A maximum principle is derived for the determination of the optimal boundary control of the lon gitudinal vibration of a variable cross-section rod in which the index of performance is a quadratic function. The control is expressed explicitly in terms of an adjoint variable and can be applied by displacement or force control, or a combination of both. The adjoint variable and the state variable are related through termi nal conditions. The results are applied to a specific problem, and numerical results are given that reveal the effectiveness of the proposed control mechanism. The numerical results are obtained using MAPLE V.
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