Free vibration analysis of inversely coupled composite laminated shell structures with general boundary condition

In this paper, the free vibration characteristics of various coupled composite laminated doubly curved revolution shells are investigated under generalized boundary conditions (BCs). The joint shell structure consists of a doubly curved revolution shell–cylindrical shell–doubly curved revolution shell structure, and here, unlike previous structures, the doubly curved revolution shells are inversely joined together. In this paper, doubly curved shells such as elliptical, paraboloidal, and spherical shells are considered. The first order shear deformation theory and multi-segment partitioning technique are adopted to establish the theoretical model of coupled shell structures. Regardless of the individual shell structures and the BCs, the displacement functions of each shell segment are expanded using ultraspherical polynomials in the meridional direction and using the standard Fourier series in the circumferential direction. In order to generalize the BCs at both ends of a coupled shell and the connecting conditions at the interface, the virtual spring technique is employed. Then, the natural frequencies and mode shapes of the coupled shell structures are obtained by the Ritz method. The reliability and accuracy of the proposed method are verified by the convergence study and numerical comparison with results of the finite element method. In addition, some numerical results are also reported for the free vibration of coupled composite laminated doubly curved revolution shell structures under classical and elastic BCs, which can provide the reference data for future studies.