Plane waves reflection from corrugated boundary of inhomogeneous pre-stressed hyperelastic waveguide

The essence of the current study is to trace out the influences of corrugation as well as non-homogeneity on the reflection coefficients of plane waves (qP/qSV) incident at the free surface of hyperelastic waveguide. To accomplish this, an analytical model is developed and solved for the waveguide that precisely composed of non-homogeneous pre-stressed nearly incompressible elastic substrate (NHPSNIESB) with corrugated free surface under stress-free boundary and rigid boundary conditions. The inhomogeneity considered in the study is based upon exponential form varying along the vertical depth. Analytical techniques incorporating substitution method, variable separable method, Fourier series expansion along with the Rayleigh’s approximation method are applied to derive closed form expressions of the amplitude ratios of the corresponding reflection coefficients for regularly reflected and irregularly reflected plane waves (qP and qSV) due to corrugated free surface with stress-free boundary as well as rigid boundary conditions. The obtained reflection coefficients are validated as special cases with the existing results of literature. The effects of associated parameters, viz., incident angle, corrugation parameter, non-homogeneity parameter and hydrostatic stress on each of the aforementioned reflection coefficients for incident qP and qSV-waves for stress-free and rigid boundary conditions are depicted graphically following a comparative approach. The computational results reveal that the corrugation and the magnitude of the amplitude ratios of irregularly reflected plane waves are directly proportional to each other, which in turn are lesser than the magnitude of amplitude ratios of regularly reflected plane waves. Also, the presence of non-homogeneity in the material medium substantially affects the reflection coefficients of plane waves by reducing most of the amplitude ratios in the considered waveguide. The outgrowth of the present study may play significant role in earthquake engineering as well as structural analysis in the design of varied structures of interest.