Free Vibration Analysis of FGM Plate Reinforced with Single Wall Carbon Nanotubes Using 3-D Elasticity Theory

In this paper، free vibration of a functionally graded rectangular plate reinforced by carbon nanotubes have been investigated. The material properties of the composite plate have been calculated by the Mori-Tanaka model and the governing differential equations of problem have been derived using 3-D elasticity. For solving the differential equations of motion we used the generalized differential quadrature (GDQ) technique by regarding the appropriate grid points. Finally، by solving the numerical example for a simply supported plate، the frequency vibration of plate by assuming the variation of problem parameters (distribution of carbon nanotubes-properties of plate-geometrical features of problem) has been calculated. Also، the convergence of the method is demonstrated and to validate the results، comparisons are made with the available references.