Structural control of thermoelastic beams for vibration suppression

The vibrations of a thermoelastic beam subject to a sudden heat input are damped by active control. The control objective is specified as the minimization of a quadratic functional in terms of displacement and velocity at a given time. The control is exercised by means of point actuators which are placed so as to minimize the maximum actuator force. The solution of the control problem is obtained by means of eigenfunction expansions. The physical problem corresponds to the suppression of vibrations of a structure suddenly entering into the daylight zone. Numerical results indicate that the displacement and velocity of the beam can be effectively reduced by means of active control exercised by point actuators.