The dynamics of vertical transportation systems: from deep mine operations to modern high-rise applications

High speed and high capacity lifting installations move heavy payloads and passengers from depths in excess of 3000m to heights of nearly 1000m. This paper discusses mathematical models to predict transient and steady-state resonant vibrations taking place in deep mine and high-rise applications. In these systems long slender continua (LSC) such as steel wire ropes and composite belts play pivotal roles as suspension means and weight-compensation members. The natural frequencies of these systems are slowly varying, rendering them non-stationary. The nonlinear dynamic interactions involve exchanges of energy between various modes of vibration. An adverse situation arises when the host structure is excited near its natural frequency and one of the slowly varying frequencies of LSC approaches the natural frequency of the structure. The models are represented by a system of nonlinear partial differential equations defined in a slowly time-variant space domain. The nature of loads acting upon the lifting systems is often nondeterministic (stochastic) so that the methods of stochastic dynamics need to be employed to predict the dynamic behaviour of the system. The results and conclusions presented in this paper demonstrate that a good understanding and prediction of the dynamic behaviour of vertical transportation systems are essential for developing vibration suppression and control strategies to minimize the effects of adverse dynamic responses so that the installation will operate without compromising the structural integrity and safety standards.