中文摘要：

以一类工程对象为背景,研究圆柱面约束下的弹性杆的摩擦平衡问题.在对圆柱面上圆截面弹性杆位形和运动分析的基础上,导出了计入分布摩擦力的弹性杆平衡微分方程并无量纲化.由此得到了无摩擦时螺旋杆解的存在条件,以及存在摩擦时的不滑动的条件.分析表明,截面章动角对弧坐标的一阶导数和自转角对弧坐标的二阶导数表达的变形是分布摩擦力所致.就5类特殊的平衡位形,分别计算了内力和分布摩擦力集度,部分进行了数值计算,给予了静止与否的判定.为曲面上弹性杆的摩擦平衡或动力学分析提供方法和思路.

英文摘要：

Under background of a class of engineering object, the problem of equilibrium with friction of an elastic rod constrained by a cylindrical surface was investigated in this paper. On the basis of the analysis of the configuration and the motion of the circular-cross-section elastic rod constrained by the cylindrical surface, differential equations of the equilibrium with the distributed friction were derived and transformed into dimensionless form. Conditions for the existence of solutions of the screw rod without the friction were obtained, as well as conditions for no relative sliding between the elastic rod and the cylinder surface with the friction. It was found that the deformation expressed by the first derivative of nutation angle and the second derivative of since angle with respect to the arc coordinate was induced by the distributed friction. For five types of special configuration of elastic rod in equilibrium, principal vector of internal forces on cross sections of the rod and distributions of friction force were predicted analytically. Then some types were discussed numerically to determine whether the rod would be balanced. This paper provides possible methods and ideas for further studying the statics and the dynamics of elastic rods constrained by surfaces with friction.