A Constructive Method for the Distributed Control of Thin Plates

Abstract This paper considers the problem of damping out the oscillations of a rectangular plate subject to various types of boundary conditions by means of distributed applied forces. The motion of the plate is initiated by given initial displacement and velocity conditions. The basic control problem is to minimize the total energy of the plate in a given period of time with the control function subject to an integral constraint. Necessary and sufficient conditions of optimality are expressed in the form of integral equations which lead to constructive expressions for the control force.

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