Piezo-viscoelastically damped nonlinear frequency response of functionally graded plates with a heated plate-surface

Abstract

A geometrically nonlinear frequency-domain analysis of functionally graded plates integrated with an active constrained layer damping (ACLD) arrangement is performed by developing an incremental nonlinear closed-loop dynamic finite element model of the overall plate. The active constraining layer is made of piezoelectric fiber reinforced composite (PFRC) and a heated substrate-plate surface is considered. The analysis is mainly for investigating the effect of temperature on the nonlinear vibration characteristics of the overall plate in the frequency domain and also, on the corresponding control authority of the PFRC constraining layer. A negative velocity feedback control strategy is utilized to achieve active damping. The temperature dependent material properties of the substrate plate are graded in the thickness direction according to a power law, and expressed in terms of the power law exponent and the constituent material (metal and ceramic) properties. Using the Golla-Hughes-McTavish method for modeling the viscoelastic material, the incremental nonlinear finite element equations of motion are derived in the frequency domain assuming periodic motion of the overall plate. An arc-length extrapolation solution technique is used in combination with a new strategy for determination of incremental arc-length. The numerical illustrations show a potential use of PFRC actuator in the ACLD arrangement and suggest an optimal thickness of viscoelastic layer for more effective use of PFRC. The analysis reveals the significant effects of initial thermal bending of the overall smart plate on its nonlinear dynamic behavior in the frequency domain. The effects of temperature, metal-volume fraction in substrate, fiber volume fraction in PFRC and the fiber orientation angle in the PFRC on the control authority of the ACLD layer are presented. For the use of the ACLD layer in the form of a patch, a new numerical strategy for determining its optimal location and optimal size for effective control is presented.