ACTIVE QUENCHING OF A SET OF PREDETERMINED VIBRATORY MODES OF A BEAM BY A SINGLE FIXED-POINT ACTUATOR

Active control of the vibratory motion of a beam by a single fixed actuator is considered. The vibratory motion is assumed to be initiated by a disturbance. An open loop strategy is constructed to eliminate the resulting motion in a finite time. The control force is determined by a linear combination offunctions, each corresponding to the natural frequencies of initially active modes. Because this strategy requires that the control force be switched off at a prespecified final time it is an open loop control. A general statement of the problem identifies appropriate conditions for constructing such a control force. A complete solution with supporting simulation results is also given for a uniform, simply supported beam controlled by a single fixed point actuator. © 1990 Taylor and Francis Group, LLC.