Dynamic model of balance rope under multiple constraints with friction is established via using non-equal-length element division method (NEL-EDM) based on absolute nodal coordinate formulation. Then, the natural frequency of balance rope under multiple constraints is derived by the proposed method. The KDP generalized-alpha scheme is expanded to differential algebraic equations (DAEs) with friction constraint equations and used to solve the DAEs proposed by this paper. Compared with the frequencies, lateral vibration displacements at four observation points, the analysis of the NEL-EDM is carried out by MATLAB, ANSYS, and RECURDYN software, and the feasibility of NEL-EDM is verified. The frequencies of balance rope with installed bushing constraints will occur frequency veering phenomenon when the balance rope moves up and down with the conveyance. Last, free responses of the balance rope under multiple constraints due to the effects of conveyance vertical motion, and those of in-plane excitation on forced responses of balance rope under multiple constraints with friction are investigated.

基于绝对节点坐标公式，采用非等长单元分割法(NEL-EDM)建立多约束摩擦平衡绳动力学模型。然后，通过提出的方法推导出多约束条件下平衡绳的固有频率。KDP 广义阿尔法方案被扩展到具有摩擦约束方程的微分代数方程 (DAE)，并用于求解本文提出的 DAE。通过MATLAB、ANSYS和RECURDYN软件对NEL-EDM的四个观测点的频率、横向振动位移进行对比分析，验证了NEL-EDM的可行性。装有衬套约束的平衡绳在随输送物上下运动时会发生频率转向现象。最后，研究了平衡绳在多约束下由于输送垂直运动的影响而产生的自由响应，以及面内激励对多约束下平衡绳受摩擦力响应的影响。