Nonlinear Vibration Analysis of the Rotating Conical Shell

Abstract

An analytical model to study the nonlinear dynamic responses of the rotating pre-twisted cantilever conical shell is developed. The varying rotational speed and forces are considered during the establishment of the model. Using Hamilton’s principle, the partial differential governing equation of motion can be derived for the rotating shell. Based on the governing equation, Galerkin’s approach is applied to obtain a two-degree-of-freedom nonlinear system. Numerical simulations are performed to investigate the nonlinear dynamic responses of the rotating shell. In summary, numerical studies show that the velocity and forces have effects on the time histories, phase portraits and power spectrum densities (PSD) of the response.