STRATEGIES FOR THE ACTIVE CONTROL OF FLEXURAL VIBRATION ON A BEAM

The active control of flexural waves on a slender beam is discussed fo r a secondary source array which comprises either point forces or pair s of moments generated by piezoelectric actuators. A model of the seco ndary source array is first developed and coupled into the beam dynami cs by using the wave approach. The behaviour of the beam when three ac tive control strategies are applied is then investigated. One of these is a wave suppression strategy and the other two are based on conside ration of power: specifically that of maximizing the power absorbed by a secondary force array, and that of minimizing the total power suppl ied to the beam by the primary and secondary forces. The control strat egies are first applied to an infinite beam to gain insight into the p hysics of the beam's behaviour, and then to a finite beam. All three c ontrol strategies are fully examined and compared. Up to two secondary forces are applied in each case and a physical explanation of the bea m's behaviour is given wherever possible. It is shown that the effects of the control strategy of maximizing the power absorbed by the secon dary forces are very different when implemented on infinite and finite beams. What appears to be an encouraging control strategy on an infin ite 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 th e beam. (C) 1995 Academic Press Limited