Dynamic analysis of hoisting viscous damping string with time-varying length

The nonlinear dynamic analysis of a hoisting viscous damping string with time-varying length is investigated. The hoisting string is modeled as a taut translating string with a rigid body attached at its low end. A systematic procedure for deriving the system model of hoisting viscoelastic string with time-varying is presented. The governing equations are developed employing the extended Hamilton's principle considering coupling of axial movement and flexural deformation of string. The Galerkin's method and the 4th Runge-Kutta method are employed to numerically analyze the resulting equations. The motions of elevator hoisting system are presented to illustrate the proposed mathematical models. The results of simulation show that the material viscous damping helps stabilize the transverse vibration. The modeling methods can represent the transverse vibration of hoisting viscous damping string with time-varying length.