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Article Dans Une Revue Mathematical Methods in the Applied Sciences Année : 2000

Shape analysis in membrane vibration

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Résumé

In order to characterize the domain Ω minimizing the normal stress on the boundary of a membrane, we are concerned with the shape derivative of the functional J(Ω) = ∫I∫∂Ω(∂y/∂n)2g dx dt, where I is the time interval, y is the solution to the wave equation and g a weight coefficient. We first recall some results on the transformation of domains and investigate the shape derivative of the state. Then we compute the derivative of J with respect to the domain. Eventually, we give a necessary condition of optimality which relies heavily on the oriented distance function and its properties around the neighbourhood of the boundary.

Dates et versions

hal-00579623 , version 1 (24-03-2011)

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John Cagnol, Jean-Paul Zolésio. Shape analysis in membrane vibration. Mathematical Methods in the Applied Sciences, 2000, 23 (11), pp.985-1010. ⟨10.1002/1099-1476(20000725)23:11<985::AID-MMA147>3.0.CO;2-L⟩. ⟨hal-00579623⟩
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