Abstract

GONZALEZ DE PAZ, Raúl B.. On the design of membranes with increasing fundamental frequency. Rev. Mat [online]. 2014, vol.21, n.1, pp.56-72. ISSN 1409-2433.

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 fundamental 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.

Keywords : variational methods for eigenvalues; shape optimization; free boundary value problems..

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