Vibration and dynamic control of piezoelectric functionally graded porous plates in the thermal environment using FEM and Shi’s TSDT

Abstract

This paper proposes a new finite element formulation based on Shi’s third-order shear deformation theory (TSDT) for controlling the vibration of piezoelectric functionally graded porous (PFGP) plates integrated with piezoelectric sensors and actuators under dynamic loading in the high temperature environment. The properties of the PFGP core vary through the plate’s thickness according to the power-law index k and porosity factor Ω, while the electric potential is a linear function via the piezoelectric sublayer thickness. To actively control the vibration of PFGP plates, a closed-loop control algorithm based on displacement and velocity feedback is applied. The motion equation of PFGP plate under mechanical and thermal load is established based on based on Galerkin weak formulation. The proposed method is evaluated through several numerical examples to demonstrate its effectiveness. Furthermore, the active vibration control of FPGP plates is detail presented.