Scattering of qSH-waves from a corrugated interface between two dissimilar nematic elastomers

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 arefound to befunctions 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.