Torsional Vibrations of Fluid-Filled Multilayered Transversely Isotropic Finite Circular Cylinder

Abstract

An analytical and numerical study for the torsional vibrations of viscous fluid-filled three-layer transversely isotropic cylinder is presented in this paper. The equations of motion of solid and fluid are respectively formulated using the constitutive equations of a transversely isotropic cylinder and the constitutive equations of a viscous fluid. The analytical solution of the frequency equation is obtained using the boundary conditions at the free surface of the solid layer and the boundary conditions at the fluid–solid interface. The frequency equation is deduced and analytically solved using the symbolic Software Mathematica. The finite element method using Comsol Multiphysics Software results are compared with present method for validation and an acceptable match between them were obtained. It is shown that the results from the proposed method are in good agreement with numerical solutions. The influence of fluid dynamic viscosity is thoroughly analyzed and the effect of the isotropic properties on the natural frequencies is also investigated.