On resonances and transverse and longitudinal oscillations in a hoisting system due to boundary excitations

On resonances and transverse and longitudinal oscillations in a hoisting system due to boundary excitations

Wang, J. (TU Delft Mathematical Physics; Tianjin Normal University, Tianjin)
van Horssen, W.T. (TU Delft Mathematical Physics)

2022

In this paper, we study transverse and longitudinal oscillations and resonances in a hoisting system induced by boundary disturbances. The dynamics can be described by an initial-boundary value problem for a coupled system of nonlinear wave equations on a slowly time-varying spatial domain. It will be shown how the boundary excitations and the nonlinear terms influence transverse and longitudinal vibrations of the system. Firstly, due to the slow variation of the cable length, a singular perturbation problem arises. By using an interior layer analysis, many resonance manifolds are detected. Secondly, it will be shown that resonances in the system are caused not only by boundary disturbances but also by nonlinear interactions. Based on these observations, a three-timescales perturbation method is used to approximate the solution of the initial-boundary value problem analytically. It turns out that for special frequencies in the boundary excitations and for certain parameter values of the longitudinal stiffness and the conveyance mass, many oscillation modes jump up from small to large amplitudes in the transverse and longitudinal directions. Finally, numerical simulations are presented to verify the obtained analytical results.

Interior layer analysis
Multiple-timescales perturbation method
Nonlinear interactions
Resonance zone
Vertically moving string

http://resolver.tudelft.nl/uuid:0844ada1-0d6c-44a5-a191-227cc4ecdc10

https://doi.org/10.1007/s11071-022-08052-8

0924-090X

Nonlinear Dynamics: an international journal of nonlinear dynamics and chaos in engineering systems, 111 (2023) (6), 5079-5106

Institutional Repository

review

© 2022 J. Wang, W.T. van Horssen