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

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 was used to truncate the infinite-dimensional partial differential equations into a set of finite-dimensional ordinary 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.