# The coupled nonlinear dynamics of a lift system

Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This paper presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.
Authors:
; ; ;  [1]
1. The University of Northampton, School of Science and Technology, Avenue Campus, St George's Avenue, Northampton (United Kingdom)
Publication Date:
OSTI Identifier:
22390784
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1637; Journal Issue: 1; Conference: ICNPAA 2014: 10. International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, Narvik (Norway), 15-18 Jul 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; BUILDINGS; ELEVATORS; EQUATIONS OF MOTION; INSTALLATION; MATHEMATICAL MODELS; MECHANICAL SHAFTS; MOMENT OF INERTIA; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; PARTIAL DIFFERENTIAL EQUATIONS; RESONANCE; SUSPENSIONS