Effects of hygro-thermal environment on dynamic responses of variable thickness functionally graded porous microplates

This paper presents a novel finite element model for the free vibration analysis of variable -thickness functionally graded porous (FGP) microplates resting on Pasternak's medium in the hygro-thermal environment. The governing equations are established according to refined higher -order shear deformation plate theory (RPT) in construction with the modified couple stress theory. For the first time, three -node triangular elements with twelve degrees of freedom for each node are developed based on Hermitian interpolation functions to describe the in -plane displacements and transverse displacements of microplates. Two laws of variable thickness of FGP microplates, including the linear law and the nonlinear law in the x -direction are investigated. Effects of thermal and moisture changes on microplates are assumed to vary continuously from the bottom surface to the top surface and only cause tension loads in the plane, which does not change the material's mechanical properties. The numerical results of this work are compared with those of published data to verify the accuracy and reliability of the proposed method. In addition, the parameter study is conducted to explore the effects of geometrical and material properties such as the changing law of the thickness, length -scale parameter, and the parameters of the porosity, temperature, and humidity on the free vibration response of variable thickness FGP microplates. These results can be applied to design of microelectromechanical structures in practice.