ABSTRACT

This paper aims to investigate the reflection and transmission phenomena of elastic waves due to incident qSH-wave at a corrugated interface between two different nematic elastomer half-spaces. The expression of the phase velocity for shear harmonic wave is derived and observed that this phase velocity depends on the angle of propagation. There exist irregularly reflected and transmitted waves besides the regular waves due to undulated nature of the interface whose nth spectrum is related through Spectrum theorem. The amplitude ratios for various reflected and transmitted waves are derived using boundary conditions. The ratios corresponding to an irregular waves are found to be functions of the incident angle, elastic constants, relaxation times, corrugation and frequency parameters. The energy distribution, and hence the energy ratios due to various reflected and transmitted waves are also obtained. It is observed that the sum of all energy ratios is approximately unity at each value of incident angle which ensures the law of conservation of energy at the interface. A particular case, $z=d\cos px$ has been performed to validate the present study for the amplitude and energy ratios. Graphs are plotted for these ratios at different values of corrugation and frequency parameters to discuss their effects.

摘要

本文旨在研究由于入射qSH波在两个不同向列弹性体半空间之间的波纹界面处引起的弹性波的反射和传输现象。推导了剪切谐波的相速度表达式，并观察到该相速度取决于传播角度。由于界面的起伏性质，除了规则波之外，还存在不规则反射波和透射波，其nth 频谱通过频谱定理关联。使用边界条件导出各种反射波和透射波的幅度比。发现对应于不规则波的比率是入射角、弹性常数、弛豫时间、波纹和频率参数的函数。还获得了能量分布，因此也获得了由各种反射波和透射波引起的能量比。观察到在每个入射角值处所有能量比的总和近似为一，这确保了界面处的能量守恒定律。一个特例，$z=d因pX$已经执行以验证本研究的振幅和能量比。在不同的波纹和频率参数值下绘制这些比率的图表，以讨论它们的影响。