Porosity-dependent nonlinear forced vibration analysis of functionally graded piezoelectric smart material plates

Abstract

This work investigates the porosity-dependent nonlinear forced vibrations of functionally graded piezoelectric material (FGPM) plates by using both analytical and numerical methods. The FGPM plates contain porosities owing to the technical issues during the preparation of FGPMs. Two types of porosity distribution, namely, even and uneven distribution, are considered. A modified power law model is adopted to describe the material properties of the porous FGPM plates. Using D’Alembert’s principle, the out-of-plane equation of motion is derived by taking into account the Kármán nonlinear geometrical relations. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. These ordinary differential equations are solved analytically by employing the harmonic balance method. The approximate analytical results are verified by using the adaptive step-size fourth-order Runge–Kutta method. By means of the perturbation technique, the stability of approximate analytical solutions is examined. An interesting nonlinear broadband vibration phenomenon is detected in the FGPM plates with porosities. Nonlinear frequency-response characteristics of the present smart structures are investigated for various system parameters including the porosity type, the porosity volume fraction, the electric potential, the external excitation, the damping and the constituent volume fraction. It is found that these parameters have significant effects on the nonlinear vibration characteristics of porous FGPM plates.