Dynamic Analysis of Axially Non-Uniform Thin Cylindrical Shells

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Abstract
Part 1 of this paper presents a new theory for the dynamic and static analysis of axially non-uniform, thin cylindrical shells. It is a hybrid of finite element and classical shell theories: the shell is subdivided into cylindrical finite elements, and the displacements within each (expressed in terms of nodal displacements), i.e., the displacement functions, are obtained using Sanders' equations for thin cylindrical shells in full. Sanders' theory gives zero strains for small rigid-body motions, so that displacement functions based on it satisfy the convergence criteria of the finite-element method. Expressions for the mass, stiffness and stress-resultant matrices are obtained, and the method for constructing the equivalent global matrices is given. This paper is supported by Part 2, where the eigenvalues of a number of shells are calculated and compared with other theories and experiments. In Part 2, the free flexural vibration characteristics of thin cylindrical shells are studied by this new, hybrid finite-element theory, where the displacement functions are determined by solution of the cylindrical thin-shell equations. Uniform shells with simply-supported, clamped and free ends are studied, as well as ring-stiffened shells and shells with thickness discontinuities. The frequencies of vibration are compared with those obtained by other theories and with the experiments of others. Agreement with other theories is good and, in the majority of cases, is even better with the experiments.