Active Control of Waves on a one Dimensional Structure With a Scattering Termination

The active control of longitudinal and flexural waves propagating on a finite beam with a scattering termination has been investigated theoretically and experimentally. The system consisted of a finite beam excited by a primary source at one end, with a control actuator placed in the middle of the beam and an asymmetric block mass at the other end, which scatters incident flexural or longitudinal waves into both flexural and longitudinal components. The scattering matrix for such a termination has been derived. The scattering between longitudinal and flexural waves is particularly strong in a frequency range which is determined by the dimensions and material of the asymmetric mass. A test is introduced to ensure that the scattering matrix is conservative. A theoretical formulation of active control is developed, which is based on a matrix approach for wave propagation. The control strategies of minimizing displacements, energy or power are analysed with reference to the coupling property of the scattering termination. Control simulations for different configurations of the primary and secondary source and error sensors are shown. When the two type of waves are controlled simultaneously it is possible to control the beam at all points beyond the control actuator. If only one of two waves is controlled, however, then the control is generally effective only at the error sensor position. The results of some experiments which support the conclusions drawn from the simulations are then presented.