Nonlinear free vibration analysis of piezoelectric laminated plate with random actuation electric potential difference and thermal loading

Abstract

Solutions to nonlinear free vibration analysis of an arbitrarily laminated thin rectangular plate subjected to thermo-piezoelectric load is investigated. The governing equation of motion is based on von Kármán’s deflection of thin plates to capture the effects of moderate geometric nonlinearity. Induced strain actuation assumption is confined to a linear model for applied low electric fields and varying temperature distribution along the thickness direction. The solution for lateral displacement field for simply supported and clamped condition edges are determined by displacement-stress; mixed formulation. The applied Galerkin’s projection reduces the governing nonlinear partial differential equation to a time dependent ordinary differential equation. Solutions are obtained using a predictor-corrector numerical integration scheme. The effects of randomly applied actuation potential and thermal loading on nonlinear frequency ratio are examined. The marginal values provided using various probabilistic methods are found to be in good agreement with each other.