Free vibration analysis of laminated composite elliptic cylinders with general boundary conditions

In this paper, a unified analysis model is proposed for the first time to study the free vibration of laminated composite elliptic cylinders with general boundary conditions including the classical boundary, elastic boundary and their combinations. The theoretical model is established by means of the modified variational principle and multilevel partition technique based on the first-order shear deformation theory. The interface continuity and boundary constraints are enforced by using the coupling and boundary spring technique. On the basis of that, the displacement components of each shell domain are expanded in the form of double Jacobi polynomials along the meridional and circumferential direction. The convergence and comparison analysis for laminated composite elliptic cylinders subject to different classical boundary conditions is conducted to show the reliability and accuracy of the present method. To make the research topic understood better, some mode shapes are also depicted. The present solutions show stable and rapid convergence characteristics, and the natural frequencies and mode shapes agree well with the Finite Element Analysis results. Some new vibration results and parameterized results are presented and may be as the reference data by other researchers in the future.