Concurrent placement of compact active and passive damping patches for vibration reduction is a developing area of research. Analytical and computational models to evaluate alternate patch configurations and structural geometries are not widely available. To overcome this void, this paper presents a simplified discrete-system model for vibrations of a beam-like structure. A disturbance input is included in the model, along with a control input from an active patch. Localized structural damping resulting from a passive patch is modeled with an equivalent loss factor. Results from the simplified model are verified using a more detailed analytical formulation, which is based on the Ritz approximation. Verification studies include the effect of a passive damping patch on modal loss factors and broadband attenuation. Finally, a few case studies are proposed which show the efficacy of the reduced-order model for parametric design studies. These studies include determining the effect of localized damping on the control system parameters that are required for attenuation of localized and global motions. The effect of patch locations on system response is also studied. This work has potential applications in industry since compact damping patches are attractive NVH treatments that add minimal weight and complexity.

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