ABSTRACT
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 flexuarl 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.