Natural vibrations of composite cylindrical shells partially filled with fluid

Abstract

The article presents the results of studies of natural vibrations of circular vertical multilayer cylindrical shells completely or partially filled with a stationary compressible fluid and subjected to hydrostatic load. The behavior of the elastic structure and the fluid medium is described using the classical shell theory and the Euler equations. The effects of sloshing on the free surface of the fluid are not considered. The linearized equations of motion for shells together with the corresponding geometric and physical relations are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the generalized differential quadrature method. The formulated boundary value problem is solved by Godunov’s method of orthogonal sweep. The natural frequencies of vibrations are calculated based on the combination of a stepwise procedure and subsequent refinement by the method of dividing in half. The reliability of the obtained results is verified by comparison with the known numerical solutions. The dependence of low vibration frequencies on the reinforcing angle and the level of the structure filling with a fluid for simply supported rigidly clamped and cantilevered two-layer and three-layer cylindrical shells with a fluid are analyzed in detail. It is demonstrated that the possibility of changing the frequencies and vibration modes through a suitable choice of the layer arrangement scheme and the reinforcing angle of the composite material is notably determined by a prescribed combination of boundary conditions for an elastic body.