Effect of corrugation and frequency parameters due to quasi harmonic-waves on a corrugated interface of two different nematic elastomers

The reflection and refraction phenomena due to incident quasi harmonic-wave at an irregular interface of two different nematic elastomer half-spaces has been investigated. The expressions of phase velocity for incident, reflected and refracted qSH-waves are obtained which depends on the angle of propagation. Besides the regular waves, there exist an irregularly reflected and refracted waves due to undulated nature of the interface whose nth spectrum is related through the spectrum theorem. Using Rayleigh’s approximation method, we assume that the amplitude and slope of corrugation are both small. The expressions of the amplitude ratios corresponding to the reflected and refracted waves are derived by using appropriate boundary conditions -continuity of (i) displacements and (ii) tractions at the irregular interface. These ratios are found to be functions of elastic constants, angle of incidence, relaxation times, corrugation and frequency parameters. The energy distribution and hence energy ratios of various reflected and refracted waves are also obtained. The amplitude and energy ratios are computed numerically for a particular model ξ ( x ) = d c o s p x and are plotted in graphs and discussed the effects of corrugation and frequency parameter. In the amplitude and energy ratios, irregularities occur between the angles 78 0 and 85 0 due to the existence of critical and moreover at 83 0 irregularities show dominant behavior. We concluded that (i) the ratios due to irregular waves are comparatively small to that due to regular waves. (ii) The amplitude and energy ratios corresponding to irregular waves show linear and non-linear increase respectively with the increase of corrugation parameter. (iii) Theoretically and numerically, the ratios corresponding to the regular waves are independent of corrugation and frequency parameters. (iv) The sum of energy ratios is approximately unity at each value of incident angle which ensures the law of conservation of energy at the interface.