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Journal of Vibration and Control
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A Maximum Principle for Optimal Boundary Control of Multiply-Connected Vibrating Plates

J.M. Sloss

Department of Mathematics, University of California, Santa Barbara, CA 93106, USA

J.C. Bruch, JR

Department of Mechanical and Environmental Engineering and Department of Mathematics, University of California, Santa Barbara, CA 93106, USA

I.S. Sadek

Department of Mathematical Sciences, University of North Carolina at Wilmington, Wilmington, NC 28403, USA

S. Adali

Department of Mechanical Engineering, University of Natal, Durban 4001, Republic of South Africa

A maximum principle is formulated for the active vibration control of plates of general shape with the control forces acting on the boundary. The applicability of the maximum principle is shown for plates that can have multiply-connected domains. The performance index is specified as a quadratic functional of displacement and velocity with a suitable penalty term involving the control forces. An explicit control law is derived with the help of an adjoint variable satisfying the adjoint differential equation and certain terminal conditions and the proposed maximum principle. The implementation of the theory is presented in two examples, and the effectiveness of the boundary control is investigated by a numerical example.

Key Words: Maximum principle • boundary control • structural control • multiply-connected plates

Journal of Vibration and Control, Vol. 6, No. 6, 875-902 (2000)
DOI: 10.1177/107754630000600604
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