A symplectic analytical approach for free vibration of orthotropic cylindrical shells with stepped thickness under arbitrary boundary conditions

Exact analytical solutions for free vibration of isotropic and orthotropic cylindrical shells with uniform and stepped thickness subject to general boundary conditions are presented by means of a symplectic analytical approach. The Reissner shell theory is adopted to formulate a theoretical model. By introducing a Hamiltonian system, the governing higher order partial differential equation is reduced to a set of ordinary differential equations which can be analytically solved by separating the variables. Applying the end boundary and interface continuous conditions, a set of analytical characteristic frequency equations are obtained, and exact solutions can be determined. To ensure accuracy and validity of the symplectic method, the analytical solutions for uniform and stepped cylindrical shells with isotropic or orthotropic material properties and with arbitrary boundary conditions are compared with available published data and FEM solution. A set of comprehensive new result for orthotropic stepped cylindrical shells under classical and elastic restraints are presented. Some typical mode shapes for various examples are illustrated. In addition, the effects of boundary conditions and orthotropic properties on vibration frequency are analyzed. The result shows that the fundamental frequency is higher for a boundary with more constraints.