Nonlinear vibrations for double inclined cables–deck beam coupled system using asymptotic reductions

Abstract

For complex cable-stayed structures, dynamic coupling between cables and deck beam is important. In this work, an asymptotically reduced coupled model, consisting of two inclined cables and one deck beam, is established for understanding dynamic interactions inherent with the cable-stayed structures, after confining oneself to the simplified case that the beam’s motion is much weaker than the cables’ and the deck beam/cable mass ratio is a large parameter. More explicitly, through focusing on the cables–deck interfaces, the double cables–deck beam coupling is decomposed into deck-induced and cable-induced weak boundary/interior modulations on each other, which are analytically characterized by three boundary coupling coefficients. Based upon the asymptotic model, two different kinds of coupled dynamics are fully investigated, the first with only one of the two cables excited, and the second with the deck beam excited, leading to the coupled system’s different nonlinear forced responses. The steady solutions’ stabilities are determined and bifurcations, such as saddle–node bifurcation, Hopf bifurcation, and pitchfork bifurcation, are all detected. Special attentions are paid to the dynamic effects caused by the deck beam/cable mass ratio, cable’s inclinations.