Nonlinear dynamic instability of edge-cracked functionally graded graphene-reinforced composite beams

This work investigates nonlinear dynamic instability of edge-cracked functionally graded (FG) graphene nanoplatelet (GNP)-reinforced composite (GNPRC) beams consist of perfectly bonded layers. GNPs with randomly orientations are uniformly dispersed in each individual layer, and GNP concentration varies along beam thickness. Micromechanics models are employed to estimate the effective material properties of the GNPRCs. Considering von Kármán-type nonlinear kinematics, nonlinear ordinary differential equations governing the motions are derived by using Lagrange equation together with Ritz method on the basis of a rotational spring model and the first-order shear deformation theory. The eigenvalue equation is derived using the Bolotin’s method and solved through an iteration procedure to determine the unstable region. Numerical analysis is conducted to study the effects of geometric nonlinearity and crack on the dynamic instability of FG-GNPRC beams in different situations.