Dynamic stiffness analysis of circular cylindrical shells

Abstract

A dynamic stiffness method is introduced to analyze thin shell structures composed of uniform or non-uniform circular cylindrical shells. A dynamic stiffness matrix is formed using frequency dependent shape functions which are exact solutions of the governing differential equations. It eliminates spatial discretization error and is capable of predicting an infinite number of natural modes by means of a small number of degrees of freedom. For harmonic oscillation, the time variable is replaced by the frequency variable. The circumferential coordinate is eliminated by Fourier series. The governing equations are reduced to a set of ordinary differential equations in the axial coordinate only. A degenerate matrix polynomial eigenproblem of order 3 and degree 4 is to be. solved for the complementary functions. The determinant equation is expanded analytically to give a scalar polynomial equation of degree 8 providing 8 integration constants for the 8 nodal (circular line) displacements of a thin shell member. The conjugate natural boundary conditions are obtained by variational calculus. The generalized nodal forces are related to the nodal displacements analytically resulting in an exact dynamic stiffness matrix. Donnell-Mushtari's and Flligge's equations are used. Numerical examples of circular cylindrical shells with various thickness and boundary conditions are presented.