Nonlinear dynamic responses of functionally graded graphene platelet reinforced composite cantilever rotating warping plate

Abstract

In this study, the nonlinear dynamic behaviors are investigated for the functionally graded graphene platelet (FGGP) reinforced composite rotating warping blade under combined the aerodynamic force and centrifugal force. The blade is simplified to a FGGP reinforced composite rotating warping cantilever plate with a rectangular cross-section. Four distribution patterns of the graphene platelets (GPLs) along the thickness of the plate are considered when establishing the dynamic model. The effective material parameters, Poisson's ratio, mass density and Young's modulus of the FGGP reinforced composite rotating warping cantilever plate are calculated based on the modified Halpin-Tsai model and mixture rule. Considering the warping effect, the dynamic governing equations of motion for the rotating FGGP reinforced composite cantilever plate subjected to the aerodynamic force and centrifugal force are established by using the first-order shear deformation theory and Hamilton's principle. Galerkin approach is exploited to transform the partial differential equations of motion to the ordinary differential equations of motion the FGGP reinforced composite rotating warping cantilever plate. Four-dimensional autonomous averaging equations of the system are obtained by using the asymptotic perturbation method. The parameter analyzes on the amplitude-frequency and force-amplitude responses of the FGGP reinforced composite rotating warping cantilever plate are carried out by considering the 1:2 internal resonance and principal parametric resonance. The stability of the steady solution of the autonomous system is discussed. The influences of the GPL distribution patterns, rotating speed, aerodynamic force and damping on the chaotic dynamics are investigated for the FGGP reinforced composite rotating warping cantilever plate.