Vibration analysis of the coupled doubly-curved revolution shell structures by using Jacobi-Ritz method

Abstract

In this paper, a unified Jacobi-Ritz formulation is presented to investigate the free vibrations of various coupled doubly-curved revolution shell structures with arbitrary boundary conditions. The combined shell structure consists of the paraboloidal, elliptical, hyperbolical, cylindrical and spherical shells. Multi-segment partitioning strategy and Flügge's thin shell theory are adopted to establish the theoretical model. Regardless of the shell components and the boundary conditions, the displacement functions of each shell segment are composed of the Jacobi polynomials along the meridional direction and the standard Fourier series along the circumferential direction. The arbitrary boundary conditions and kinematic compatibility and physical compatibility conditions at the interface are imitated by the boundary and coupling spring technique, respectively. Then, the natural frequencies and mode shapes of the coupled shell structures are decided by using the Rayleigh–Ritz method. The credibility and exactness of the proposed method are validated by the results of the previous literature and finite element method (FEM). And some numerical results are also reported for the free vibration of the coupled doubly-curved revolution shell structures with classical and elastic boundary conditions, which can provide reference data for future studies.