The present paper is devoted to study the propagation of Love wave in a piezoelectric layer overlying an inhomogeneous half-space. This paper deals with two different piezoelectric layers, one is an electrically open and another is an electrically short circuit. As mathematical tools, the method of separation of variables and Whittaker’s function are applied to obtain the dispersion equation of Love wave. In a particular case the dispersion equation reduces to the classical equation of Love wave when the layer is not piezoelectric and half-space is homogeneous. The numerical values of the dimensionless phase velocities are calculated and presented graphically to illustrate the effects of inhomogeneity, piezoelectricity and dielectric constants. It is observed that the phase velocities decrease with the increase of inhomogeneity parameters and electricity constant. It is also found that the phase velocity increases with the increases of the dielectric constant. Graphical user interface software has been developed by using MATLAB software to generalize the effect of various parameters.

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The present paper deals with the effect of point source on the propagation of Love wave in a heterogeneous layer and inhomogeneous half-space. The upper heterogeneous layer is caused by consideration of exponential variation in rigidity and density. Also in half-space inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of Love wave has been obtained by using Green’s function technique. As a special case when the upper layer and lower half-space are homogeneous, our computed equation coincides with the general equation of Love wave. The propagation of Love waves are influenced by inhomogeneity parameters. The dimensionless phase velocity has been plotted against the dimensionless wave number for different values of inhomogeneity parameters. We have observed that the velocity of wave increases with the increase of inhomogeneity parameters.

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In the present paper we study the effect of rigid boundary on the propagation of torsional waves in a homogeneous layer over a semi-infinite heterogeneous half-space, where the heterogeneity is both in rigidity and density. The present study demonstrates that torsional waves can propagate in the layer. The velocities of torsional waves have been calculated numerically as a functions of K H, (where K is the wave number and H is the thickness of the layer) and are presented in a number of graphs. It is also observed that, for a layer over a homogeneous half-space, the velocity of torsional waves does not coincide with that of Love waves in the presence of the rigid boundary whereas it does at the free boundary.

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