Axial magnetic field effect on wave propagation in bi-layer FG graphene platelet-reinforced nanobeams

Abstract

This paper aims to investigate the size-dependent wave propagation in functionally graded (FG) graphene platelet (GPL)-reinforced composite bi-layer nanobeams embedded in Pasternak elastic foundation and exposed to in-plane compressive mechanical load and in-plane magnetic field. The small-scale effects are taken into account by employing the nonlocal strain gradient theory that contains two different length scale parameters. The present two nanobeams are made of multi-composite layers. Each layer is composed of a polymer matrix reinforced by uniformly distributed and randomly oriented GPLs. The GPLs weight fraction is graded from layer to other according to a new piece-wise rule and then four distribution types will be established. Our technique depends on applying the four-variable shear and normal deformations theory to model the wave propagation problem. The equations of motion are obtained using Hamilton principle. These equations are then analytically solved to obtain the wave frequencies and phase velocities of the waves. The calculated results are compared with those published in the literature. The impacts of the length scale parameters, foundation stiffness, in-plane magnetic field, weight fraction of graphene, graphene platelets distribution type and beam geometry on the propagating waves in the FG GPLs nanobeams are discussed in details. It is found that the strength of the composite beams may be enhanced with increasing in the GPLs weight fraction and magnetic field leading to an increment in the phase velocity and wave frequency of the present system.