Active control of resiliently-mounted beams with a moment pair actuator

Abstract

Various strategies are considered for the active control of a flexible beam, mounted onsprings at either end. As the spring stiffness is decreased from an infinite value to zero,the boundary conditions of the beam change from being simply supported tobeing free–free, and a rich variety of behaviour is observed. Feedforward control ofeither the beam’s kinetic energy or radiated sound power using a moment pairactuator is considered first. It is found that for small spring stiffness minimization ofradiated sound power leads to significant increases in overall beam vibration.The stability and performance of feedback controllers is then considered. It is found thatusing a moment pair actuator and a velocity sensor the feedback controller is onlyconditionally stable, particularly when the actuator and the sensor are close to the ends ofthe beam and the supporting stiffness is small. The reductions in sound and vibration aresmall under these conditions.