Active piezoelectric vibration control for a Timoshenko beam

Optimal piezoelectric vibration control problem for a Timoshenko beam is considered. The performance index function to be minimized by using the minimum level of the control voltage consists of a weighted quadratic function of displacement and velocity of the beam and also includes a quadratic functional of the control voltage function as a penalty term. The optimal control function is derived by means of a maximum principle which transforms the control problem to an initial-boundary-terminal value problem. In order to show the effectiveness of the control actuation, numerical results are given by MATLAB in table and graphical forms.