Effect of Sinusoidal Corrugated Geometries on the Vibrational Response of Viscoelastic Nanoplates

The vibrational behavior of viscoelastic nanoplates with a corrugated geometry is a key topic of practical interest. This problem is addressed here for wrinkled nanoplates with small corrugations related to incorrect manufacturing. To this end, a new One-Variable First-order Shear Deformation plate Theory (OVFSDT) is proposed in a combined form with a non-local strain gradient theory. The Kelvin–Voigt model is employed to describe the viscoelastic behavior of the nanoplate, whereby the frequency equations are solved numerically according to Navier’s approach, for simply-supported nanostructures. A comparative evaluation between the proposed theory and other approaches in the literature is successfully performed. It follows a large parametric study of the vibration response for varying geometry corrugations and non-local parameters.