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力学与实践 ›› 2010, Vol. 32 ›› Issue (2): 103-107.doi: 10.6052/1000-0879-2009-197

• 应用研究 • 上一篇    下一篇

横向磁场中细长压杆的分岔特性

王平 白象忠 刘立静 王知人   

  1. 燕山大学建筑工程与力学学院
  • 收稿日期:2009-05-05 修回日期:2009-07-22 出版日期:2010-04-08 发布日期:2010-04-08

BIFURCATION OF AN EULER'S POLE IN A TRANSVERSE MAGNETIC FIELD

wang ping   

  • Received:2009-05-05 Revised:2009-07-22 Online:2010-04-08 Published:2010-04-08

摘要: 在磁弹性非线性运动方程、物理方程、电动力学方程及洛仑兹力表达式的基础上,应 用Lagrange描述法建立了横向磁场中两端铰支受压细长杆的非线性磁弹性动力学模型. 通过 对该模型的简化,分别讨论了静力学模型、线性动力学模型和含三次非线性项的动力学模型 的分岔特性. 最后通过数值计算,给出了横向磁场中受压细长杆的失稳临界载荷与相关参量 之间的关系曲线,并对计算结果及其变化规律进行了分析讨论.

关键词: 磁弹性, 洛仑兹力, 欧拉杆, 分岔, 失稳, 临界载荷

Abstract: Based on the nonlinear magnetic-elasticity kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz force, a nonlinear dynamic model of Euler pole is established by using the Lagrangian description method. After the simplifications of the nonlinear dynamic model, the bifurcations of a nonlinear static model, a linear dynamic model and a simplified nonlinear dynamic model with a cubic nonlinear item are analyzed, respectively. As an example, the curves of the critical buckling load vs. related the relative parameters are obtained when a pole is applied with compressive force in a magnetic field. The calculated results are discussed.

Key words: Magnetic-elasticity, Lorentz force, Euler pole, bifurcation, buckling, Critical load