Applications of the Sherman-Morrison matrix inversion formula are reviewed and demonstrated for several problems in sound and vibration control. The inversion formula enables one to easily separate the effect of a perturbation or subcomponent on the dynamic behavior of the overall system. Applications of this technique that are demonstrated here include: identifying optimal PZT electrical shunt parameter values to minimize sound radiation from a PZT-plate structure, identifying the optimal location and parameter values of a tuned dynamic vibration absorber attached to a multi-degree of freedom, damped system, and identifying and quantifying an isolated non-linearity in an otherwise linear system. Extensions to active control system design are also discussed.

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