Vibration of an infinite inhomogeneous transversely isotropic viscoelastic medium with cylindrical hole

Abstract

This paper investigates the influences of higher order viscoelasticity and the inhomogeneities of the transversely isotropic elastic parameters on the disturbances in an infinite medium, caused by the presence of a transient radial force or twist on the surface of a cylindrical hole with circular cross section. Following Voigt’s model for higher order viscoelasticity, the nonvanishing stress components valid for a transversely isotropic and higher order viscoelastic solid medium have been deduced in terms of radial displacement component. Considering the power law variation of elastic and viscoelastic parameters, the stress equation of motion has been developed. Solving this equation under suitable boundary conditions, due to transient forces and twists, radial displacement and relevant stress components have been determined in terms of modified Bessel functions. The problem for the presence of transient radial force has been numerically analysed. Modulations of displacement and stresses due to different order of viscoelasticity and inhomogeneity have been graphically depicted. The numerical study of the disturbance caused by the presence of twist on the surface may be similarly done but is not pursued in this paper.