Exact analysis of the plane-strain vibrations of thick-walled hollow poroelastic cylinders

Abstract

The paper deals with the plane-strain vibrations of thick walled hollow, composite poroelastic cylinder. The frequency equations of axially and non-axially symmetric vibrations, each for pervious and impervious surfaces are obtained using the analytical model based on Biot’s theory of wave propagation in fluid-saturated porous media. In case of axially symmetric vibrations, dilatational and shear modes are uncoupled, while in non-axially symmetric vibrations, dilatational and shear modes are coupled. The plot of frequency versus ratio of wall thickness to inner radius of composite cylinder for different materials is presented, and then discussed. For axially symmetric vibrations, two limiting cases of ratio of wall thickness to inner radius of composite cylinder are considered, i.e., when these ratios are very small and very large. The first limiting case corresponds to modes of thin poroelastic shell and plate, while in the second limiting case, modes of poroelastic solid cylinder is obtained. Thus, the problem of axially symmetric vibrations describes a transition from the case of plate, thereby thin shell to analogous pochammer case of poroelastic solid cylinder. The results of purely elastic solid are shown as a special case.