Zhilin Hou

A sonic band gap based on the locally resonant phononic plates with stubs

Using the finite element method, we have studied the acoustic properties of a novel phononic crystal (PC) structure constructed by periodically depositing single-layer or two-layer stubs on the surface of a thin homogeneous plate. Numerical results show that the extremely low frequency band gap (BG) of the Lamb waves can be opened by the local resonance (LR) mechanism. We found that the width of such a BG depends strongly on the height and the area of cross section of the stubs. The displacement field distribution of the oscillating modes is given to explain how the coupling of the modes induces the opening of the BG. The physics behind the opening of the LRBG in our phononic structures can be understood by using a simple spring-mass model.

Propagation of acoustic waves and waveguiding in a two-dimensional locally resonant phononic crystal plate

We demonstrate the waveguiding of Lamb waves in a locally resonant phononic crystal (LRPC) and we present an analysis of the guiding of elastic waves in straight and bent waveguides. The finite element method combined with the supercell technique was used to analyze the band gap and the dispersion relation of LRPC waveguides. Unlike the traditional phononic crystals, we show the possibility of guiding only one confined mode inside a LRPC waveguide. We discuss the confinement and the transmission of the guided mode as a function of the width of the waveguide based on both the band structure and the displacement field.

Broadband plate-type acoustic metamaterial for low-frequency sound attenuation

We show experimentally that plate-type acoustic metamaterials can serve to totally prohibit low frequency structure-borne sound at selective resonance frequencies ranging from 650 to 3500 Hz. Our metamaterial structures are consisting of a periodic arrangement of composite stubs (tungsten/silicone rubber) deposited on a thin aluminium plate. We report that these metamaterials present a broadband gap of out-of-plane modes at frequencies where the relevant sound wavelength in air is about three orders of magnitude larger than the plate thickness. Confinement and waveguiding of structure-borne sound in this sub-wavelength resonant regime is also experimentally evidenced and discussed.

Opening a large full phononic band gap in thin elastic plate with resonant units

In this paper, the mechanism for opening a locally resonant band gap in a thin elastic plate is investigated. Two previously suggested structures, which are constructed by periodically drilling holes on elastic plate and then filling them with the rubber-coated masses, or just by periodically stubbing the rubber rods with mass cap on the plate, are revisited. We find that, because of the partial band gaps for in-plane and out-of-plane plate modes cannot be appropriately overlapped, the full band gaps in both of the structures are generally narrow. The reason for this phenomenon is based on the selective coupling between the different resonant patterns of the resonant units and the in-plane and out-of-plane plate modes. Based on the understanding, a new structure with the three-layered spherical resonant units is proposed. Numerical results show that, making use of such kind of resonant units, a large sub-wavelength full band gap can be opened.

Analysis of surface acoustic wave propagation in a two-dimensional phononic crystal

In this paper, we present a numerical technique to calculate the surface acoustic wave (SAW) in a two-dimensional phononic crystal (PC). By the technique, the SAW in the system, which is obtained by adding an additional composite surface layer on the xy-cut surface of a two-dimensional PC, is investigated. Result shows that the behavior of SAW in the studied system is mainly determined by the residual penetration depth of the SAW into the PC structure. Based on this understanding, we show that the SAW in the band gap of the PC can be controlled efficiently by changing the structure of the surface layer.

Tunable solid acoustic metamaterial with negative elastic modulus

We report in this letter on a tunable solid acoustic metamaterial with negative elastic modulus by means of piezoelectric composite. The theoretical formulae for one-dimensional layer-stacked metamaterial embedding a piezoelectric material by means of external shunted inductors are presented. The acoustic band structure of the composite is calculated by the transfer matrix method. Results show that a band gap can be opened and tuned by the resonant behavior of the LC circuit. It is found further by the formulae that piezoelectric material with large piezoelectric constant and small elastic modulus will be beneficial for opening a wide band gap. The effective elastic constant of the system is also calculated by the unit-cell-boundary-averaging method. Result shows that the system behaves as an effective medium with a negative elastic modulus. This property is quite different from the typical solid metamaterial achieved by dispersing heavy inclusions coated with a soft layer into a matrix for which only the negative mass density can be obtained.

Tunable elastic parity-time symmetric structure based on the shunted piezoelectric materials

We theoretically and numerically report on tunable elastic Parity-Time (PT) symmetric structure based on shunted piezoelectric units. We show that the elastic loss and gain can be archived in piezoelectric materials when they are shunted by external circuits containing positive and negative resistances. We present and discuss, as an example, the strongly dependent relationship between the exceptional points of a three-layered system and the impedance of their external shunted circuit. The achieved results evidence the PT symmetric structures based on this proposed concept can actively be tuned without any change of their geometric configurations.

Band Gap in Phononic Crystal Thin Plate with/without Mirror Plane

The mechanism of opening a band gap in the free phononic crystal (PC) thin plate with or without a mirror plane is investigated. It is found that, in a PC plate with a mirror plane, the permitted modes can be separated into symmetric and antisymmetric modes, and the band gap in such a system can be opened by the interaction between the modes of the same kind and/or the breaking of the degeneracy of the mode at the edge of the Brillouin zone. However, for a PC plate without a mirror plane, mode separation can no longer be performed, and interaction can occur between any two permitted modes. As a result, a new kind of band gap can be opened.

Computation of plate wave dispersion diagrams and surface wave velocities without explicit boundary conditions

For the evaluation of the dispersion relation of surface acoustic waves (SAW) or plate (Lamb) waves, it is generally necessary to form a determinant of the boundary conditions and to seek its zeros as a function of the wave vector for a fixed frequency. Finding all zeros can be a numerically difficult problem. The plane wave expansion (PWE) method is used in the field of phononic crystals to formulate eigenvalue problems to compute dispersion diagrams for solid-solid compositions. We discuss in this paper how the boundary conditions can be included implicitly in the form of the PWE solution, thus leading to an efficient eigenvalue problem. The solutions of the eigenvalue problem represent waves propagating in the plate with a given wave vector along the surface. Furthermore, SAW velocities can be estimated from the slowest wave for large wave vectors. The PWE numerical algorithm is fast and accurate. Examples for a single plate and a multilayer plate are given, and extension to piezoelectric materials is discussed. The method can be of value for numerical codes requiring a generic method for wave dispersion that does not require an initial guess for the solution.