Stability of Cracked Functionally Graded Graphene-Reinforced Beams under Magnetic Field

Abstract

This paper studies linear dynamic stability of cracked functionally graded (FG) graphene platelet (GPL)-reinforced composite laminated beams subjected to the combined action of magnetic field and a periodic axial force. GPL weight fraction follows a layer-wise variation across the beam thickness. Effective material properties are estimated by micromechanics models, and the bending stiffness of the cracked section is evaluated by a rotational spring model. The governing equation is derived by Ritz method and Lagrange equation within the framework of the first-order shear deformation theory. The linear principle unstable regions of the cracked beams are determined by Bolotin method. Numerical results show that magnetic field intensity, GPL distribution pattern, boundary condition, crack depth and location have significant influence on the linear dynamic stability behaviors of the cracked beams.