Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium

The vibration characteristics of a simply supported viscoelastic nanoplate are studied using the nonlocal plate theory by including the effect of viscoelastic foundation. The material properties of nanoplate are assumed to be orthotropic and viscoelastic and the viscoelastic medium is modeled as Kelvin–Voigt foundation. The complex frequency which is associated with the nonlocal parameter, structural damping of the nanoplate and foundation effects is obtained in a closed-form expression. The predicted results are validated by carrying out the comparison studies for the isotropic elastic nanoplates against existing results in the literature. Moreover, the effects of different parameters such as the nonlocal parameter, structural damping, the stiffness and damping coefficient of the foundation and the aspect ratio on the frequency are elucidated. The results show that the frequency significantly decreases with increasing the structural damping coefficient as well as the damping coefficient of foundation.