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A model for passive damping of a membrane

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We introduce a model in which a wire made of shape memory alloy is used to passively damp the vibrations of a membrane. The mechanical energy of the membrane is transformed into heat via the thermo-elastic properties of the shape memory alloy. We describe the model and prove existence and uniqueness of solutions. Finally we will show that for suitable initial and boundary conditions, the energy of the entire system is a decreasing function.
Rocznik
Strony
325--337
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
  • Department of Mathematics California State University Northridge Northridge, CA 91330-8313, USA
  • Institut Elie Cartan, Laboratoire de Mathematiques Universite Henri Poincare, Nancy I, B. P. 239 54506 Vandoeuvre les Nancy Cedex, France
Bibliografia
  • Brokate, M. and Sprekels, J. (1996) Hysteresis and Phase Transitions. Springer Verlag, Berlin.
  • Bubner, N. (1995) Modellierung dehnungsgesteuerter Phasenubergange in Formgedachtnislegierungen Dissertation, Essen.
  • Bubner, N., Horn, W. and Sokołowski, J. (2001) Weak solutions to joined non-linear systems of PDEs. J. Appl. Math. Phys. (ZAMP), 52 (5), 713-729.
  • Bubner, N. and Sprekels, J. (1998) Optimal control of martensitic phase transitions in a deformation driven experiment on shape memory alloys. Adv. Math. Sci. Appl. 8 (1), 299–325.
  • Grisvard, P. (1989) Controlabilite exacte des solutions de l’equation des ondes en presence de singularites. J. Math. Pures et Appl. 68, 215–259.
  • Horn, W. and Sokołowski, J. (2000) Models for Adaptive Structures using Shape Memory Actuators. Procedings of MTNS 2000, Perpignan (electronic).
  • Horn, W. and Sokołowski, J. (2002) An elastic membrane with an attached nonlinear thermoelastic rod. Applied Mathematics and Computer Science 12 (4), 479-487.
  • Kokotov, A.Yu. and Plamenevsky, B.A. (2000) On the Cauchy-Dirichlet Problem for Hyperbolic Systems in a wedge. St. Petersburg Math. J. 11 (3), 497–534.
  • Kozlov, V.A., Mazya, V.G. and Rossmann, J. (1997) Elliptic Boundary Value Problems in Domains with Point Singularities. American Mathematical Society, Providence, R. I.
  • Kozlov, V.A. and Mazya, V.G. (1999) Comparison Principles for Nonlinear Operator Differential Equations in Banach Spaces. Amer. Math. Soc. Transl. 189, 149–157.
  • Muller, I. and Seelecke, S. (1998) Adaptive air foil with shape memory allays. 1st Meeting of the TMR Research Project “Phase Tarnsitions in Crystalline Solids” FMRX-CT98-0229. http://www.dmsa.unipd.it/tmr/meetingRoma98/node18.html.
  • Nazarov, S.A. and Plamenevsky, B.A. (1994) Elliptic Problems in Domains with Piecewise Smooth Boundaries. Walter de Gruyter, Berlin.
  • Sprekels, J. and Zheng, S. (1989) Global Solutions to the Equations of a Ginzburg–Landau Theory for structural Phase Transitions in Shape Memory Alloys. Physica D 39, 59–76
  • Zheng, S. (1995) Nonlinear Parabolic Equations and coupled Hyperbolic-Parabolic Systems. Longman House, Burnt Mill, UK.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0007-0092
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