A semi-analytical method for vibration analysis of stepped doubly-curved shells of revolution with arbitrary boundary conditions

Abstract In this paper, the free vibration of the stepped doubly-curved shells of revolution is investigated by using a semi-analytical method with arbitrary boundary conditions. The stepped doubly-curved shells of revolution are divided into their segments in the meridional direction according to the steps of the structures, and the analysis of the theoretical model is formulated by using Flugge’s thin shell theory. The Jacobi polynomials along the revolution axis direction and the standard Fourier series along the circumferential direction consist of the displacement functions of shell segments. The boundary conditions at the ends of the stepped doubly-curved shells of revolution and the continuity conditions at two adjacent segments were enforced by penalty method. Then, the accurate solutions about the vibration characteristic of the stepped doubly-curved shells of revolution were solved by the method of Rayleigh–Ritz. For arbitrary boundary conditions, the present method does not need any changes to the mathematical model or the displacement functions, and it is very effective in the analysis of free vibration for the stepped doubly-curved shells of revolution. The accuracy and reliability of the proposed method are verified with the results of finite element method (FEM), and some numerical results are reported for free vibration of the stepped doubly-curved shells of revolution under arbitrary boundary conditions. Results of this paper can provide reference data for future studies in related field.

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