Vibration of FG-CNT reinforced composite thick quadrilateral plates resting on Pasternak foundations

Abstract

This paper considers the free vibration behaviors of functionally graded carbon nanotube (FG-CNT) reinforced composite thick straight-sided quadrilateral plates resting on Pasternak foundations. The IMLS-Ritz method is used in this study. The FG-CNT reinforced composite plates considered are having the CNT reinforced uniaxially aligned in the axial direction with its material properties graded in the thickness direction. The first-order shear deformation theory (FSDT) is employed for formulation of the energy functional to incorporate the effects of transverse shear deformation and rotary inertia. Several example problems are considered with different boundary conditions. Convergence studies for the example problems are performed to demonstrate the numerical stability of the improved moving least-squares Ritz (IMLS-Ritz) method. Besides, the accuracy of the IMLS-Ritz results is examined by comparing with the published values. Close agreement is found from the comparison study. Parametric studies are conducted for various types of CNTs distributions, CNT ratios, aspect ratios, plate geometries and thickness-to-height ratios under different boundary conditions.