Propagation of torsional surface waves in an inhomogeneous layer over an initially stressed inhomogeneous half-space

Abstract

This paper has been framed to study the propagation of torsional surface waves in an inhomogeneous layer of finite thickness over an initially stressed inhomogeneous half-space. Rigidity, density and initial stress of the half-space are assumed to have linear variation, and in layers linear variation in rigidity and density are also considered. It has been observed that the inhomogeneity parameter and the initial stress play an important role for the propagation of the torsional surface wave. The method of separation of variables is applied to find the displacement field. The dispersion equation of phase velocity is derived. The velocities of torsional waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. Graphical user interface has been developed using MATLAB to generalize the effect of the various parameters discussed. As a particular case it has been seen that the dispersion equation is in agreement with the classical result of the Love wave when the initial stresses and inhomogeneity parameters are neglected.

Torsional wave propagation in an inhomogeneous crustal layer over an inhomogeneous elastic half space

“…Gupta et al [3] considered the influence of rigid boundary on the propagation of torsional wave in a homogeneous layer over a heterogeneous half space. The works by Chattopadhyay et al [4], Gupta et al [5], and Vishwakarma et al [6] on torsional wave propagation cannot be overlooked as their contributions are commendable. Kakar and Gupta [7] studied torsional surface waves in a nonhomogeneous isotropic layer over a viscoelastic half space.…”

Effect of irregularity on torsional surface waves in an initially stressed anisotropic porous layer sandwiched between homogeneous and non-homogeneous half-space

“…The presence of initial stress has remarkable effect on the phase velocity of surface wave. Gupta et al (2013b) discussed the propagation of torsional surface waves in an inhomogeneous layer over an initially stressed inhomogeneous halfspace. Kepceler (2010) examined and found the existence of torsional wave dispersion relations in a pre-stressed bi-material compounded cylinder with an imperfect interface.…”

Dispersion of torsional surface wave in an intermediate vertical prestressed inhomogeneous layer lying between heterogeneous half spaces

“…Similarly, the work on torsional surface waves by Gupta et al. (2010), Gupta et al. (2013), Vishwakarma et al.…”

“…Najafov et al (2013) has also shown the stability of functionally graded orthotropic cylindrical shells on elastic foundations toward torsional vibration. Similarly, the work on torsional surface waves by Gupta et al (2010), Gupta et al (2013), Vishwakarma et al (2014) and Kumari and Sharma (2014) cannot be ignored. Kumar and Partap (2011) discussed propagation of wave in micropolar thermoviscoelastic plate.…”