Harmonically exited nonlinear vibration of heated functionally graded plates integrated with piezoelectric composite actuator

Abstract

A nonlinear frequency response analysis of a smart functionally graded plate operating under a heated substrate plate surface is presented. The analysis is mainly for investigating the effect of temperature on the harmonically exited nonlinear vibration characteristics of smart functionally graded plates and also on the corresponding control authority of piezoelectric fiber–reinforced composite actuator bonded to the substrate plate surface. A negative velocity feedback control strategy is utilized so as to achieve smart damping. The temperature-dependent material properties of the ceramic metal–based functionally graded plate are graded in the thickness direction. Based on the von Karman nonlinear strain–displacement relations and assuming periodic motion, a nonlinear dynamic incremental finite element model of the overall smart functionally graded plate is developed. An arc-length extrapolation technique with a new strategy for determining the arc length is used for numerical solutions. The analysis reveals significant effects of temperature and metal volume fraction in substrate on the structural dynamic behavior of the overall plate. The analysis also reveals the effects of temperature, metal volume fraction in substrate, fiber volume fraction in piezoelectric fiber–reinforced composite, and fiber orientation in piezoelectric fiber–reinforced composite on the smart damping. For using the piezoelectric fiber–reinforced composite actuator in the form of a patch, its optimal location and size are numerically determined.