Nonlinear free vibration of cracked functionally graded graphene platelet-reinforced nanocomposite beams in thermal environments

The present paper studies the nonlinear free vibration of edge-cracked graphene nanoplatelet (GPL)-reinforced composite laminated beams resting on a two-parameter elastic foundation in thermal environments. GPL nanofillers are assumed to be randomly oriented and are functionally graded distributed in a layer-wise pattern along the beam thickness. The temperature field considered is assumed to be a uniformly distributed in the domain of the beam. Effective material properties of the GPL-reinforced nanocomposite (GPLRC) are estimated by micromechanical models. Stress intensity factors are calculated based on the finite element methods. In the framework of the first order shear deformation beam theory, the equations of motion of cracked GPLRC beams are established including the von Kármán-type geometric nonlinearity. The bending stiffness of the cracked section is evaluated by the massless rotational spring model. The differential quadrature method is used to calculate the linear and nonlinear natural frequencies of the cracked beams. Numerical results illustrate the effects of GPL distribution pattern and concentration, GPL geometry and size, crack length, foundation stiffnesses and temperature variation on the linear and nonlinear free vibration characteristics of the cracked GPLRC beams.