This research is devoted to address the reflection of plane waves at a flat surface in a coupled nonlocal viscoelastic medium, focusing on the effects of in-homogeneity and rotation. Nonlocal viscoelastic functionally graded materials (FGMs), characterized by their dependence on spatial interactions beyond immediate neighbors, exhibit complex wave propagation behavior, which is further influenced by material in-homogeneity and rotational motion. We first describe a mathematical model incorporating these factors and write the governing equations in component form for wave propagation in the medium under study. The dispersion equations are derived analytically which interpret that due to the rotational effects in FGM, two coupled plane waves, namely, a quasi-longitudinal (QL) wave and a quasi-shear (QS) wave, are found in the medium. For the incidence of a QL wave on a flat boundary with zero stress, there may exist two types of reflected waves, namely, QL and QS waves. The reflection coefficients are obtained using the boundary conditions at the stress-free surface in the medium. Analytical solutions of the reflection coefficients are presented, highlighting the influence of the nonlocal parameters, functionally graded factor, and the rotation on wave reflection characteristics. Numerical simulations are performed to illustrate the theoretical findings, showing how these factors alter the phase speeds, attenuation factors, and the amplitude of the reflected waves. The results provide deeper insights into the wave dynamics in the considered media, which have implications for advanced material design and applications in seismology, materials science, and engineering disciplines.
Sharma et al. (Mon,) studied this question.