Eshelby-Mori-Tanaka approach for vibrational behavior of functionally graded carbon nanotube-reinforced plate resting on elastic foundation

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of functionally graded (FG) nanocomposite plates reinforced by randomly-oriented straight single-walled carbon nanotubes (SWCNTs) resting on an elastic foundation are considered. Material properties are graded in the thickness direction of the plate according to the volume fraction power law distribution. An embedded carbon nanotube (CNT) in a polymer matrix and its surrounding inter-phase which is perfectly bonded to surrounding resin is replaced with an equivalent fiber to predict the mechanical properties of the carbon nanotube/polymer composite. The Mori-Tanaka approach is employed to calculate the effective elastic moduli of the plate. The natural frequencies of the plate are obtained by means of the generalized differential quadrature (GDQ) method. Detailed parametric studies have been carried out to investigate the influences of the CNT volume fraction, Winkler foundation modulus, shear elastic foundation modulus and various geometrical parameters on the vibration behavior of the functionally graded carbon nanotube-reinforced (FG-CNTR) plates.