Nonlinear Vibration and Tip Tracking of Cantilever Flexoelectric Nanoactuators

Abstract

This paper examines the nonlinear vibration and tracking of cantilever nanoactuators made of isotropic nanodielectric materials with flexoelectric effect. The nonlinear governing equation of Euler–Bernoulli nanoactuators is derived based on non-classical continuum mechanics making use of material length scale parameters. By employing a higher-order curvature relation, the governing nonlinear partial deferential equations of motion are obtained by using the Hamilton’s principle. Incorporating the Galerkin method, the nonlinear partial deferential equation is reducing into a set of nonlinear ordinary differential equations. The obtained reduced-order model is solved by a perturbation method for free vibration response in semi-closed form. By introducing a new set of variables, the state space model of nanobeam is derived. The sliding mode control algorithm is employed to achieve a desired output for tip tracking, and Lyapunov stability theory is used to prove convergence in finite time. The effectiveness of the proposed control algorithm and input voltage is illustrated by numerical simulations. Regarding to the finding of this paper, it can be found that the sliding mode controller has better performance than linear controller, e.g., fuzzy controller.