Dynamic Stability of Liquid-Filled Cylindrical Shells Under Periodic Shearing Forces

Abstract

Theoretical analyses are presented for the dynamic stability of a cylindrical shell partially filled with liquid, under periodic shearing forces. In the analyses, the dynamic version of the Donnell equations and the velocity potential theory are used for the motions of the shell and the contained liquid, respectively. The problem was solved by using the Galerkin method and the equations of motions coupling the shell and the liquid were derived from a type of coupled Mathieu’s equation. The instability boundaries where parametric resonance occurs were determined by using Hsu’s method. Numerical calculations were carried out for cylinders with various dimensions, i.e., radius-thickness and length-radius ratios. The effects of the liquid-filling ratio and the static shearing forces on the instability boundaries were clarified. It is found that the instability regions enlarge with increasing liquid and that the principal instability regions appear under the simultaneous action of the static shearing force.