Small-scale effects on the free vibrational behavior of embedded viscoelastic double-nanoplate-systems under thermal environment

The present paper deals with the theoretical investigation of small-scale effect on the thermo-mechanical vibration of double viscoelastic nanoplate-system made of functionally graded materials (FGMs). The small scale effect is taken into consideration via Eringen's nonlocal elasticity theory. It is considered that a Kelvin-Voigt viscoelastic layer connects two parallel viscoelastic nano-plates that surrounded by a Pasternak elastic foundation. The material properties in the thickness direction vary according to power low distribution. On the basis of nonlocal elasticity theory and employing Hamilton's principle, the exact solution for complex natural frequencies of a double nanoplate-system is determined for two types of vibrations, out-of-phase and in-phase. The detailed manner of deriving equations based on Navier method are presented and numerical studies are carried out to illustrate the influence of structural damping of the nanoplates, damping coefficient of viscoelastic medium, nonlocal parameter, higher wave numbers, aspect ratio, temperature change and other factors on the behavior of double nanoplate-system. Results from the analytical solution reveal that the temperature raising decreases the natural frequencies.