Abstract
Nonlinear free vibrations of suspension bridges with a bisymmetrical stiffening girder are investigated by using the method of multiple scales in two cases: when a two-to-one or one-to-one internal resonance takes place. The influence of the initial conditions on the vibrational processes’ character is shown. Three types of the energy-exchange mechanism between vertical and torsional modes are determined: two-sided energy exchange (a periodic motion); one-sided energy interchange (an aperiodic motion); and, energy exchange does not occur (stationary vibrations). The solutions describing the one-sided energy exchange are demonstrated to correspond with soliton-like solutions in the form of a single kink. On the hydrodynamic analogy, the qualitative method of analysis of suspension bridge non-linear free vibrations is proposed. This procedure allows one to determine the types of vibrational process, to investigate the stability of each vibrational regime, to define the character of amplitude and phase dependences from the initial conditions etc. Using five examples, the non-linear free vibrations of the Golden Gate Bridge in San Francisco are considered for the cases of two-to-one and one-to-one internal resonances. All quoted examples verify the qualitative hydrodynamic analysis.
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