Dispersion of shear wave propagating in vertically heterogeneous double layers overlying an initially stressed isotropic half-space

The present paper investigates the propagation of horizontally polarised shear wave in distinct vertically heterogeneous double layers overlying an isotropic half-space under horizontal initial stress. The vertical heterogeneity in the uppermost layer is caused due to quadratic variation only in rigidity, whereas vertical heterogeneity in the sandwiched layer is caused due to exponential variation in rigidity and density both. The closed form of velocity equation is obtained which leads to the dispersion equation as its real part and damping equation as its imaginary part. The validation of dispersion relation with the classical case is made by using Debye asymptotic expansion which is the major highlight of this study. The significant effect of the width ratio of the layers, heterogeneity parameters of both the layers and horizontal compressive/tensile initial stress on the phase velocity and damped velocity of SH-wave have been traced out. The comparative study and some important peculiarities have been revealed by means of graphical illustrations.