Static and dynamic stability results for a class of three-dimensional, configurations of Kirchhoff elastic rods

PHYSICA D-NONLINEAR PHENOMENA

卷:253

Article

Majumdar, Apala¹  Goriely, Alian² 

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Univ Oxford, Inst Math, OCCAM, Oxford OX1 3LB, England

关键词: Elastic rods;    Static stability;    Dynamic stability;    Euler buckling;    Energy minimizers;    Local drag models;   

DOI  :  10.1016/j.physd.2013.03.003

来源: Elsevier

【 摘 要 】

We analyze the dynamical stability of a naturally straight, inextensible and unshearable elastic rod, under tension and controlled end rotation, within the Kirchhoff model in three dimensions. The cases of clamped boundary conditions and isoperimetric constraints are treated separately. We obtain explicit criteria for the static stability of arbitrary extrema of a general quadratic strain energy. We exploit the equivalence between the total energy and a suitably defined norm to prove that local minimizers of the strain energy, under explicit hypotheses, are stable in the dynamic sense due to Liapounov. We also extend our analysis to damped systems to show that static equilibria are dynamically stable in the Liapounov sense, in the presence of a suitably defined local drag force. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free