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The bifurcation problem for a rod under torsion

The bifurcation problem for a rod under torsion Differential Equations, Vol. 36, No. 5, 2000, pp. 662-668. Translated from Differentsial'nye Uravneniya, Vol. 36, No. 5, 2000, pp. 598-604. Original Russian Text Copyright ~) 2000 by Zeragiya. ORDINARY DIFFERENTIAL EQUATIONS The Bifurcation Problem for a Rod Under Torsion D. P. Zeragiya Muskhelishvili Institute for Computational Mathematics, Georgian Academy of Sciences, Georgia Received May 20, 1998 Consider a rod whose axis coincides with the x-axis (in a fixed reference system Oxyz). The lower end (s = 0) of the rod is clamped, and the upper end (s = l) is cylindrically hinged. The rod is loaded by a torque H. The bending of the rod axis is described by the system of equations au"(s) = [M0u -I- Q~(s -t- u)] z'(s) - [M0~ - Qu(s -t- u)] y'(s), ay"(s) + Hz'(s) - Mo~ + sQy = [Qzy(s) - Q~z(s)] z'(s) + (Mo~ - sQy) u'(s) - Q~u(s)[1 + u'(s)], (1) az"(s)- Hy'(s) + Moy + sQz = [Qyz(s)- Q~y(s)] y'(s) -(Moy + sQ~)u'(s) - Q~u(s)[1 -t- u'(s)] with the boundary conditions = u'(0) = u(0) = y(1) = = z(l) = y'(0) = y'(l) = z'(0) = = 0, (2) where u(s) = x(s) - s, s is the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

The bifurcation problem for a rod under torsion

Differential Equations , Volume 36 (5) – Nov 15, 2007

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Publisher
Springer Journals
Copyright
Copyright © 2000 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1007/BF02754223
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 36, No. 5, 2000, pp. 662-668. Translated from Differentsial'nye Uravneniya, Vol. 36, No. 5, 2000, pp. 598-604. Original Russian Text Copyright ~) 2000 by Zeragiya. ORDINARY DIFFERENTIAL EQUATIONS The Bifurcation Problem for a Rod Under Torsion D. P. Zeragiya Muskhelishvili Institute for Computational Mathematics, Georgian Academy of Sciences, Georgia Received May 20, 1998 Consider a rod whose axis coincides with the x-axis (in a fixed reference system Oxyz). The lower end (s = 0) of the rod is clamped, and the upper end (s = l) is cylindrically hinged. The rod is loaded by a torque H. The bending of the rod axis is described by the system of equations au"(s) = [M0u -I- Q~(s -t- u)] z'(s) - [M0~ - Qu(s -t- u)] y'(s), ay"(s) + Hz'(s) - Mo~ + sQy = [Qzy(s) - Q~z(s)] z'(s) + (Mo~ - sQy) u'(s) - Q~u(s)[1 + u'(s)], (1) az"(s)- Hy'(s) + Moy + sQz = [Qyz(s)- Q~y(s)] y'(s) -(Moy + sQ~)u'(s) - Q~u(s)[1 -t- u'(s)] with the boundary conditions = u'(0) = u(0) = y(1) = = z(l) = y'(0) = y'(l) = z'(0) = = 0, (2) where u(s) = x(s) - s, s is the

Journal

Differential EquationsSpringer Journals

Published: Nov 15, 2007

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