Nonlinear combined resonance of graphene platelet-reinforced metal foam beam

At present, current research on graphene platelet-reinforced metal foam (GPLRMF) beam' resonance is limited to single excitation levels, such as main resonance and internal resonance. To fill the gap in this field, this article aims to study the dynamic characteristics of beams under combined lateral and longitudinal excitations. First, a displacement field was established based on the Euler-Bernoulli beam model, and the motion equations were derived using Hamilton's principle. Subsequently, the Galerkin method was used to discretize the equations, and the amplitude-frequency response of the system was obtained via the amplitude variation method (AVM). The article discusses in detail nonlinear behaviors such as jumps and bifurcations. The correctness of the model was verified by comparing the results with published literature. Numerical results indicate that the frequency sweep curve of combined resonance (stable solution domain, amplitude peak, hardening characteristics, etc.) is influenced by multiple parameter combinations, including material properties, damping coefficients, external loads, and initial phase angles. Additionally, the amplitude-frequency response curve of combined resonance can exhibit multiple jumps, a phenomenon not observed in internal resonance.