Nonlinear combined resonances of axially moving graphene platelets reinforced metal foams cylindrical shells under forced vibrations

As a crucial basic structure in aviation and aerospace field, axially moving cylindrical shells exhibit complex dynamic behavior. However, the nonlinear dynamics of axially moving cylindrical shells under multi-source excitation is hard to find in literature. Inspired by this, the current paper aims to predict the combined resonance behavior of axially moving cylindrical shells under coupled longitudinal and transverse excitations. Considering graphene platelets reinforced metal foams (GPLRMF) and Donnell's nonlinear thin shell theory, Hamilton principle is applied for formulating the motion equations. Subsequently, the method of varying amplitudes (MVA) is established to determine the vibration response for GPLRMF cylindrical shells subjected to coupled transverse and longitudinal excitations, where the jump, bifurcation as well as multiple stable solutions analysis are conducted. Through validation research, the accuracy of the current calculation method is verified. Numerical results reveal that unexpected internal stable/unstable loop may occur, and the internal stable/unstable loop whether or not exist, it depends on the values of key parameters including external excitation amplitude, initial phase angle and damping coefficient. Additionally, the bifurcation curves of combined resonance can be regulated and supported by parametric resonance. Furthermore, unlike internal resonance, the amplitude frequency response curves of combined resonance exhibit different multi-jump phenomena.