Nonlinear forced vibrations of rotating cylindrical shells under multi-harmonic excitations in thermal environment

Multi-harmonic excitations are commonly observed in rotor systems and affect their nonlinear characteristics significantly. However, most of the published nonlinear studies on rotating structures only consider single-harmonic excitation. Compared with single-harmonic issues, multi-harmonic excitations increase the difficulty of calculation and solution exponentially. The purpose of this paper is to establish the nonlinear coupled mechanical model and analyze nonlinear forced vibrations of rotating shells subjected to multi-harmonic excitations in thermal environment. The nonlinear governing equations, considering the Coriolis forces, centrifugal force, initial hoop tension and thermal effect, are obtained by the improved Donnell nonlinear shell theory and Hamilton principle, and then, the multi-mode Galerkin technique is introduced to transform the partial differential equations into multi-degree-of-freedom nonlinear ordinary differential equations (ODEs). Afterward, numerical simulations are conducted by the pseudo-arc-length continuation algorithm. The verification of the solutions with available results in the literature and the convergency of the results are presented. At last, the effects of main factors on nonlinear dynamic response of rotating shells are evaluated. It can be observed that since the multi-DOF coupled system, which is excited by multi-harmonics, exhibits complex nonlinear dynamic responses of rotating shells, the nonlinear multiple internal resonances occur.