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Model of an electro-rheological shock absorber and coupled problem for partial and ordinary differential equations with variable unknown domain

Published online by Cambridge University Press:  01 August 2007

W. G. LITVINOV ,
T. RAHMAN  and
R. H. W. HOPPE
W. G. LITVINOV
Affiliation:
Institute of Mathematics, University of Augsburg, Universitätsstr. 14, D-86159 Augsburg, Germany email: litvinov@math.uni-augsburg.de
T. RAHMAN
Affiliation:
Department of Mathematics, University of Bergen, Allégaten 41, N-5007 Bergen, Norway email: talal.rahman@math.uib.no
R. H. W. HOPPE
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204, U.S.A., and Institute of Mathematics, University of Augsburg, Universitä tsstr. 14, D-86159 Augsburg, Germany email: rohop@math.uh.edu
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Abstract

Amortization of a shock in an electro-rheological shock absorber is carried out in the motion of a piston in an electrorheological fluid. The drag force acting on the piston is regulated by varying the voltage applied to electrodes. A model of an electrorheological shock absorber is constructed. A problem on shock absorber reduces to the solution of a coupled problem for motion equation of the piston and non-linear equations of fluid flow in an unknown domain that varies with the time. A method of semi-discretization for approximate solution of the coupled problem is considered. Results on the existence and on the uniqueness of the solution of the coupled problem are obtained. Convergence of approximate solutions to the exact solution is proved. Numerical simulation of the operation of the shock absorber is performed.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 4 , August 2007 , pp. 513 - 536
Copyright
Copyright © Cambridge University Press 2007

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