Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates

Abstract

The nonlinear electroelastic vibration behavior of viscoelastic nanoplates is investigated based on nonlocal elasticity theory. Employing nonlinear strain–displacement relations, the geometrical nonlinearity is modeled while governing equations are derived through Hamilton’s principle and they are solved applying semi-analytical generalized differential quadrature (GDQ) method. Eringen’s nonlocal elasticity theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. Based on Kelvin–Voigt model, the influence of the viscoelastic coefficient is also discussed. It is demonstrated that the GDQ method has high precision and computational efficiency in the vibration analysis of viscoelastic nanoplates. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as electric voltage, small-scale effects, van der Waals interaction, Winkler and Pasternak elastic coefficients, the viscidity and aspect ratio of the nanoplate on its nonlinear vibrational characteristics. It is explicitly shown that the electroelastic vibration behavior of viscoelastic nanoplates is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of viscoelastic nanoplates which are fundamental elements in nanoelectromechanical systems.