任意变长度柔性提升系统纵向振动分析与能量变化

Analyses of Longitudinal Vibration and Energetics on Flexible Hoisting Systems with Arbitrarily Varying Length

基于Hamilton原理,建立了任意变长度柔性提升系统纵向振动的运动微分方程和能量方程,通过Galerkin方法将无限维的偏微分方程转化为具有时变系数的有限维的常微分方程,并使用数值方法进行求解.最后,以电梯悬挂提升系统为例对所建模型进行了验算.仿真结果表明,连续系统建模和能量方法能有效地表现柔性提升系统的纵向振动状态,并从纵向振动的角度揭示了某些高速电梯上行过程中的强烈振动这一现象.

The governing equation and energy equation of longitudinal vibration of flexible hoisting system with arbitrarily varying length were developed using the Hamilton＇s principle. The Galerkin＇s method wasused to truncate the infinite-dimensional partial differential equations into a set of finite-dimensional ordina- ry differential equations with time dependent coefficients, which can be solved with numerical methods. The motions of elevator systems were illustrated to evaluate the proposed model. The results of simulation show that the methods of continuous system and energetics can represent the longitudinal vibration of flexible hoisting system. Additionally, the undesired nonstationary longitudinal vibration is revealed when the high-speed elevator traveling upwards.