Robust adaptive vibration control of nonlocal strain gradient nanobeams

Document Type : Invited by Davoud Younesian


1 University of Tehran

2 Department of Mechanical Engineering, Michigan State University, 48824, East Lansing, USA.

3 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran



In this paper, a robust adaptive sliding mode control is designed to suppress the nonlinear vibration of an uncertain Euler–Bernoulli nanobeam with immovable ends. Through Hamilton’s principle, governing nonlinear partial differential equations of motion are obtained based on the nonlocal strain gradient theory. The Galerkin scheme is applied to convert the obtained non-dimensional partial differential equation to a nonlinear ordinary differential equation. Then, the robust sliding mode control is designed to stabilize the nonlinear vibration of uncertain nanobeam. Considering the uncertain dynamics of the micro/nano-systems, there is a paucity of accurate information about the states of the system; therefore, the proposed controller is equipped with an extended Kalman filter. Finally, simulation results are presented under various initial conditions in order to illustrate the effectiveness of the designed control scheme as well as the estimation algorithm. Also, the superiority of the proposed robust adaptive controller over the traditional control techniques is demonstrated.


Main Subjects