Free Vibration Behaviors of Nanoplates Resting on Viscoelastic Medium

In this study, for the first time, the free vibrations of a nanoplate that is resting on a viscoelastic substrate are investigated while also taking into consideration the flexoelectricity effect that is derived from the classical plate theory. To properly find the natural frequency of the nanoplate, first, the equilibrium equation of the plate is established based on Hamilton’s principle. Then, based on the analytic solution form, the natural frequency of the nanoplate is determined. The presence of the viscoelastic component of the elastic foundation is the primary factor that contributes to the natural frequency expression of the nanostructure. This is because the presence of the viscoelastic component causes the natural frequency of the plate to vibrate in the general case with both real and imaginary components. The findings of the numerical calculation make it abundantly evident that the natural vibration frequency will have a variety of loss rates that are determined by the values of the viscous resistance characteristics of the foundation, as well as the temperature, size effect, and compression force. The validity of this study has been validated via the use of computational theory in conjunction with previously published research. This important work calculates the nanoplate structures based on flexoelectric and viscoelastic materials under different loads. This is necessary before they can be made and used in real life.