Hybrid damping models using the Golla-Hughes-McTavish method withinternally balanced model reduction and output feedback

Abstract

Viscoelastic materials (VEMs) are used to increase passive dampingin structures. The damping capabilities of the VEM can be enhanced byattaching a constraining layer to the VEM. If this constraining layer isactive, the treatment is called active constrained layer damping (ACLD). Inthe last few years, ACLD has proven to be superior in vibration control toactive or passive damping. The active element allows for more effectivevibration suppression than purely passive constrained layer damping. On theother hand, the VEM provides a fail-safe in case of breakdown of the activeelement that is not present for purely active control. It has been shown thatthe control effort needed to damp vibration using ACLD can be significantlyhigher than purely active control. In order to combine the inherent damping ofpassive control with the effectiveness of the active element, differentvariations of active, passive and hybrid damping are explored. Some of thevariations included in this paper are passive constrained layer damping (PCLD)separate from the active element, but on the same side of beam and PCLDseparate from the active element on the opposite side of the beam. Thediscretized system equations are obtained using the assumed modes method andLagrange's equation. The damping is modeled using the Golla-Hughes-McTavish(GHM) method. This method adds `dissipation coordinates' to the structure inorder to account for the damping present. These additional modes areeliminated using a reduction method, rendering the method more practical. Alinear quadratic regulator and output feedback are used to actively controlvibration.