Effects of modal coupling on the dynamics of parametrically and directly excited cylindrical shells

• We derive a consistent modal solution for the analysis of interacting nonlinear vibration modes.
• We deduce a consistent reduced order model for the analysis of interacting modes with the same linear vibration frequency.
• This model allows the identification of multiple coexisting solutions in shells under lateral pressure and axial loads.
• A bifurcation analysis in the resonance region is performed leading to determination of instability boundaries in force control space.
• Modal interaction leads to unsafe nonlinear phenomena and decrease the load carrying capacity of the shell.

Cylindrical shells exhibit a dense frequency spectrum, especially in the lowest frequency range. In addition, due to the circumferential symmetry, frequencies occur in pairs. So, in the vicinity of the lowest natural frequencies, several equal or nearly equal frequencies may occur, leading to multiple internal resonances. The aim of the present work is to investigate the dynamic behavior and stability of cylindrical shells under lateral and axial forcing with equal natural frequencies. The shell is modeled using the Donnell nonlinear shallow shell theory. A consistent modal solution for this problem is deduced and used to discretize the equations of motion by applying the Galerkin method. A parametric analysis is conducted to clarify the influence of the modal interaction among these nonlinear vibration modes on coexisting solutions, bifurcations, resonances curves and stability boundaries of the shell.