Bending and vibration analysis of bi-directional porous functionally graded micro-plate resting on non-linear visco-elastic foundation under hygro-thermal loads

Functionally graded (FG) materials are used in potential applications in several engineering systems mainly with their property tailoring ability. Especially, the micro FG structures possessing high strength to weight ratios, good energy efficiency and absorption ability and high thermal conductivities often have a wide usage in applications like micro-sensors and actuators, micro-resonators. The present work focuses on the static bending and vibration characterization of functionally graded porous micro-plates resting on nonlinear visco-elastic foundation under hygro-thermal loads. Bi-directional material grading with porosity distribution are considered. Material modeling and dynamic analysis are carried-out using higher order shear deformation formulation with modified couple stress theory (MCST). Navier’s approach is followed to solve the equations of motion. The effects of power law indices, material length scale parameter, foundation stiffness parameters, temperature rise and moisture content on the natural frequencies and static response are studied in detail. The outcome of this study is benchmark for the design of micro-devices such as paddle like resonators, tunable micro-resonators etc.