Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

This paper deals with axially symmetric vibrations of composite poroelastic spherical shell consisting of two spherical shells (inner one and outer one), each of which retains its own distinctive properties. The frequency equations for pervious and impervious surfaces are obtained within the framework of Biot’s theory of wave propagation in poroelastic solids. Nondimensional frequency against the ratio of outer and inner radii is computed for two types of sandstone spherical shells and the results are presented graphically. From the graphs, nondimensional frequency values are periodic in nature, but in the case of ring modes, frequency values increase with the increase of the ratio. The nondimensional phase velocity as a function of wave number is also computed for two types of sandstone spherical shells and for the spherical bone implanted with titanium. In the case of sandstone shells, the trend is periodic and distinct from the case of bone. In the case of bone, when the wave number lies between 2 and 3, the phase velocity values are periodic, and when the wave number lies between 0.1 and 1, the phase velocity values decrease. 1. Introduction In day-to-day problems, composite structures play an important role. The term composite is applied to materials that are created by mechanically bonding two or more different elastic materials together. On the other hand, in structural engineering, spherical shell shape trims the internal volume and minimizes the surface area that saves material cost. Spherical shell forms an important class of structural configurations in aerospace as well as ground structures as they offer high strength-to-weight and stiffness-to-weight ratios. Besides some of manmade structures, the skull and the bones at shoulder joint and ankle joint are approximately in the shape of spherical shells. The said composite spherical structures are poroelastic in nature. Kumar [1] studied the axially symmetric vibrations of fluid-filled spherical shells employing three-dimensional equations of linear elasticity. For torsional vibrations of solid prolate spheroids and thick prolate spheroidal shells, frequency equations and mode shapes are presented in analytic form [2]. Paul [3] studied the radial vibrations of poroelastic spherical shells. Employing Biot’s theory [4], Shah and Tajuddin [5, 6] discussed torsional vibrations of poroelastic spheroidal shells and axially symmetric vibrations of fluid-filled poroelastic spherical shell. In the paper in [5], they derived frequency equations for poroelastic thin spherical shell, thick spherical