Active Control of Geometrically Nonlinear Vibrations of Laminated Composite Beams Using Piezoelectric Composites by Element-Free Galerkin Method

Abstract

In this article, active control of geometrically nonlinear transient vibrations in laminated composite beams has been demonstrated using an advanced piezoelectric composite (PZC) layer as the active layer with a proper control strategy. A nonlinear mesh free (MF) model is derived for analyzing the dynamic characteristics of the laminated composite beams integrated with the PZC patch based on the element-free Galerkin (EFG) method within the framework of a layer wise beam theory considering transverse shear deformations. The Von Kármán type nonlinear strain–displacement relationships are considered for formulating the coupled electromechanical nonlinear MF model. Both in-plane and transverse actuation by the PZC layer have been taken into consideration for deriving the model. Various geometrical shapes of the PZC layers have been considered for the analysis to understand the geometrical shape dependency of the PZC layer in attenuating vibration in the structure. The numerical results indicate that the PZC layer significantly improves the dynamic characteristics of the laminated beams by suppressing the geometrically nonlinear transient vibrations induced in them. It has been also noticed that the irregular shaped PZC patches like triangular PZC patches perform better as compared to the regular rectangular PZC patches in alleviating vibration the structure.