STRATEGIES FOR THE ACTIVE CONTROL OF FLEXURAL VIBRATION ON A BEAM

The active control of flexural waves on a slender beam is discussed for a secondary source array which comprises either point forces or pairs of moments generated by piezoelectric actuators. A model of the secondary source array is first developed and coupled into the beam dynamics by using the wave approach. The behaviour of the beam when three active control strategies are applied is then investigated. One of these is a wave suppression strategy and the other two are based on consideration of power: specifically that of maximizing the power absorbed by a secondary force array, and that of minimizing the total power supplied to the beam by the primary and secondary forces. The control strategies are first applied to an infinite beam to gain insight into the physics of the beam's behaviour, and then to a finite beam. All three control strategies are fully examined and compared. Up to two secondary forces are applied in each case and a physical explanation of the beam's behaviour is given wherever possible. It is shown that the effects of the control strategy of maximizing the power absorbed by the secondary forces are very different when implemented on infinite and finite beams. What appears to be an encouraging control strategy on an infinite beam has a detrimental affect on the overall response of a finite beam. The best overall control strategy for global control on a finite beam is shown to be that of minimizing the total power supplied to the beam. (C) 1995 Academic Press Limited