Torsional Vibrations of Coated Hollow Poroelastic Spheres

Abstract

Torsional vibrations of coated hollow poroelastic spheres are studied employing Biot’s theory of wave propagation in poroelastic solid. The dilatations of solid and liquid media are zero, therefore the frequency equation of torsional vibrations is same both for a permeable and an impermeable surface. The coated poroelastic sphere consists of an inner hollow poroelastic sphere bounded by and bonded to a sphere made of distinct poroelastic material. The inner sphere is designated as core and outer sphere as casing. Core and casing are bonded at the curved surfaces. The inner and outer boundaries of the coated hollow poroelastic sphere are free from stress and at the interface of core and casing the displacement and stresses are continuous. It is assumed that the each material of coated sphere is homogeneous and isotropic. The frequency equation of torsional vibrations of a coated poroelastic hollow sphere is obtained when the material of the core vanishes. Also a coated poroelastic solid sphere is obtained as the limiting case of the frequency equation of coated hollow poroelastic sphere when the inner radius of core approaches to zero. Non-dimensional frequency as a function of ratio of thickness of core to that of inner radius of core is determined and analyzed. It is observed that the frequency and dispersion increase with the increase of the thickness of the coating.