Elastic-wave propagation through disordered and/or absorptive layered systems

A Review of Acoustic Metamaterials and Phononic Crystals

As a new kind of artificial material developed in recent decades, metamaterials exhibit novel performance and the promising application potentials in the field of practical engineering compared with the natural materials. Acoustic metamaterials and phononic crystals have some extraordinary physical properties, effective negative parameters, band gaps, negative refraction, etc., extending the acoustic properties of existing materials. The special physical properties have attracted the attention of researchers, and great progress has been made in engineering applications. This article summarizes the research on acoustic metamaterials and phononic crystals in recent decades, briefly introduces some representative studies, including equivalent acoustic parameters and extraordinary characteristics of metamaterials, explains acoustic metamaterial design methods, and summarizes the technical bottlenecks and application prospects.

Locally Resonant Phononic Crystals at Low frequencies Based on Porous SiC Multilayer

In this work, a one-dimensional porous silicon carbide phononic crystal (1D-PSiC PnC) sandwiched between two rubber layers is introduced to obtain low frequency band gaps for the audible frequencies. The novelty of the proposed multilayer 1D-PnCs arises from the coupling between the soft rubber, unique mechanical properties of porous SiC materials and the local resonance phenomenon. The proposed structure could be considered as a 1D acoustic Metamaterial with a size smaller than the relevant 1D-PnC structures for the same frequencies. To the best of our knowledge, it is the first time to use PSiC materials in a 1D PnC structure for the problem of low frequency phononic band gaps. Also, the porosities and thicknesses of the PSiC layers were chosen to obtain the fundamental band gaps within the bandwidth of the acoustic transducers and sound suppression devices. The transmission spectrum of acoustic waves is calculated by using the transfer matrix method (TMM). The results revealed that surprising low band gaps appeared in the transmission spectra of the 1D-PSiC PnC at the audible range, which are lower than the expected ones by Bragg's scattering theory. The frequency at the center of the first band gap was at the value 7957 Hz, which is 118 times smaller than the relevant frequency of other 1D structures with the same thickness. A comparison between the phononic band gaps of binary and ternary 1D-PSiC PnC structures sandwiched between two rubber layers at the micro-scale was performed and discussed. Also, the band gap frequency is controlled by varying the layers porosity, number and the thickness of each layer. The simulated results are promising in many applications such as low frequency band gaps, sound suppression devices, switches and filters.

A Numerical Method for Flexural Vibration Band Gaps in A Phononic Crystal Beam with Locally Resonant Oscillators

The differential quadrature method has been developed to calculate the elastic band gaps from the Bragg reflection mechanism in periodic structures efficiently and accurately. However, there have been no reports that this method has been successfully used to calculate the band gaps of locally resonant structures. This is because, in the process of using this method to calculate the band gaps of locally resonant structures, the non-linear term of frequency exists in the matrix equation, which makes it impossible to solve the dispersion relationship by using the conventional matrix-partitioning method. Hence, an accurate and efficient numerical method is proposed to calculate the flexural band gap of a locally resonant beam, with the aim of improving the calculation accuracy and computational efficiency. The proposed method is based on the differential quadrature method, an unconventional matrix-partitioning method, and a variable substitution method. A convergence study and validation indicate that the method has a fast convergence rate and good accuracy. In addition, compared with the plane wave expansion method and the finite element method, the present method demonstrates high accuracy and computational efficiency. Moreover, the parametric analysis shows that the width of the 1st band gap can be widened by increasing the mass ratio or the stiffness ratio or decreasing the lattice constant. One can decrease the lower edge of the 1st band gap by increasing the mass ratio or decreasing the stiffness ratio. The band gap frequency range calculated by the Timoshenko beam theory is lower than that calculated by the Euler-Bernoulli beam theory. The research results in this paper may provide a reference for the vibration reduction of beams in mechanical or civil engineering fields.

Propagation of shear elastic and electromagnetic waves in one dimensional piezoelectric and piezomagnetic composites

Coupled shear (SH) elastic and electromagnetic (EM) waves propagating oblique to a one dimensional periodic piezoelectric and piezomagnetic composite are investigated using the transfer matrix method. Closed-form expression of the dispersion relations is derived. We find that the band structures of the periodic composite show simultaneously the features of phononic and photonic crystals. Strong interaction between the elastic and EM waves near the center of the Brillouin zone (i.e., phonon-polariton) is revealed. It is shown the elastic branch of the band structures is more sensitive to the piezoelectric effect while the phonon-polariton is more sensitive to the piezomagnetic effect of the composite.

Comparison of the transmission properties of self-similar, periodic, and random multilayers at normal incidence

The effect of self-similarity on acoustic and elastic wave propagation at normal incidence is investigated using Classical Cantor and Fibonacci multilayered structures. They are made of two sorts of orthotropic plies having differently oriented orthotropic axes with respect to the propagation direction. The properties of their transmission coefficient are presented using a unidirectional numerical model based on a transfer matrix formalism. It was found that stack self-similarity influences the acoustic transmission properties. Transmission coefficients of self-similar stacks present a self-similar shape and behavior. A self-similar process, applied to layer orientation allows multilayered stacks to be created. A thickness-equivalent model was developed to compare these structures with standard self-similar multilayers which are finally compared to periodic and random stacks. The transmission coefficient of a deterministic self-similar Fibonacci structure is similar to that of an averaged transmission coefficient of random stacks.

Wave localization in two-dimensional porous phononic crystals with one-dimensional aperiodicity

The localization properties of in-plane elastic waves propagating in two-dimensional porous phononic crystals with one-dimensional aperiodicity are initially analyzed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method in this paper. The band structures characterized by using localization factors are calculated for different phononic crystals by altering matrix material properties and geometric structure parameters. Numerical results show that the effect of matrix material properties on wave localization can be ignored, while the effect of geometric structure parameters is obvious. For comparison, the periodic porous system and Fibonacci system with rigid inclusion are also analyzed. It is found that the band gaps are easily formed in aperiodic porous system, but hard for periodic porous system. Moreover, compared with aperiodic system with rigid inclusion, the wider low-frequency band gaps appear in the aperiodic porous system.

Bleustein-Gulyaev-Shimizu surface acoustic waves in two-dimensional piezoelectric phononic crystals

In this paper, we present a study on the existence of Bleustein-Gulyaev-Shimizu piezoelectric surface acoustic waves in a two-dimensional piezoelectric phononic crystal (zinc oxide, ZnO, and cadmium-sulfide, CdS) using the plane wave expansion method. In the configuration of ZnO (100)/CdS(100) phononic crystal, the calculated results show that this type of surface waves has higher acoustic wave velocities, high electromechanical coupling coefficients, and larger band gap width than those of the Rayleigh surface waves and pseudosurface waves. In addition, we find that the folded modes of the Bleustein-Gulyaev-Shimizu surface waves have higher coupling coefficients.

Effect of dielectric responses on localization in one-dimensional random periodic-on-average layered systems

Dielectric response effects on wave localization in random periodic-on-average layered systems are studied. Based on Monte Carlo simulations and products of random matrices, statistics of the Lyapunov exponent are determined efficiently for very long systems. An oscillatory behavior for Lyapunov exponent is found and explained for mildly strong scattering conditions. We also show the emergence of strongly localized states in metallic layered systems with intermediate disorder for frequencies above the plasma frequency omega(p) of metals, as is not shown in dielectrics. Furthermore, the violation of universal single parameter scaling behaviors in different regimes of multiple scattering is discussed.

Optical properties of an ionic-type phononic crystal

An ionic-type phononic crystal composed of two ferroelectric media with opposite spontaneous polarization aligned periodically in a superlattice structure was studied theoretically and experimentally. The coupling between vibrations of the superlattice and the electromagnetic waves results in various long-wavelength optical properties, such as microwave absorption, dielectric abnormality, and polariton excitation, that exist originally in ionic crystals. The results show that this artificial crystal structure can be used to simulate the microscopic physical processes in real crystals.