On the design of membranes with increasing fundamental frequency
By means of a relaxation approach, we study the shape design of a stiff inclusion with given area in a membrane in order to maximize its fun- damental frequency. As an eigenvalue control problem, the fundamental frequency is a concave function of the control, which is not described by the membrane s...
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| Format: | Article |
| Language: | Spanish |
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Universidad de Costa Rica
2014-04-01
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| Series: | Revista de Matemática: Teoría y Aplicaciones |
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| Online Access: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/14138 |
| Summary: | By means of a relaxation approach, we study the shape design of a stiff inclusion with given area in a membrane in order to maximize its fun- damental frequency. As an eigenvalue control problem, the fundamental frequency is a concave function of the control, which is not described by the membrane shape, but by an element in a function space. First order optimality conditions allow to describe the optimal shape by means of a free boundary value problem. |
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| ISSN: | 2215-3373 |