Spin-induced internal resonance in circular cylindrical shells

Abstract

Internal resonances in circular cylindrical shells, induced by the spinning motion, are explored in this research. The mathematical model of spinning cylindrical shells is established by employing Donnell’s nonlinear shell theory and the Lagrange equations of motion. Then, the nonlinear forced vibration responses of the shells are solved by using the pseudo-arclength continuation technique. Some comparisons are conducted to verify the accuracy of the present model and method The results show that internal resonances can be caused by the spinning motion of the shells, which cover a wide range of spinning speeds. Different types of internal resonances can occur, such as 1:1, 1:1:1, and 1:2 internal resonances. Energy exchanges between different modes with internal resonance relationships. Both softening and hardening nonlinearities exist in the frequency response of the spinning cylindrical shells. The excitation amplitude has a threshold to excite the internal resonances. It is found that the internal resonances can be avoided by tuning the spinning speed of the shells.