Vibration and Stability of Coaxial Cylindrical Shells with a Gap Partially Filled with Liquid

Abstract

The problem of vibration and stability of coaxial circular cylindrical shells of finite length is considered when the region between the shells is partially filled with an incompressible liquid. The frequencies of vibration of the hydroelastic system are found depending on the filling depth and the gap thickness. A loss of static stability of the inner shell under the influence of hydrostatic pressure is identified. The equations to investigate the stability and natural oscillations of the studied hydroelastic system are presented. The value of the critical depth of liquid at which the shell loses stability is analytically computed. It is shown that, with fixed physical and geometric parameters of the examined system, there exists a critical number of waves around the circumference that leads to instability. The characteristic equation to compute the frequencies of oscillations of the hydroelastic system is also determined, and both nonphase and common-mode cases of oscillations are documented.