REDUCED ORDER MODEL FOR THE NONLINEAR VIBRATION ANALYSIS OF A PRESSURE LOADED CYLINDRICAL SHELL
A reduced order model for the nonlinear vibration analysis of a thin-walled, simply-supported circular cylindrical shell based on the use of a standard perturbation procedure and on the proper orthogonal decomposition is derived. First, using Donnell shallow shell nonlinear equations of motion, a modal solution is obtained by a perturbation technique leading to a multi-mode solution that captures the inherent modal coupling, thus describing correctly the nonlinear modes of vibration, and satisfies all boundary and continuity conditions. Based on this solution, the proper orthogonal modes and values are obtained, identifying the most important modes in the modal expansion. Then, different reduced models are derived and used to analyze the vibrations and resonance of the shell under a harmonic lateral pressure.