Adaptive Control of Flexural Waves Propagating in a Beam

Abstract

Broadband active control of flexural (bending) waves propagating along a beam is investigated theoretically and experimentally. In particular, a simple practical arrangement is studied in which the output of a single detection sensor (an accelerometer) is used to drive a single secondary force via a feedforward controller. The feedforward controller is implemented as an adaptive digital filter, the coefficients of which are adjusted to minimize the mean square output from a single downstream error sensor (another accelerometer). Fundamental limits on the performance of such an active control system are found at low and high frequencies. The low frequency limit is caused by the near field of the secondary source corrupting the output of the error sensor. The increasing group velocity of bending waves in the beam with frequency imposes a high frequency limit on the performance, because of the electrical delay in the controller. The bandwidth of useful operation imposed by these low and high frequency limits is found to increase as the thickness of the beam is reduced. Experimental results on a 6 mm steel beam confirm the predicted high frequency limit, although in practice the low frequency limit of control was found to be determined by a lack of coherence between the detection and error sensor due to background noise. Attenuations in the bending wave amplitude of between 10 and 30 dB were measured in the experiments over a frequency range from 100 to 600 Hz.