In this article, free vibration analysis of simply supported sandwich plates with a flexible core and two functionally
graded nanocomposite face sheets resting on two-parameter elastic foundation is carried out using Navier’s solution. The
nanocomposite face sheets are reinforced by randomly oriented and aggregated carbon nanotube (CNT). The material
properties of the nanocomposites plates are graded along the thickness and are estimated though the Eshelby–Mori–
Tanaka approach. In the proposed theory, 3-D elasticity theory and first order shear deformation theory are used for core
and face sheets, respectively. Also, Hamilton’s variational principle is used to derive the equations of motion.