Active control of flexural vibrations

Abstract

The active control of disturbances propagating along a waveguide is considered with particular reference to the control of flexural vibrations in thin beams. The control system consists of a number of point sensors and point exciters distributed in some manner along the waveguide. The sensor measurements are used as inputs to a controller which forms the required excitations such that incoming disturbances are completely cancelled. A method by which this ideal controller can be synthesized is presented. The stability of the system is considered. In general the system reflects the downstream cancelled disturbances while upstream disturbances are both reflected and transmitted. Active control of flexural waves in beams is then considered and two possible active control systems are examined. The first consists of measurements of displacement and rotation at a point and the application of a point force and point moment while the second comprises displacement measurements at two points and the application of two point forces. In both cases the ideal active controller is derived and some aspects of the systems' performances examined.