On the longitudinal vibration of a moving elevator cable-car system

In this work, a new mathematical model for the longitudinal vibration of a moving elevator cable-car system with an arbitrary movement profile is developed. The car is modeled as a mass-spring-damper subsystem attached to the lower end of the cable. Both the Newtonian method and Hamilton's principle are used to derive the governing equations of the moving cable-car system.;The assumed modes method and a new spatial discretization method are used to discretize either the governing partial differential equation of the moving cable or the Lagrangian of the system before the application of Lagrange's equations. The rate of change of the total mechnaical energy is analyzed from the system viewpoint and the control volume viewpoint. Numerical simulation of the responses from three spatial discretization schemes are obtained and compared. The new spatial discretization method can achieve uniform convergence and overcome the drawbacks of the classical assumed modes method.