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Optimal distribution of an active layer for transient vibration control of a flexible plate

A new optimization framework for distribution of an active damping layer is formulated for transient vibration suppression of a flexible structure, proposing an objective function and design variables appropriate for the problem. The process yields the optimal distribution of an active damping layer which consumes minimum control energy for the specified system performance. A cantilever plate treated with a piezoelectric layer is used for numerical examples taking a linear quadratic regulator of single input as a controller. The numerical results show that there is a critical coverage ratio over which additional treatment of the active layer is not profitable. It is shown that the optimal distribution depends on the desired system performance level because each vibration mode has a different optimal distribution, and has a different contribution to the total suppression for different performance levels. The presented design variables produce a topologically optimized distribution which can give information about the optimal number, size and location of active layer patches at the same time.