Nonlinear transient response of graphene platelets reinforced metal foams beam considering initial geometrical imperfection and viscoelastic elastic foundation

At present, the dynamics research of beams is mostly limited to free vibration and forced vibration, and the research on nonlinear transient response is little, and no one has studied the nonlinear transient response of beams with initial geometric imperfection under pulse loads. Based on this fact, the transient response characteristics of graphene platelet reinforced metal foams (GPLRMF) beams with initial geometric defects are discussed for the first time in this paper. Firstly, three kinds of graphene platelet (GPL) distribution patterns and foam metal porosity distribution patterns were considered, and the material properties were calculated by means of micromechanical models and mixture diffusion rules, and then, considering initial geometric defects, a dynamic model was established based on Euler-Bernoulli beam theory and von-Kármán nonlinear theory. Then, based on the Hamilton principle, the motion equation of the GPLRMF beam is derived. Finally, the corresponding transient response curve is obtained using the fourth-order Runge-Kutta method. In the study, the convergence of the model is verified to ensure the rationality and accuracy of the analysis results. In addition, a detailed study is conducted, including the distribution patterns and coefficients of porosity, the dispersion and weight fraction of GPLs, pulse load parameters, initial geometric imperfections and damping coefficient.