Analytical solution for free vibration of functionally graded carbon nanotubes (FG-CNT) reinforced double-layered nano-plates resting on elastic medium

In this paper, free vibration of an embedded double-layered nano-plate reinforced by functionally graded carbon nanotubes (FG-CNT) is analytically investigated. Carbon nanotubes are distributed through the thickness in two ways: uniform distribution and symmetrically linear distribution (or decreasing-increasing layup). To accurately model this nanocomposite behavior, the elastic medium around the nano-plate is modeled by Pasternak elastic foundation and the Van der waals forces between two nano-plates are taken into account. Governing equations of motions are obtained using energy method in association with Eringen nonlocal theory and solved by Navier method for a simply-supported rectangular plate. Finally, the effect of elastic foundation parameters, different distributions of CNT and nonlocal parameters are investigated on the vibration behavior of orthotropic double-layer nano-plate. Results show that natural frequencies of a double-layer nano-plate increase by increasing the Winkler elastic constants while Pasternak elastic constant has less effect on the results. Also, increasing the nonlocal parameter at a constant length decreases the natural frequencies. By increasing the length to thickness ratio (L/h) of nano-plate, the nonlocal frequencies reduce and natural frequency of symmetrically linear distribution is more than those of uniform distribution for constant value of L/h.