A geometrically non-linear plate model including surface stress effect for the pull-in instability analysis of rectangular nanoplates under hydrostatic and electrostatic actuations

Presented herein is a comprehensive investigation on the size-dependent pull-in instability of geometrically non-linear rectangular nanoplates including surface stress effects undergoing hydrostatic and electrostatic actuations. To this end, based on the Gurtin–Murdoch theory, a non-classical continuum plate model capable of incorporating size-effects is developed; then, by means of the principle of virtual work, the governing equations of the actuated nanoplate are obtained. Subsequently, the generalized differential quadrature (GDQ) method is used to discretize the governing equations and associated boundary conditions, before solving numerically by the pseudo arc-length algorithm. Finally, the influences of important parameters including the geometrical non-linearity, thickness of the nanoplate, surface elastic modulus, residual surface stress and boundary conditions on the pull-in behavior of the actuated nanoplate are thoroughly studied. In addition, the effect of the material on the pull-in voltage and pressure is investigated by comparing the results obtained from nanoplates made of two different materials including aluminum (Al) and silicon (Si). •Development of a geometrically non-linear nanoplates model including surface stress effect.•Prediction of pull-in voltage and hydrostatic pressure for nanoplates with different edge conditions.•Exploring influences of the nanoplate thickness, surface elastic modulus and residual surface stress.•Comparing the pull-in voltage and hydrostatic pressure predicted by linear and non-linear models.•Comparing the classical, non-classical theories in predicting the pull-in voltage and hydrostatic pressure.