受力螺旋作用的非圆截面弹性直杆的Lyapunov稳定性  

LYAPUNOV STABILITY OF A STRAIGHT ELASTIC ROD WITH NON CIRCULAR CROSS SECTION UNDER FORCE SCREW

作　　者：薛纭[1] 陈立群[2] 

机构地区：[1]上海应用技术学院机械与自动化工程学院,上海200235 [2]上海大学力学系,上海200444

出　　处：《动力学与控制学报》2008年第3期198-201,共4页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(10472067)~~

摘　　要：基于Kirchhoff动力学比拟思想,研究非圆截面压扭弹性细直杆的Lyapunov稳定问题.用Cardano角表示截面的姿态,根据Kirchhoff方程建立杆的平衡微分方程,得到了两端受力螺旋作用时的直线平衡特解,导出了具有周期系数的线性化扰动方程,其周期与扭矩和杆长成正比,与抗扭刚度成反比,圆截面情形为其特例.用Floquet理论讨论了其Lyapunov稳定性,算例表明对于给定的弹性杆,扭矩和压力对稳定是有利的,而拉力是不稳定的主要因素.Lyapunov stability of an elastic rod with non circular cross section in straight equilibrium was studied based on the thought of Kirehhoff kinetic analogy in the paper. Expressing the attitude of a section of the rod by Cardano angles,the equilibrium differential equation was established in terms of Kirehhoff theory of the rod, and its special solution when two ends of the rod were acted by a pair of force screws was found which stands for straight equilibrium state. The linear perturbation equation with periodic coefficient was obtained, where the period is directly proportional to the torque of the end and the length of the rod, and inversely as the torsion rigidity of the rod. The circular cross section of the rod was its special case. Lyapunov stability of equilibrium in the straight state was discussed according to the Floquet theory. It is explained that the torque and compressive force were advantageous to the stability and the tensile force wasnt by numerical examples.

关 键 词：压扭变形 弹性细杆 KIRCHHOFF方程 直杆 LYAPUNOV稳定性 FLOQUET理论 

分 类 号：O343.9[理学—固体力学]