Nonlinear nonlocal analysis of electrostatic nanoactuators

This study investigates the small scale effect on the nonlinear static and dynamic response of a capacitive nanoactuator subjected to a DC voltage. The nanoactuator is modeled as a Euler–Bernoulli beam cantilever beam and beam clamped at its both ends. The model accounts for residual stresses, initial deflection, the von Kármán nonlinear strains, and the electrostatic forcing. The intermolecular forces, such as the Casimir and von der Waals forces, are also included in the model. Hamilton’s principle is used to derive the governing equations and boundary conditions for the nonlinear Euler–Bernoulli beam with Eringen’s nonlocal elasticity model. The differential quadrature method (DQM) is used to solve the governing equations. First, the static response to an applied DC voltage is determined to investigate the influence of scale effect on the maximum stable deflection and pull-in voltage of the device. Next, the dynamic response is investigated by examining the small scale effect on the natural frequencies of the system.