Multiple internal resonances in nonlinear vibrations of rotating thin-walled cylindrical shells

Multiple internal resonances in nonlinear vibrations of rotating thin-walled cylindrical shells are investigated in the paper. Considering the Coriolis forces as well as the initial hoop tension, the dynamic model of rotating thin-walled cylindrical shells is derived by using Lagrange equations. Based on this model, linear vibration characteristics are given and two kinds of multiple internal resonances are then proposed and illustrated. One is the internal resonances caused by opportune geometric parameters, and the other is the internal resonances caused by the rotation of shells. Finally, further numerical investigations are carried out using harmonic balance method combined with arc length continuation technique, as well as direct integral approach. Nonlinear vibration characteristics of rotating thin-walled cylindrical shells with 1:1:1:1 internal resonances are shown in detail.

Automated summary

The paper investigates multiple internal resonances in the nonlinear vibrations of rotating thin-walled cylindrical shells, considering Coriolis forces and initial hoop tension. A dynamic model is derived using Lagrange equations, and linear vibration characteristics are given. Two types of multiple internal resonances are proposed, one caused by opportune geometric parameters and the other by rotation of the shells. Numerical investigations using harmonic balance method and direct integral approach show detailed nonlinear vibration characteristics with 1:1:1:1 internal resonances.