On Shape Optimization for an Evolution Coupled System

  • G. Leugering
  • A. A. Novotny
  • G. Perla Menzala
  • J. Sokołowski
Open Access
Article

Abstract

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.

Keywords

Piezoelectricity Electromechanical interaction Shape sensitivity analysis 

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  • G. Leugering
    • 1
  • A. A. Novotny
    • 2
  • G. Perla Menzala
    • 2
  • J. Sokołowski
    • 3
    • 4
  1. 1.Department of MathematicsUniversity of Erlangen NurembergErlangenGermany
  2. 2.Laboratório Nacional de Computação Científica LNCC/MCTCoordenação de Matemática Aplicada e ComputacionalPetrópolisBrasil
  3. 3.Institut Elie Cartan, UMR 7502 (Nancy Université, CNRS, INRIA), Laboratoire de Mathématiques, Université Henri Poincaré Nancy IVandoeuvre-lès-Nancy CedexFrance
  4. 4.Systems Research Institute of the Polish Academy of SciencesWarszawaPoland

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