A semi-analytical approach to analyze vibration characteristics of uniform and stepped annular-spherical shells with general boundary conditions

By Haichao Li, Fuzhen Pang, Hai-long Chen. European Journal of Mechanics - A/Solids, 2019

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Abstract In this paper, the free vibration characteristics of uniform and stepped annular-spherical shells are investigated by using a semi-analytical approach with general boundary conditions. The theoretical model of annular-spherical shell is established by using Flugge's thin shell theory, and the annular-spherical shells are divided into their segments along the axial direction. The displacement functions of shell segments are consist of the Jacobi polynomials along the axial direction and the standard Fourier series along the circumferential direction. The boundary conditions at the ends of the shells and the continuity conditions at two adjacent segments were enforced by penalty method of spring stiffness technique. Then, the accurate solutions about the vibration characteristics of uniform and stepped annular-spherical shells were solved by method of Rayleigh–Ritz. The accuracy and reliability of the proposed method are verified with the results of FEM and published literatures. The results show that the present method has good convergence ability and excellent accuracy. In addition, some numerical results of uniform and stepped annular-spherical shells with various geometric parameters and boundary conditions are reported, which can be used as reference data for future researchers.

Subfields: Civil and Structural Engineering, Mechanical Engineering, Mechanics of Materials

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