[ Stabilité d'un tube déformable par la méthode des perturbations ]
Volume 10, Issue 2, February 2015, Pages 480–488
Edouard Diouf1
1 Laboratoire de Mathématiques et Applications, Université de Ziguinchor, BP 523 Ziguinchor, Sénégal
Original language: French
Copyright © 2015 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider a nonlinear hyperelastic tube subjected to a deformation radial. We study then the phenomena of asymptotic stability of the tube. We use techniques for obtaining approximations to periodic time solutions of nonlinear second-order differential equations subject to a harmonic forcing term, and to limit cycles of autonomous equations. These approximations take the form of an expansion in integer powers of a small parameter, having coefficients that are functions of time.
Author Keywords: Hyperelastic, Compressibility, Nonlinear differential equations, Perturbation methods, stability.
Volume 10, Issue 2, February 2015, Pages 480–488
Edouard Diouf1
1 Laboratoire de Mathématiques et Applications, Université de Ziguinchor, BP 523 Ziguinchor, Sénégal
Original language: French
Copyright © 2015 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider a nonlinear hyperelastic tube subjected to a deformation radial. We study then the phenomena of asymptotic stability of the tube. We use techniques for obtaining approximations to periodic time solutions of nonlinear second-order differential equations subject to a harmonic forcing term, and to limit cycles of autonomous equations. These approximations take the form of an expansion in integer powers of a small parameter, having coefficients that are functions of time.
Author Keywords: Hyperelastic, Compressibility, Nonlinear differential equations, Perturbation methods, stability.
Abstract: (french)
Dans cette étude, le comportement d'un tube creux hyperélastique, compressible et soumis à des déformations radiales est analysé. Le but est l'étude du problème de la stabilité asymptotique du comportement d'un tube régie par d'une équation différentielle non linéaire. Cette approche est réalisée par la méthode de la linéarisation obtenue par dérivation au sens Gâteaux. Des possibilités d'instabilité ont été mises en évidence. Ces différents comportements dépendent uniquement de la loi constitutive du matériau aux travers des coefficients qui dépendent eux-mêmes des dérivées du potentiel par rapport aux invariants.
Author Keywords: Hyperélasticité, Compressibilité, Equations différentielles non linéaires, Méthodes des perturbations, Stabilité.
How to Cite this Article
Edouard Diouf, “Stability of a deformable tube by the perturbation method,” International Journal of Innovation and Applied Studies, vol. 10, no. 2, pp. 480–488, February 2015.
