Transient dynamics of 2D-FG porous microplates under moving loads using higher order finite element model

Abstract

This study presents the higher order finite element model to explore the transient vibration of two-dimensional functionally graded (2D-FG) porous microplate under harmonic moving loads, that can be helped in design of nanoplate devices such as NEMS, nanofilters, nanoresonators, and nanoswitches. A normal and shear deformable plate theory with five unknowns is exploited with the modified couple stress theory to portray the kinematic relations, constitutive stress–strain equations, and size-dependence effect. This complicated problem is investigated for the first time based on Newmark’s method to obtain time history analysis of 2D-FG porous microplates having in-plane inhomogeneity. In-plane displacements and stretching component of the transverse displacement are interpolated by using Bogner-Fox-Schmit rectangular element with four degrees of freedom (DOF) for each node satisfying the C1 continuity requirement. In addition, bending and shear components of the transverse displacement are presented by a nonconforming rectangular element with six DOF for each node satisfying the C2 continuity requirement. Various boundary conditions are considered to evaluate the influences of the thickness to material length parameter, aspect ratio, gradient index in two directions, material loss due to porosity in two directions, load velocity parameter and load excitation frequency ratio. It is revealed based on the results that dynamic deflections of 2D-FG porous microplates are significantly affected by the variation of the analysis parameters mentioned above.