Fundamental solution and influence of initial stress and gravity on the surface wave propagation in non-local elastic medium having double porosity

The primary objective of this research is to study the effect of initial stress and gravity at the interface of two exponentially graded non-local elastic material with double porosity. Also, the fundamental solution for steady oscillations is derived. Reflection and refraction of plane waves under initial stress and gravity is studied to obtain the reflection/refraction coefficient and energy ratios when a longitudinal or transverse wave is incident. We obtained four reflected and four refracted waves. We noticed three longitudinal and one transverse wave in both the medium. Analytical analysis reveals that the velocity of propagation of waves depend upon the direction of propagation, gravity field, non-locality of the medium and initial stress. The result indicates that the effect of initial stress and gravity field are very pronounced. The reflection/refraction coefficients and energy ratios are calculated in closed form and shown graphically. The findings highlight the crucial influence of gravity and initial stress on wave propagation, while contributing to theoretical understanding and potential applications in material science and engineering.