Natural vibrations of loaded noncircular cylindrical shells containing a quiescent fluid

Abstract

The paper deals with a solution of three-dimensional problems of natural vibrations and stability of loaded cylindrical shells with circular and arbitrary cross sections containing a quiescent ideal compressible fluid. A mathematical formulation of the problem has been developed based on the variational principle of virtual displacements taking into account the pre-stressed undeformed state caused by the action of static forces on the shell. The motion of potential compressible non-viscous fluid is described by a wave equation, which is transformed using the Bubnov–Galerkin method. The solution of the problem reduces to the computation of complex eigenvalues of a coupled system of two equations. Based on the developed finite element algorithm several numerical examples have been considered to analyze the influence of fluid levels, ratio of ellipse semi-axes, shell thickness and boundary conditions on the natural frequencies and vibration modes of circular and elliptical cylindrical shells loaded by mechanical forces. It has been found that the value of the external uniformly distributed pressure giving rise to instability does not depend on the level of fluid in the shell. The results allow us to conclude that the dynamic characteristics of the system are specified not only by the equivalent added mass of the fluid but also by hydroelastic interaction at the wetted surface.