Combined resonance of graphene platelets reinforced metal foams cylindrical shells with spinning motion under nonlinear forced vibration

The recent studies on dynamical behavior of spinning cylindrical shells are mainly concerned on the principal and internal resonances, however, there is a lack of study on coupled resonance of spinning graphene platelets reinforced metal foams (GPLRMF) cylindrical shells. To remedy this defect, the present work attempts to investigate the combined resonances of spinning cylindrical shells under multi-source excitations. Considering Reddy's higher order shear deformation theory (HSDT), the highly dimensional nonlinear governing motion equations is derived and then discretized through Galerkin truncation. Afterwards, the method of varying amplitudes (MVA) is applied to obtain the steady-state approximate solution, in which the jump phenomenon and bifurcation behavior are discussed. Additionally, the dynamic model is confirmed via comparing with existing literature. Eventually, numerical analyses indicate the internal stable/unstable loops may appear unexpectedly, and the existence of the loop mainly depends on the variations of initial phase angle, external excitation amplitude, damping coefficient and so on. In addition, the amplitude frequency response curve of nonlinear vibration can be adjusted and supported through parametric resonance, and different from internal resonance, the multi-jump phenomenon of combined resonance will take place in the spinning cylindrical shells.