Hybrid Active/Passive Models with Frequency Dependent Damping

Abstract

To add damping to structures, viscoelastic materials (VEM) are added to structures. In order to enhance the damping effect of the VEM, a constraining layer is attached, creating a passive constrained layer damping treatment (PCLD). When this constraining layer is an active element, the treatment is called active constrained layer damping (ACLD). Recently, the investigation of ACLD treatments has shown it to be an effective method of vibration suppression. In this work, two new hybrid configurations are introduced by separating the passive and active elements. In the first variation, the active and passive element are constrained to the same side of the beam. The other variation allows one of the treatments to be placed on the opposite side of the beam. A comparison will be made with pure active, PCLD, ACLD and a variation which places the active element underneath PCLD. Energy methods and Lagrange's equation are used to obtain equations of motion, which are discretized using assumed modes method. The frequency dependent damping is modeled using the Golla-Hughes-McTavish (GHM) method and the system is analyzed in the time domain. GHM increases the size of the original system by adding fictitious dissipation coordinates that account for the frequency dependent damping. An internally balanced model reduction method is used to reduce the equations of motion to their original size. A linear quadratic regulator and output feedback are used to actively control vibration. The length and placement of treatment is optimized using different criteria. It is shown that placing the active element on the opposite side of the passive element is capable of vibration suppression with lower control effort and more inherent damping. If the opposite surface is not available for treatment, a suitable alternative places the PZT underneath the PCLD. LQR provides the best control, since it assumes all states are available for feedback. Usually only select states are available and output feedback is used. It is shown that output feedback, while not as effective as full state feedback, is still able to damp vibration.