of the mass, and negative effective mass came from translation resonation of the mass. Based on this design, we successively made sub wavelength double negative metamaterial, and confirmed its negative refraction behavior through experiments.

R Zhu, XN Liu, GK Hu, CT Sun, GL Huang, Negative refraction of elastic waves at deep-subwave length scale in a single-phase metamaterial, Nature Communication, 5, 5510, 2014.

### Study on dynamic effective features of thin plate acoustic metamaterial

Because of the lightweight feature of thin plate, it has various applications in engineering. If microstructure resonator is properly introduced, then the plate will have improvement on sound absorption effect in some ranges of frequency. Based on the theoretical model, we analytically calculate the sound response of the multilayer thin plate with periodic local resonator imbedded. Then we use correctional transfer matrix to calculate the effective parameter of the structure. For single layer thin plate, we have analytical expression for effective density and effective modulus when acoustic wave incident perpendicularly to the surface. By analyzing parameters, we found that for different range between resonators, effective negative mass can be depicted through Lorentz or Drude model. In the range of negative mass, effective parameters won't change with layers count. When incident acoustic wave is inclined and wavelength is far larger than periodic cell's geometry parameters, effective parameters won't change with incline angle. Otherwise, effective parameters will change with incline angle, and thus effective density will have space dispersion effect.

P Li, SS Yao, XM Zhou, GL Huang and GK Hu, Effective medium theory of thin-plate acoustic metamaterials, J. Acoust. Soc. Am., 135, 1686, 2014

### Application of acoustic metamaterial in sealed cavity and the study of sound absorption

In free space, acoustic metamaterial can absorb acoustic wave effectively in negative mass frequency range. As for sealed cavity, it's still indefinite whether acoustic metamaterial will have abosption effect. So we studied that effect to inner sound source of the circular sealed cavity consist of thin plate metamaterial. Results showed that if sound source is positioned in center, monopolar/dipolar/four polar sound source can only excite corresponding resonant mode of the cavity, and cause severe sound radiation in negative mass frequency range. If we increase the thickness of the metamaterial, sound absorption effect will be enhanced, and finally can achieve sound attenuation in the whole frequency range of negative mass. If sound source is positioned on in center, then whatever polar sound source we use, it will excite similar sound radiation resonant mode, and thus there will be multiple hard radiation frequency in negative mass range. Just like the case in which source is positioned in center, increasing thickness of the metamaterial will improve the effect of sound radiation absorption.

SS Yao, P Li, XM Zhou and GK Hu, Sound reduction by metamaterial-based acoustic enclosure, AIP Advances, 4, 124306, 2014

### Theoretical model for interaction between sub wavelength membrane and acoustic wave

According to experiment, fully pre-stretched membrane with small metal pieces attached on is well for low frequency sound absorption. Based on point matching method, we depict the influence of metal pieces on deformation of the membrane. Then we build up theoretical model to calculate the acoustic wave response precisely, results are well fit with FEM's. So this model can be used to systematically analyze the influence of metal piece's weight, shape, geometry, count and position on sound absorption. In this analytical model, pre-stretched membrane is depicted by membrane function with pre stress. The corresponding structure is mainly used for low frequency sound insulation. As for sound absorption, we use thin plate function to depict absorption mechanism conducted by in-plane strain energy dissipation. It's worth to mention that, through this analytical model we know that sound absorption ratio of membrane structure has a limit as 50%. This limit has no connection with any microstructure's parameter or any dissipation ratio of the membrane. That conclusion helped us revised some results of experiments.

YY Chen, XM Zhou, GK Hu and GL Huang, Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials: membrane model, J. Acoust. Soc. Am., 136, 969, 2014

YY Chen, GL Huang, XM Zhou, GK Hu and CT Sun, Analytical coupled vibroacoustic modeling of membrane-type acoustic metamaterials: plate model, J. Acoust. Soc. Am., 136, 2926, 2014

### Design of ultra thin structure targeting low frequency sound absorption

Propagation range of acoustic wave in cavity is about a quarter of a wavelength, so that it can achieve high efficiency in sound absorption. But to achieve equivalent effect in low frequency sound, it needs more thicker materials. To minimize the thickness, we convert the parallel acoustic cavity to helix, and 3D print the prototype. We found in numerical simulation and experimental test that around the range of frequency where satisfy the wavelength condition as 1/4 wavelength, it can achieve a high efficiency sound absorption, and the thickness of the structure is 1/50 of the wavelength. We further design the Helmholtz resonance cavity, both simulation and experiment show that this structure can realize absorption effect in much lower frequency range. And the thickness of the structure is only 1/102 of the wavelength.

XB Cai, QQ Guo, GK Hu and J Yang, Ultrathin low-frequency sound absorbing panels based on coplanar spiral tubes or coplanar Helmholtz resonators, Applied Physics Letters, 105, 121901, 2014.

### Broadband vibration control of chiral lattice structure

Chiral lattice structure is lightweight and has high frequency range band gap, but it's hard to attenuate low frequency vibration. Introducing local resonance unit to chiral lattice structure and tuning the local resonant frequency can realize the low frequency vibration attenuation of chiral lattice structure. Besides, both theory and experiment show that by introducing resonance unit with different resonant frequency, we can get broader band gap to control vibration.

R. Zhu, XN Liu, GK Hu, CT Sun and GL Huang, A chiral elastic metamaterial beam for broadband vibration suppression, Journal of Sound and Vibration, 333:2759 , 2014.

### Homogenization of anisotropy chiral lattice material

Using orthogonal irreducible decomposition of tensor method, we get the general form of elastic tensor of two dimensional micropolar. This form is able to depict chiral features and other symmetry features, such as hexagonal symmetry and quadrilateral symmetry. Based on that form, we homogenized the chiral lattice structure composed of circular beam, and analytically got the macroscopic effective elastic constants related to geometry parameters. We also studied the elastic constants with change of geometry parameters, and the propagation features of this anisotropy structure.

Y Chen, XN Liu, GK Hu, QP Sun, QS Zheng, Micropolar continuum modelling of bi-dimensional tetrachiral lattices, Proceedings of the Royal Society A, 470(2165), 20130734, 2014.

### Complex space transform of elastic wave and realization of absorption boundary layer

Elastic wave absorption boundary layer is significant in calculation and experiment. It can eliminate boundary reflection and thus be used to simulate infinite space with finite space. Besides, measurement of elastic wave also needs it to eliminate boundary reflection. So far the elastic wave absorption boundary layer is only mathematical, and mainly be used in numerical calculation. Using elastic wave transform method, we can develop it to complex space. And by controlling imaging parts of material constants, we can realize the manipulation of dissipation of elastic wave's propagation. And then we can design the elastic wave absorption boundary layer in reality.

### Experimental study of acoustic wave's super resolution imaging based on resonant tunneling

Lens is composed of aluminum plate with periodic drilled holes, and radius of the hole is changing periodically along the axis of the hole. Considering the large impedance mismatch between aluminum plate and air, lens's mass along the surface can be treated as infinite. Wave propagation along the axis of the hole can satisfy the complete transfer condition conducted by resonant tunneling effect. Because the microstructure of designed metamaterial lens is sub wavelength, it solved the problem that nowadays' super resolution lens is geometrically massive. Using acoustic field testing system, we got the imaging result of two sound sources (distance = 11cm) on lens surface around resonant tunneling frequency (wavelength = 38cm). From the result we can get that distance between sound sources is sub wavelength, but still distinguishable, which proves that designed lens is able to break the diffraction limit of imaging.

Z. Chang, DK Guo, XQ Feng and GK Hu, A facile method to realize perfectly matched layers for elastic waves, Wave Motion, 11,1170, 2014

HJ Su, XM Zhou, XC Xu and GK Hu, Experimental study on acoustic subwavelength imaging of holey-structuredmetamaterials by resonant tunneling, J. Acoust. Soc. Am., 135, 1686, 2014.