Vibration analysis for coupled composite laminated axis-symmetric doubly-curved revolution shell structures by unified Jacobi-Ritz method

In this paper, a unified Jacobi-Ritz method is presented and implemented to study the free vibration analysis of coupled composite laminated axis-symmetric doubly-curved revolution shell structures with general boundary conditions in the framework of the first-order shear deformation theory. The substructure of coupled structures mainly contains the laminated elliptical, hyperbolical, paraboloidal and cylindrical shells. In the theoretical analysis model, the multi-segment partitioning strategy is adopted. The displacement functions of each shell segment are uniformly expanded in the form of a double mixed series in which Jacobi polynomials are along the meridional direction and the standard Fourier series is along the circumferential direction, regardless of the shell components and the boundary conditions. The vibration results including frequency parameters and mode shapes of coupled composite laminated axis-symmetric doubly-curved revolution shell structures are easily obtained by means of the Ritz method. The major advantages of the present solutions for coupled structure are to eliminate the need of changing the displacement or the equations of motion and to improve the efficiency of modeling. The accuracy and reliability of the proposed method are verified with the FEM and literature results, and various numerical examples are presented for the free vibration of the various coupled structures of composite laminated axis-symmetric shell, and these results can be used as reference data.