Free and forced vibration analysis of uniform and stepped circular cylindrical shells using a domain decomposition method

Abstract

This paper presents a domain decomposition technique for solving vibration problems of uniform and stepped cylindrical shells with arbitrary boundary conditions. Multilevel partition hierarchy, viz., stepped shell, shell segment and shell domain, is adopted to accommodate the computing requirement of high-order vibration modes and responses. The interface continuity constraints are enforced by using a modified variational principle and least-squares weighted residual method. The displacement components of each shell domain are expanded in the form of a double mixed series: Fourier series for the circumferential variable and polynomials/series (i.e., the Chebyshev orthogonal polynomials, Legendre orthogonal polynomials, and simple power series) for the axial variable. Free, steady-state and transient vibrations of uniform and stepped cylindrical shells are examined under different combinations of free, shear-diaphragm, simply-supported, clamped and elastic-supported boundaries. Comparisons with previously published results and finite element analyses show that the technique is computationally accurate and efficient. Effects of structural damping, stepped thickness and boundary conditions on the forced vibration responses of stepped cylindrical shells are also presented.