On the design of membranes with increasing fundamental frequency

• González De Paz, Raúl B. ^[1]
  1. [1] Universidad del Valle de Guatemala

     Universidad del Valle de Guatemala

     Guatemala

     
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 21, Nº. 1, 2014, págs. 55-72
• Idioma: inglés
• DOI: 10.15517/rmta.v21i1.14138
• Títulos paralelos:
  • Sobre el diseño de membranas con frecuencia fundamental creciente
• Enlaces
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• Resumen
  • español

     Mediante un método de relajación, se estudia la forma de una inclusión rígida de área dada en una membrana de manera que se maximice su fre- cuencia fundamental. Analizado como un problema de control de valores propios, la frecuencia fundamental es una función cóncava del control, el cual no es descrito por la forma de la membrana, sino por un elemento de un espacio de funciones. Las condiciones de optimalidad de primer or- den permiten describir la forma óptima mediante un problema de frontera libre.   

  • English

      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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