On the design of membranes with increasing fundamental frequency

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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Bibliographic Details
Main Author: Raúl B. González De Paz
Format: Article
Language:Spanish
Published: Universidad de Costa Rica 2014-04-01
Series:Revista de Matemática: Teoría y Aplicaciones
Subjects:
variational methods for eigenvalues
shape optimization
free boundary value problems
Online Access:https://revistas.ucr.ac.cr/index.php/matematica/article/view/14138
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spelling doaj-9bd0d1d57860486b871e82c3aab62c4a2020-11-25T01:13:32ZspaUniversidad de Costa RicaRevista de Matemática: Teoría y Aplicaciones2215-33732014-04-01211557210.15517/rmta.v21i1.1413813214On the design of membranes with increasing fundamental frequencyRaúl B. González De Paz0Universidad del Valle de Guatemala, Departamento de MatemáticasBy 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.https://revistas.ucr.ac.cr/index.php/matematica/article/view/14138variational methods for eigenvaluesshape optimizationfree boundary value problems
collection DOAJ
language Spanish
format Article
sources DOAJ
author Raúl B. González De Paz
spellingShingle Raúl B. González De Paz
On the design of membranes with increasing fundamental frequency
Revista de Matemática: Teoría y Aplicaciones
variational methods for eigenvalues
shape optimization
free boundary value problems
author_facet Raúl B. González De Paz
author_sort Raúl B. González De Paz
title On the design of membranes with increasing fundamental frequency
title_short On the design of membranes with increasing fundamental frequency
title_full On the design of membranes with increasing fundamental frequency
title_fullStr On the design of membranes with increasing fundamental frequency
title_full_unstemmed On the design of membranes with increasing fundamental frequency
title_sort on the design of membranes with increasing fundamental frequency
publisher Universidad de Costa Rica
series Revista de Matemática: Teoría y Aplicaciones
issn 2215-3373
publishDate 2014-04-01
description 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.
topic variational methods for eigenvalues
shape optimization
free boundary value problems
url https://revistas.ucr.ac.cr/index.php/matematica/article/view/14138
work_keys_str_mv AT raulbgonzalezdepaz onthedesignofmembraneswithincreasingfundamentalfrequency
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