DSC regularized Dirac-delta method for dynamic analysis of FG graphene platelet-reinforced porous beams on elastic foundation under a moving load

Abstract

This work presents a novel computational approach, the DSC regularized Dirac-delta method, for the vibration analysis of functionally graded graphene-platelet reinforced (FG-GPLR) porous beams resting on a Winkler–Pasternak elastic foundation under a moving load. Based on the Timoshenko beam theory, the energy functional of the beam model is represented by a newly constructed basis function and is minimized under the variational principle. To account for the properties of composite materials, the Halpin–Tsai model is used to predict the elastic modulus of graphene-reinforced composites. A coupling of the DSC regularized Dirac-delta method and the Newmark–β integration scheme is then adopted for solving the dynamic problem. The DSC-based approach exhibits controllable accuracy for approximations and shows excellent flexibility in handling time-dependent moving load problems, because the equally spaced grid system used in the DSC numerical approach can achieve a preferable representation of moving load sources. An intensive parametric study is provided with a particular focus on the influence of moving loads, foundation supports and material properties (e.g., weight fraction, porosity distribution, dispersion pattern and geometry size of graphene reinforcements). First-known solutions reported in tabular and graphical forms should be useful for researchers and engineers in designing such beam problems.