Effects of initial compression/tension, foundation damping and pasternak medium on the dynamics of shear and normal deformable GPLRC beams under moving load

Abstract

An attempt is made in this research to investigation the free vibration and dynamic response of an arbitrary thick composite beam which is reinforced with graphene platelets (GPLs). Distribution of GPLs in the layers may be different which leads to a functionally graded media. To this end a shear and normal deformable beam is adopted. The developed beam model has four unknowns and takes the non-uniform shear strains and also thickness stretching into account. Also the effects of compressive or tensile force, a two parameter Pasternak elastic foundation and also foundation damping are taken into account for both free and forced vibration responses. The governing equations of the beam are established using the Hamilton principle. By applying the Navier solution method suitable for simply supported edges, results of the present studies are provided. It should be noted that for forced vibration problem, Newmark time marching method is applied. For dynamic response the case of moving load is assumed. Results of this study are first compared with the available data in the open literature especially with those developed by 3D elasticity to show the accuracy of the developed formulation. After that novel results are given to discuss the effects of different parameters. It is highlighted that weight fraction and distribution pattern of GPLs are two important factors on the dynamic response of the structure.