Nonlinear vibration control of functionally graded plate with piezoelectric layers in thermal environment

Abstract

In this paper, large amplitude vibration control of functionally graded material (FGM) plates under thermal gradient and transverse mechanical loads using integrated piezoelectric sensor/actuator layers is investigated. In this regard, finite element formulation based on higher order shear deformation plate theory is developed. The von Karman nonlinear strain-displacement relationship is used to account for the large deflection of the plate. The material properties of FGM are assumed to be temperature-dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The temperature field is assumed to be constant in the plane and varied only in the thickness direction of the plate. In order to control the large amplitude vibration of the plate, two control algorithms are employed: classical displacement-velocity feedback control and robust H2 control. Also, the uncertainty which arises from external disturbances (low-frequency sine-wave sensor noise and high-frequency Gaussian white sensor noise) is considered. Active control of both the static deflection due to thermal gradient and dynamic oscillation is studied. Numerical results are presented to investigate the effectiveness of the mentioned control algorithms to control nonlinear vibration and thermally induced deflection of the FGM plate. Also, robustness of the controllers in the face of sensor noise is investigated. Effects of the design parameters on performance of each controller are studied and finally, the two control methods are compared.