Active constrained layer damping of geometrically nonlinear vibrations of functionallygraded plates using piezoelectric fiber-reinforced composites

Abstract

In this paper, a geometrically nonlinear dynamic analysis has been presented forfunctionally graded (FG) plates integrated with a patch of active constrained layerdamping (ACLD) treatment and subjected to a temperature field. The constraining layer ofthe ACLD treatment is considered to be made of the piezoelectric fiber-reinforcedcomposite (PFRC) material. The temperature field is assumed to be spatiallyuniform over the substrate plate surfaces and varied through the thickness ofthe host FG plates. The temperature-dependent material properties of the FGsubstrate plates are assumed to be graded in the thickness direction of the platesaccording to a power-law distribution while the Poisson’s ratio is assumed tobe a constant over the domain of the plate. The constrained viscoelastic layerof the ACLD treatment is modeled using the Golla–Hughes–McTavish (GHM)method. Based on the first-order shear deformation theory, a three-dimensional finiteelement model has been developed to model the open-loop and closed-loop nonlineardynamics of the overall FG substrate plates under the thermal environment. Theanalysis suggests the potential use of the ACLD treatment with its constraininglayer made of the PFRC material for active control of geometrically nonlinearvibrations of FG plates in the absence or the presence of the temperature gradientacross the thickness of the plates. It is found that the ACLD treatment is moreeffective in controlling the geometrically nonlinear vibrations of FG plates than incontrolling their linear vibrations. The analysis also reveals that the ACLD patch ismore effective for controlling the nonlinear vibrations of FG plates when it isattached to the softest surface of the FG plates than when it is bonded to the stiffestsurface of the plates. The effect of piezoelectric fiber orientation in the activeconstraining PFRC layer on the damping characteristics of the overall FG plates is alsodiscussed.