Nonlinear free and forced vibration of porous piezoelectric doubly-curved shells based on NUEF model

Abstract

In this paper, the nonlinear free and forced vibration of porous piezoelectric doubly-curved shells resting on visco-Pasternak foundation is performed within the framework of the nonuniform electric field (NUEF) model and von Kármán geometric nonlinearity assumption. Three types of porosity distribution are adopted to study the effect of porosity on the nonlinear dynamic responses of the current system. According to Hamilton’s principle, the nonlinear governing differential equations are obtained. For the nonlinear free vibration of porous piezoelectric doubly-curved shells, an analytical solution is achieved by utilizing the harmonic balance method. For the nonlinear forced vibration of the present system, the numerical solution is obtained by means of Runge–Kutta method. Through numerical examples, the relationship between nonlinear free vibration responses and nonlinear forced vibration responses is explored under different amplitudes of external excitation, width to thickness ratios, types of porosity distribution, electric field models and elastic foundation parameters. The main novelty of the present study is that the nonlinear frequency ratio that is calculated based on the nonlinear free vibration, is in excellent agreement with the resonant frequency ratio which is determined on the basis of the nonlinear forced vibration.