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<p>We deal with an optimal control problem governed by a hyperbolic variational inequality describing perpendicular vibrations of a simply supported anisotropic elastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. The state problem is not uniquely solved. In order to overcome the problem of a priori estimates of states we restrict the admissible set to solutions obtained through a penalization method. We verify the existence of an optimal thickness function as a limit of the sequence of thicknesses solving the case of the penalized state problem.</p>

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An optimal control problem with respect to variable thicknesses for a vibrating elastic plate in a contact with a rigid obstacle

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  • 发表日期：

    2025年1月25日

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  • Igor Bock

摘要

We deal with an optimal control problem governed by a hyperbolic variational inequality describing perpendicular vibrations of a simply supported anisotropic elastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. The state problem is not uniquely solved. In order to overcome the problem of a priori estimates of states we restrict the admissible set to solutions obtained through a penalization method. We verify the existence of an optimal thickness function as a limit of the sequence of thicknesses solving the case of the penalized state problem.