Effect of non-linear modal interaction on the dynamic instability of axially excited cylindrical shells

The non-linear vibrations and instabilities of cylindrical shells under pulsating axial loads are investigated using Donnell’s shallow shell equations. Based on physical and mathematical reasoning, a meaningful low dimensional model is derived and used together with Galerkin method to obtain a set of coupled non-linear equations of motion. Particular attention is paid to the investigation of modal interaction between non-linear vibration modes with equal or nearly equal natural frequencies and to its influence on parametric instability and snap-through buckling. A parametric analysis using continuation techniques identifies the relevant bifurcations connected with the modal interaction and highlights their relevance in design.