Dynamic response of porous E-FGM thick microplate resting on elastic foundation subjected to moving load with acceleration

Abstract

For the first time, dynamic analysis of exponentially functionally graded material (E-FGM) including porosities is investigated. As a first endeavor, forced vibration response of thick microplates made of porous E-FGM when subjected to moving loads with an acceleration in speed is studied in this research study. The role of a two-parameter elastic foundation is also included. A powerful mathematical formulation supported by the assumptions of the general third-order shear deformation theory (GTSDT) as well as the modified couple stress theory (MCST) is developed to find an accurate model for thick size-dependent microplates. The effective material properties of imperfect FGM, which change exponentially along the z-direction, are established via developing a modified rule of mixture which includes the porosity imperfection. The governing equations for simply-supported microplate is found using a virtual work of Hamilton principle, and afterwards they are solved by developing a state space method (SSM) in conjunction with a set of mathematical series. The numerical results attempt to indicate the influence of variation in volume fraction index, porosity index, elastic foundations, and small-scale parameter, highlighted by different load speeds, acceleration ratios, and time histories of moving load under upper surface of E-FGM thick microplate. The parametrical studies can be used in better designing of micro/nanostructures made of porous FGMs under accelerated moving loads.