On Shape Optimization for an Evolution Coupled System
- University of Erlangen Nuremberg, Department of Mathematics (Germany)
- Institut Elie Cartan, UMR 7502 (Nancy Universite, CNRS, INRIA), Laboratoire de Mathematiques, Universite Henri Poincare Nancy I (France)
A shape optimization problem in three spatial dimensions for an elasto-dynamic piezoelectric body coupled to an acoustic chamber is introduced. Well-posedness of the problem is established and first order necessary optimality conditions are derived in the framework of the boundary variation technique. In particular, the existence of the shape gradient for an integral shape functional is obtained, as well as its regularity, sufficient for applications e.g. in modern loudspeaker technologies. The shape gradients are given by functions supported on the moving boundaries. The paper extends results obtained by the authors in (Math. Methods Appl. Sci. 33(17):2118-2131, 2010) where a similar problem was treated without acoustic coupling.
- OSTI ID:
- 22043838
- Journal Information:
- Applied Mathematics and Optimization, Vol. 64, Issue 3; Other Information: Copyright (c) 2011 Springer Science+Business Media, LLC; Article Copyright (c) 2011 The Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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