Vibration boundary control of micro-cantilever Timoshenko beam using piezoelectric actuators

One of the methods of force/moment exertion on micro beams is utilizing piezoelectric actuators. In this paper, considering the eects of the piezoelectric actuator on asymptotic stability achievement, the boundary control problem for the vibration of a clamped-free micro-cantilever Timoshenko beam is addressed. To achieve this purpose, the dynamic equations of the beam actuated by a piezoelectric layer laminated on one side of the beam are extracted. The control law was implemented so that vibrations of the beam could be decayed. This control law was achieved based on feedback of time derivatives of boundary states of the beam. The obtained control was applied in the form of piezoelectric voltage. To illustrate the impact of the proposed controller on the micro beam, the niteelement method and Timoshenko beam element were used, and then simulation operation was performed. The simulation shows that not only does this control voltage reduce the vibration of the beam, but also the mathematical proofs proposed in this article are precise and implementable.