Natural Vibrations of a Cylindrical Shell with Fluid Partly Resting on a Two-Parameter Elastic Foundation

Abstract

This paper presents the results of studies on natural vibrations of circular cylindrical shells containing liquid and resting on an elastic foundation, which is described by the Pasternak two-parameter model. In the meridional direction, the elastic medium is nonuniform and represents an alternation of sections in which the foundation is present or absent. The behavior of the elastic structure and the compressible fluid is described in the framework of classical shell theory based on the Kirchhoff–Love hypothesis and the Euler equations. The equations of motion of the shell are reduced to a system of ordinary differential equations with respect to new unknowns. The wave equation written for pressure in the fluid also reduces to a system of ordinary differential equations using the straight line method. The solution of the formulated boundary value problem is found by the Godunov orthogonal sweep method. The validity of the results obtained is confirmed by comparison with the known numerical-analytical solutions. The dependences of the minimum vibration frequencies on the characteristics of elastic medium with variable nonuniformity along the length of the structure have been obtained for cylindrical shells with different boundary conditions. It has been found that the violation of smoothness of the derived dependences is caused by a change of the vibration mode with minimum frequency and is determined both by the ratio of the size of the elastic foundation to the entire length of the shell and its stiffness, and also by a combination of boundary conditions set at the edges of the thin-walled structure.