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| One-to-one internal resonance of cable-stayed beam in the case of beam primary resonance |
| Received:August 11, 2014 Revised:December 18, 2014 |
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| DOI：10.7511/jslx201601008 |
| KeyWord:cable-stayed bridge cable-stayed beam bending rigidity primary resonance 1:1 internal resonance |
| Author | Institution |
| 吕建根 |
仲恺农业工程学院 城市建设学院, 广州 |
| 康厚军 |
湖南大学 土木工程学院, 长沙 |
| 赵跃宇 |
湖南大学 土木工程学院, 长沙 |
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| Abstract: |
| The one-to-one internal resonance of cable-stayed beam in the case of beam primary resonance is investigated.The longitudinal inertia force of cable-stayed beam is neglected, the influence of bending rigidity, sagging and geometric nonlinearity on cable are considered during the deduction, the nonlinear partial differential equations of cable-stayed beam are formulated based on Hamiltonian principle.Then, the Galerkin method is used to discretize these equations.Subsequently, the averaged equations and bifurcation equations of 1:1 internal resonance of the cable-stayed beam in the case of primary resonance of the beam are obtained using the Multiple Scales Method as one of the perturbation techniques.A case study of cable-stayed bridge, the interaction and time-history curve between the cable and beam for internal resonance are analyzed.As a result, the cable is easy to appear the resonance, and the vibration is strong nonlinear characteristics; the vibrations of beam have a significant impact on the vibration of cable, while the vibrations of cable have little effect on that of beam; the energy exchanges between the cable and the beam when the system appear internal resonance, in addition, the amplitude of the cable increased with the decrease of the amplitude of the beam in the course of internal resonance. |
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