Coupling between torsional and vertical modes of wind-induced nonlinear vibrations in suspension bridges due to suspender-loosening

摘要

Motivated by the work of Lazer and Mckenna (1990), Chau (1995a,b) recently presented an important result that the maximum amplitude of vertical vibrations in suspension bridges under wind load may be underestimated by up to 500percent, based on the numerical stimulations on Tsing Ma bridge with a wind intensity equivalent to "Typhoon Signal No. 8" of Hong Kong. However, for simplicity Chau (1995a,b) considered only nonlinear effect due to suspender-loosening. This paper, therefore, presents the nonlinear effect that may arise as the nonlinear terms for both large deflection and rotation, as well as those for the suspender-loosening, are retained. Surprisingly, for cases of steadily-blowing wind and fluctuated wind conditions, the nonlinear coupling due to torsional and vertical modes is virtually non-existent; that is, the main nonlinear effect is due to suspender-loosening. However, for sudden gusty wind condition (i.e. the cables and bridge deck are assumed to be displaced initially by gusty wind then are set free) numerical results suggest that the torsional vibrations set in as time evolves, despite the fact that there is no initial torsional deflection. As time increases further, the vertical vibration becomes extremely large. Such large deflection should damage structural components and leads eventually to the final collapse of the suspension bridge. This whole scenario clsely resembles what actually happened in the case of the collapse of the Tacoma Narrows Bridge. This is the first time that the transition of vertical modes to vertical-torsional coupled modes is predicted in theoretical analysis.