A new Hamiltonian-based approach for free vibration of a functionally graded orthotropic circular cylindrical shell embedded in an elastic medium. (November 2017) - Ni, Yiwen; Tong, Zhenzhen; Rong, Dalun; Zhou, Zhenhuan; Xu, Xinsheng
Abstract: Exact solutions for free vibration of functionally graded (FG) orthotropic circular cylindrical shells embedded in an elastic medium with arbitrary classical boundary conditions are obtained by a Hamiltonian-based method. Based on the Reissner shell theory and symplectic mathematics, all six possible general solutions instead of trial functions in classical inverse or semi-inverse methods are determined analytically. The determination of natural frequency and vibration mode shape is reduced to an eigen-problem of the Hamiltonian matrix in symplectic space. Numerical examples are provided to verify the validity of the present method. Some new results are also given. Graphical abstract: Highlights: An analytical method is proposed for free vibration of a circular cylindrical shell. Exact solutions are obtained with analytical determined general solutions. The solution procedure is rigorously rational without any trial functions. New results are presented and can be used as benchmarks.