Propagation of Longitudinal Waves in Microporous Slab Sandwiched between Elastic Half-Spaces

Abstract

A granular composite that consists of stiff inclusions embedded in a weaker matrix produces a well defined micro-structure. This composite is extensively used in the passive noise control field in sound absorbers. In classical continuum mechanics, the basic assumption is that the micro-structure of a material does not govern the mechanical behavior. However, classical theory and experimental results have some discrepancies, revealing the potential importance of the micro-structure. For instance, acoustic waves are characterized by high frequencies and small wavelengths, particularly in microporous materials with various stiffness values. Consequently, unlike for a homogeneous isotropic elastic medium with only two elastic constants, linear elastic micropolar theory utilizes 6 degrees of freedom and its results can hence be regarded as being a function of the micro-structure. This investigation explores the reflected and transmitted wave fields of an incident longitudinal plane wave that propagates in elastic–microporous–elastic interfaces. The numerical study demonstrates a through transmission in the sandwiched problem in situation of interest. This property of the half-wave microporous layer allows it to be regarded as a frequency or direction filter. Two sets of the forward and backward transverse plane waves are present in the sandwiched microporous layer. The specified work frequency and the width of the intermediate microporous layer affect all of the described phenomena.

Wave Propagation Through a Micropolar Slab Sandwiched by Two Elastic Half-Spaces

“…In order to validate the numerical results, the energy flux ratios of various waves with respect to the incident wave are further evaluated and the energy conservation is checked. The comparison between present work and that in literature [19] is performed, the deviations are analyzed and some mistakes in literature [19] are pointed out. Based on these numerical results, the influences of micropolar elastic constants and the nondimensional thickness of slab are discussed and some conclusions are obtained.…”

“…In order to make a comparison with that in literature [19], the dependences of energy ratios on the absolute thickness of the sandwiched layer are shown in Fig. 4.…”

“…The bi-interface problem will be much more complicated due to the multiple reflection and transmission process between the two interfaces. Hsia and Su [19] studied the propagation of longitudinal waves in microporous slab sandwiched between elastic half-spaces. However, the interface conditions between the classic elastic solid and the micropolar solid are disputable and the numerical results are not validated by the energy conservation.…”

“…The micropolar elastic waves in the slab are divided into two groups, i.e., the forward and the backward waves, which are different for incident P wave and incident SH wave. The interface conditions between the micropolar slab and the classic elastic half-spaces used by Hsia and Su [19] are modified, which includes the microrotation and the couple stresses, and are used to form a set of algebraic equations from which the amplitude ratios of various waves with respect to the incident wave are obtained. In order to validate the numerical results, the energy flux ratios of various waves with respect to the incident wave are further evaluated and the energy conservation is checked.…”

Reflection and transmission through a microstructured slab sandwiched by two half-spaces

“…Although the reflection and transmission through a slab characteristic of the classical elasticity had been studied, the study on the wave propagation through a slab with microstructure is less reported. Recently, Hsia and Su (2008) studied the wave propagation through a microporous slab characteristic of micropolar elasticity. Khurana and Tomar (2009) studied the wave propagation through a chiral slab characteristic of noncentrosymmetry.…”