Study of Torsional Vibrations of Composite Poroelastic Spherical Shell-Biot’s Extension Theory

Torsional vibrations of composite poroelastic dissipative spherical shell are investigated in the framework of Biot’s extension theory.Here composite poroelastic spherical shell consists of two spherical shells, one is placed on other, and both are made of different poroelastic materials. Consideration of the stress-free boundaries of outer surface and the perfect bonding between two shells leads to complex valued frequency equation. Limiting case when the ratio of thickness to inner radius is very small is investigated numerically. In this case, thick walled composite spherical shell reduces to thin composite spherical shell. For illustration purpose, four composite materials, namely, Berea sandstone saturated with water and kerosene, Shale rock saturated with water and kerosene are employed. The particular cases of a poroelastic solid spherical shell and poroelastic thick walled hollow spherical shell are discussed.  If the shear viscosity of fluid is neglected, then the problem reduces to that of classical Biot’s theory. Phase velocity and attenuation are computed and the results are presented graphically. Comparison is made between the results of Biot’s extension theory and that of classical Biot’s theory. It is conclude that shear viscosity of fluid is causing the discrepancy of the numerical results.

Keywords:

Torsional vibrations , Composite spherical shell , Frequency equation , Phase velocity , Attenuation