# The coupled nonlinear dynamics of a lift system

Rafael Sánchez Crespo, Stefan Kaczmarczyk, Philip Picton, Huijuan Su

Research output: Contribution to Book/ReportConference Contributionpeer-review

## Abstract

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.
Original language English 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2014 Melville, NY AIP Publishing LLC 245-252 9 9780735412767 https://doi.org/10.1063/1.4904585 E-pub ahead of print - 17 Feb 2015 ICNPAA 2014 World Congress: 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences - Narvik University, Narvik, NorwayDuration: 15 Jul 2014 → 18 Jul 2014http://icnpaa.com/index.php/icnpaa/2014

### Conference

Conference ICNPAA 2014 World Congress: 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences Norway Narvik 15/07/14 → 18/07/14 http://icnpaa.com/index.php/icnpaa/2014

## Keywords

• Coupled nonlinear dynamics
• Lift system

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