Nonlinear vibrations of FG-GRLCC rectangular variable cross-section plate subjected to transverse and parametric excitations in thermal environment

Abstract

This paper investigates the linear and nonlinear vibration responses for the functionally graded graphene-reinforced laminated composite cantilever (FG-GRLCC) rectangular variable cross-section plate subjected to the transverse and parametric excitations under the thermal environment. Halpin-Tsai model is used to calculate the material properties of the graphene-reinforced structure. Using the classical laminated plate theory, von Karman large deformation theory, Hamilton principle and Galerkin method, the dynamic model is given for the FG-GRLCC rectangular variable cross-section plate. The natural frequencies and mode shapes are analyzed for the FG-GRLCC rectangular variable cross-section plate under the thermal environment through using Rayleigh-Ritz method. The averaged equations of the system are obtained based on the multiple scale perturbation (MSP) under the primary, 1/2 sub-harmonic and 1:1 internal resonances. The comparisons between the theoretical algorithm and finite element method are proposed to illustrate the accuracy of the present model. The results about the frequency veering phenomenon and mode shape interaction have been illustrated. The amplitude-frequency response curves and force-amplitude response curves are depicted for the FG-GRLCC rectangular variable cross-section plate. The nonlinear and chaotic vibrations for the FG-GRLCC rectangular variable cross-section plate is studied by using the bifurcation diagrams and max Lyapunov exponents.