Coupled vibrations of a varying length flexible cable transporter system with arbitrary axial velocity

Modeling for coupled vibrations of a varying length flexible cable transporter system with arbitrary axial velocity is presented using the extended Hamilton´s principle. Both transverse and longitudinal vibrations are considered simultaneously in the derivation. The inertia and damping of the pulleys and actuators are included in the model. The derived governing equations provide guidelines for future research on cable systems. Numerical solution of the derived nonlinear coupled partial differential equations (PDEs) is obtained using Galerkin´s method. Simulation results show that increase in damping of the system can reduce the longitudinal vibration dramatically, but has little effect on the transverse vibration.