On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations

In the current paper, the nonlinear resonance response of functionally graded graphene platelet reinforced (FGGPLRC) beams by considering different boundary conditions is investigated using the Euler-Bernoulli beam theory. Four different graphene platelets (GPLs) distributions including UD and FG-O, FG-X, and FG-A are considered and the effective material parameters are calculated by Halpin-Tsai model. The nonlinear vibration equations are derived by Euler-Lagrange principle. Then the perturbation method is used to discretize the motion equations, and the loadings and displacement are all expanded, so as to obtain the first to third order perturbation equations, and then the asymptotic solution of the equations can be obtained. Then the nonlinear amplitude-frequency response is obtained with the help of the modified Lindstedt-Poincare method (Chen and Cheung 1996). Finally, the influences of the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions on the resonance problems are comprehensively studied. Results show that the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions have a significant effect on the nonlinear resonance response of FG-GPLRC beams.