Vibration analysis of conical-cylindrical-spherical shells by a novel linear expression method

Composite shells are increasingly used in underwater vehicles, aerospace and other engineering fields. In this study, a linear expression method (LEM) was developed for the efficient vibration analysis of conical-cylindrical-spherical shell structures. Herein, the constraint and continuity conditions were expressed in matrix form, and a full -rank matrix was derived via the Gaussian elimination method. Then, it was possible to linearly express the unknown coefficients in the original equations. Consequently, combined with the energy method, the vibration characteristics of composite shells could be obtained. A conical-cylindrical-spherical shell was considered as an example. Its natural frequencies, vibration modes, and forced vibration analysis were carried out, and the results are compared for verification with those obtained by the finite element method (FEM) and those found in the literature. It is shown that the proposed LEM can be up to five times faster than FEM. Concentrated mass points and forced vibration were also considered, and the partial coupling between the shell and the mass points led to the breaking down of the circumferential symmetry of the cylindrical shell. The convergence of LEM is related only to the number of truncated terms of the shape functions; thus, it exhibits strong convergence and reduced computational cost, and offers a wide range of potential applications.