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The application of a spatially shaped distributed actuator for the vibration control of a simply supported beam is studied both analytically and experimentally. The actuator consists of a layer of polyvinylidene fluoride (PVF 2 ) bonded to one face of the beam. A summary of the underlying theory is presented, with emphasis on how controllability requirements affect the choice of the film's spatial distribution. The requisite film controller has a linearly varying spatial distribution that facilitates the control of both even- and odd-order vibrational modes. Experimental results are presented for the control of the beam's first three modes, using both the linearly varying as well as a uniform spatial distribution. The linearly varying distribution is shown to be effective in controlling both even- and odd-order modes, serving to increase the modal loss factors by up to a factor of 4.5. In addition, the experimental results are found to corroborate a simplified computer model of the controller.
Burke et al. (Sat,) studied this question.