Free vibration and buckling analysis of FG graphene origami-enabled auxetic metamaterial beams in a thermal environment

Functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterials (FG-GOEAM) have received much attention due to their excellent mechanical properties. In this study, the buckling and free vibration behaviours of FG-GOEAM beams supported by elastic foundations in a thermal environment are investigated. Three temperature distributions were considered: uniform temperature profile (UTP), linear temperature profile (LTP), and sinusoidal temperature profile (STP). By assuming that the temperature at the geometrical neutral planes of any layer in an FG-GOEAM beam represents the temperature of the entire layer, this study determines the correction function for the material parameters associated with FG-GOEAM beams under LTP and STP. Mechanical response analysis of FG-GOEAM beams under LTP and STP was not reported. The effect of the thermal environment is described in the form of thermal strain energy. The control equations were derived based on refined beam theory (RBT) and Lagrange equations. Numerical results were obtained using the Chebyshev-Ritz method. The accuracy of the study in this paper was verified by comparing the results with the existing literature. It should be noted that bifurcation buckling does not occur for FG-GOEAM beams that exhibit asymmetric material distribution and temperature profiles in the thickness direction. Therefore, these asymmetric distributions are not considered in the buckling analysis. Emphasis was placed on the effects of temperature profiles, weight fraction, and degree of folding of Gori on the buckling and vibrational behaviour of FG-GOEAM beams under various boundary conditions. These numerical results provide important insights for the further design and development of FG-GOEAM beams.