Axially Symmetric Vibration of a Complete Conic Shell

Abstract

We develop a variational method for the solution of the spectral problem of free axially symmetric vibration of a thin-walled conic shell with vertex. The procedure of construction of systems of basis functions for the approximation of displacements of the shell is based on the account of the formal structure of the fundamental system of integrals of the original equations established as a result of the asymptotic integration of a singularly perturbed system of equations with regular singular point. We present examples of numerical analyses of specific conic shells illustrating the efficiency of the proposed algorithm for the solution of the problem.