Vibrations of longitudinally traveling functionally graded material plates with porosities

Abstract

Abstract Vibrations of longitudinally traveling functionally graded material (FGM) plates with porosities are studied for the first time. The FGM plates contain porosities owing to the technical issues during the preparation of FGMs. Two different porosity distributions, namely, even and uneven distribution, are considered in this paper. The large-amplitude motion of FGM plates is taken into account so that the present model includes both geometry and material nonlinearities. The governing equation of the present system is derived by using the D'Alembert's principle. The Galerkin method is utilized to discretize the governing equation to a system of ordinary differential equations. The method of harmonic balance is adopted to perform an approximately analytical analysis on the present model. Then the analytical results are validated by the comparison with numerical solutions, which are obtained by using the adaptive step-size fourth-order Runge-Kutta method. Moreover, the stability of steady-state analytical solutions is analyzed. Nonlinear vibrational responses for both FGM plates with evenly distributed porosities (EDP) and unevenly distributed porosities (UEDP) are examined. A 1:1 internal resonance behavior is discovered and it is found that this behavior can be excited by very small external excitation. Furthermore, the effects of porosity volume fraction, damping and constituent volume fraction on the dynamic response of the system are highlighted.