A continuous model of coupled cable-tower-decks and its resonance vibration

A nonlinear coupled vibration model of towers and cables and bridge decks and its 2:2:1 or 1:1:1 resonance is investigated with taking the initial sag,the angle of the cable and the air damping into consideration.The deck is simplified as a Bernoulli-Euler beam which fixed on one end and attached to the spring on the other end,the tower as a concentrated mass that subject to the spring and damp.A nonlinear vibration system of tower-cable-deck is established.With the application of the method of multiple scales,the condition of yielding the inner resonance and the formula of the amplitude of the steady —state vibration are obtained.The validity of the analysis is verified by the numerical simulation.The results show that the 2:2:1 and 1:1:1 internal resonance will occur under some initial conditions in the cable and the deck,while the tower just provide a restriction on the occurrence of internal resonance but doesn't take part in the energy exchange of the system in the first order approximation.The phenomena of chaos are also found.