Hygro-Thermo-Mechanical Vibration Behavior of Viscoelastic Nanosheets Resting on Visco-Pasternak Medium Taking into Account Flexoelectric and Actual Surface Effects

For the first time, flexoelectric and actual surface effects are applied to analyze the free oscillation of viscoelastic nanosheets resting on visco-Pasternak medium in hygro-temperature environment. The material characteristics of nanosheets are viscoelastic based on the Kelvin–Voigt model, and the visco-Pasternak medium has two layers, in which the sliding layer and the other layer are described as a spring system interspersed with a damping system. The general equation of motion of the nanosheets is established by applying Kirchhoff plate theory along with Hamilton's principle and the nonlocal strain gradient hypothesis. To solve the free vibration equations of nanosheets with various boundary conditions, the Navier and Galerkin approaches are employed. The presence of the viscoelastic component causes the nanosheets' inherent frequency to oscillate in the general situation with both imaginary and real components. Finally, the impact of coefficients on vibration of viscoelastic nanosheets is discussed in the numerical examples. This is the work that calculates the flexoelectric, surface effects, and viscoelastic-based nanosheet structures under varied loads, which serves as a precondition for their manufacture and use in reality. The present work is general because it combines the theories of nonlocal strain gradient, flexoelectricity, and actual surface effects for viscoelastic nanoplate. Currently, no research has been performed on this issue, and this study makes clear on understanding the underlying physics of electromechanical coupling at the nanoscale.