Free vibration of conical shells under arbitrary elastic boundary and simulation verification

This paper presents an analysis of free vibration characteristics of truncated conical shells under complex boundary conditions. Firstly, the geometric equation of conical shells are obtained by using Reissner shell theory. Then, by using Rayleigh- Ritz method with improved Fourier series, the motion equations of modal parameters (modal stiffness, modal mass, natural frequency and model shapes) with elastic boundary are obtained. The mode shapes and natural frequencies of conical shells can be obtained by solving the motion equations. Moreover, by comparing the results for simulation numerical method and finite element method(FEM) respectively, the validity of present methodology has been verified.