The Dynamic Interactions and Control of Long Slender Continua and Discrete Inertial Components in Vertical Transportation Systems

Dynamic phenomena such as transient and steady-state resonant vibrations in vertical transportation systems deployed to move goods and passengers in the modern built environment affect the performance of the entire installation. In extreme high rise structures traction drive elevator systems comprise long slen-der continua such as ropes and cables with discrete mass elements that exhibit low-frequency modes and nonlinear modal interactions. This results in the need to predict and control their non-linear stationary and non-stationary dynamic responses. The underlying causes of these dynamic responses / vibrations are varied. They include low frequency sway motions of the host structure induced by high winds and seismic activities. Consequently, conditions for external, par-ametric and autoparametric resonances can readily arise during the operation of such installations. In this context, a general approach to model the dynamic be-haviour of a typical vertical transportation system is demonstrated. Subsequent-ly, a mathematical model is developed which is solved numerically to predict the non-stationary / nonlinear dynamic responses. An active control strategy is then proposed to minimize the effects of adverse dynamic responses of the system.