An analytical method for free vibration analysis of multi-layered transversely isotropic cylindrical shells

This work presents an effective analytical method based on displacement potential functions (DPF) for solving 3-D free vibration problem of thick and multi-layered transversely isotropic cylindrical shells with simply supported end boundary conditions. By using the DPF method, the three-dimensional elasticity equations are simplified and decoupled into two linear partial differential equations of fourth and second order as governing differential equations. These equations are analytically solved using the separation of variables method in terms of fields that exactly satisfy end boundary conditions and the continuity of a closed cylinder in the hoop direction. One of the advantages of the present work is the analysis of thick cylindrical shells using an exact method without any approximations and simplifying assumptions in the distribution of stress or strain along the thickness of the shells. The analysis is extended to multi-layered cylindrical shells by applying appropriate boundary conditions at the interfacial surfaces of the layers. Numerical comparisons to other analytical works shows the accuracy of the present work and also due to the lack of study for multi-layered transversely isotropic cylindrical shells, 3-D finite element analysis has been performed for comparison. In addition, various more involved problems are studied and solved analytically for single and multi-layered shells of transversely isotropic material and the effect of various parameters such as shell dimensions, mechanical properties, number of layers and other parameters on shell behavior are evaluated. The results of the present study can be used as benchmark solutions for other studies.