Premium
Shape analysis in membrane vibration
Author(s) -
Cagnol John,
Zolésio JeanPaul
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/1099-1476(20000725)23:11<985::aid-mma147>3.0.co;2-l
Subject(s) - mathematics , omega , domain (mathematical analysis) , mathematical analysis , boundary (topology) , neighbourhood (mathematics) , boundary value problem , derivative (finance) , interval (graph theory) , function (biology) , combinatorics , physics , quantum mechanics , evolutionary biology , financial economics , economics , biology
Abstract 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 \def\d{\,{\rm d}}$J(\Omega)=\int_I\int_{\partial\Omega}(\partial y/\partial n)^2\,g\d x\d t$ , 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. Copyright © 2000 John Wiley & Sons, Ltd.