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

Viscoelastic materials (VEMs) are used to increase passive damping in structures. The damping capabilities of the VEM can be enhanced by attaching a constraining layer to the VEM. If this constraining layer is active, the treatment is called active constrained layer damping (ACLD). In the last few years, ACLD has proven to be superior in vibration control to active or passive damping. The active element allows for more effective vibration suppression than purely passive constrained layer damping. On the other hand, the VEM provides a fail-safe in case of breakdown of the active element that is not present for purely active control. It has been shown that the control effort needed to damp vibration using ACLD can be significantly higher than purely active control. In order to combine the inherent damping of passive control with the effectiveness of the active element, different variations of active, passive and hybrid damping are explored. Some of the variations included in this paper are passive constrained layer damping (PCLD) separate from the active element, but on the same side of beam and PCLD separate from the active element on the opposite side of the beam. The discretized system equations are obtained using the assumed modes method and Lagrange's equation. The damping is modeled using the Golla-Hughes-McTavish (GHM) method. This method adds `dissipation coordinates' to the structure in order to account for the damping present. These additional modes are eliminated using a reduction method, rendering the method more practical. A linear quadratic regulator and output feedback are used to actively control vibration.