弹性细杆弯扭度有突变时的Lagrange方程  

LAGRANGE EQUATIONS OF THIN ELASTIC ROD WITH MUTATION OF CURVATURE-TWISTING VECTOR

作　　者：薛纭 王鹏[2] Xue Yun;Wang Peng(School of Mechanical Engineering,Shanghai Institute of Technology,Shanghai 201418,China;School of Civil Engineering and Architecture,University of Jinan,Ji′nan 250022,China)

机构地区：[1]上海应用技术大学机械工程学院,上海201418 [2]济南大学土木建筑学院,济南250022

出　　处：《动力学与控制学报》2019年第5期473-477,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11372195)~~

摘　　要：根据弹性细杆静力学的Kirchhoff动力学比拟方法,将弹性细杆截面的弯扭度和形心应变矢有突变的弹性变形比拟为动力学中的打击运动现象.分别从精确Cosserat弹性细杆和Kirchhoff弹性细杆静力学的Lagrange方程出发,导出了弯扭度和形心应变矢有突变时的Lagrange方程,其形式与打击运动的Lagrange方程形式相同.分析了弯扭度和形心应变矢的突变对挠曲线光滑性的影响.为弹性细杆弯扭度有突变时的平衡分析提供分析力学方法.According to the Kirchhoff kinetic analogy method,the elastic deformation of a thin elastic rod with mutation of either curvature twisting vector or strain vector at section center was analogized as the striking motion.Based on the Cosserat and Kirchhoff thin elastic rod model,respectively,the Lagrange equations of the elastic rod with mutation of curvature twisting vector or section center strain vector were derived.It was found that the derived equations have the same forms as the Lagrange equation of striking motion.Finally,the effects of the mu tation of curvature twisting vector or strain vector at section center on the smoothness of the deflection curve were analyzed.This study provides an analytical mechanics method for the equilibrium analysis of the elastic rod with mutation of curvature twisting vector or strain vector at section center.

关 键 词：弹性细杆 分析力学 弯扭度突变 动力学比拟 打击运动 

分 类 号：O17[理学—数学]