垂直提升系统中钢丝绳的非线性横向振动研究

以一个简化的、非运行状态的垂直提升系统物理模型为研究对象，建立了提升钢丝绳与悬挂重物的运动方程。通过变量代换，发现钢丝绳的运动方程是一个典型的Mathieu方程。根据Mathieu方程的有关理论，分析了钢丝绳作等幅横向振动、衰减振动、发散振动及其相互转化的原因。通过数字仿真和实验对理论分析结果进行了验证，从而为解决垂直提升系统运行时钢丝绳可能出现的大幅度横向振动问题奠定了基础。

Nonlinear Lateral Vibration of the Hoist Rope in Vertical Hoist System

Aiming at a simplified and static hoist system in the vertical direction, the equations of motion for a rope and hoist object attached at the lower end of the rope were established. By means of the variables substitution, it is found that the equation of motion for the rope is just a Mathieu equation. Based on the theory about Mathieu equation, the reasons that cause the rope to vibrate laterally with constant, decaying and emanative amplitude were analyzed. Some simulation and experiment were performed to verify the theoretical results. Consequently, the foundation to solve the problem of the large-amplitude lateral vibration of the rope in a running vertical hoist system was established.