Natural Vibrations of Laminated Orthotropic Shells of Revolution

Abstract

Frequencies and mode shapes of axisymmetric and asymmetric vibrations for laminated orthotropic shells of revolution are deter mined. The shell may be composed of an arbitrary number of bonded elastic orthotropic layers, each of which may have different properties and thickness. Finite element method, where the basic element is the conical frustum is employed to model the shell struc ture. First, the governing equations are formulated using nodal (generalized) coordinates, and then they are transformed into a system of reduced generalized coordinates. The direct solution of the eigenvalue problem is effected in this reduced system of generalized coordinates. The advantages of this method, which is related to the Rayleigh-Ritz technique, are twofold: Computational effort is con siderably reduced and the lowest eigenvalues and eigenvectors are found. Four examples are given to demonstrate the accuracy, speed, and versatility of this method.