Analysis on two types of internal resonance of a suspended bridge structure with inclined main cables based on its sectional model

Abstract

Abstract This study investigated the internal resonance phenomenon of a suspended bridge structure with a 6-Degree-of-Freedom sectional model. The primary resonance of the second mode of the system under harmonic excitation is firstly studied. The one-to-two internal resonance between the second and third modes, and one-to-three internal resonance between the second and fourth modes may be induced if the corresponding natural frequency ratios are close to 2.0 and 3.0, respectively. Numerical analysis also shows that the two-to-one internal resonance between the third and second modes can be induced under different scenarios of excitation. The first one happens with the second mode being excited, resulting in two response peaks in the frequency response curves . The second one may occur when the third mode is excited with sufficient large excitation where most of the energy input will be transmitted to the second mode. Hopf bifurcation can also be found in the frequency response curve of the system. Lastly, the three-to-one internal resonance between the fourth and second modes is also found when the second mode is excited. The response of the second mode is slightly reduced with a distinct increase in the response of the fourth mode due to the internal resonance. All these behaviors of this dynamic system indicate the meaningful role played by a variety of internal resonances in the design of mega-scale cable-supported bridge structure.