This paper focuses on the investigation of the autoparametric coupling effects and modal
interactions in a suspension rope system with a time varying length. Equations of motion of a
multi-degree-of-freedom discrete, non-stationary and non-linear model are presented and are used to analyze the dynamic response of an elevator suspension rope system under resonance conditions. The equations of motion involve quadratic and cubic non-linear terms which are responsible for the modal interaction between the lateral and longitudinal oscillations of the rope and the car motions. The model takes into account the periodic excitations caused by motion of the host structure. The
results confirm that adverse responses may arise and internal autoparametric resonance phenomena
may occur