关键词: 单摆, 数学模型, 微分方程, 差分法

Abstract: In order to accurately simulate movements of suspended cable during the operations of aerial winchs, one type of hydraulic winch was used as a case study herein. A hanging swing mathematical model was set up based on pendulum theory. According to the vibration characteristics of flexible cables, nonlinear differential equation of vibrations of the cable was deduced and solved by explicit difference method. Through simulations, the swing angle variations of lifting loads under different excitation frequencies and the influences of hanging head displacements on the cables were analyzed, accuracy of the algorithm was proved herein. Conclusions drawn from this paper may provide theoretical basis for practical engineering designs and may be used for the air winch lifting system cable vibrations forecasting and reduction.

Key words: simple pendulum, mathematical model, differential equation, differential quadrature method