Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates

The nonlinear thermomechanical vibration behavior of viscoelastic nanoplates is investigated based on nonlocal elasticity theory. Based on Kelvin–Voigt model and nonlinear strain–displacement relations, the geometrical nonlinearity is modeled while governing equations are solved applying semi-analytical differential quadrature method (DQM). The detailed derivations are presented while the emphasis is placed on investigating the effects of thermal environment, small scale effects, Winkler and Pasternak elastic coefficients and the viscidity and aspect ratio of the nanoplate on its nonlinear vibrational characteristics. Numerical results are presented to serve as benchmarks for the analysis of viscoelastic nanoplates, which are fundamental elements in nanoelectromechanical systems.