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目的为准确把握索-桥耦合的非线性共振本质,提出振动控制策略及控制方法,解决斜拉桥拉索在桥面激励下的非线性动力学特性问题.方法考虑拉索前两阶模态组合的影响,建立索-桥耦合的无量纲非线性运动方程组;利用多尺度法进行近似解析求解,讨论桥面质量块与拉索的频比取值不同时,耦合系统的动力响应特性;以实际工程拉索为研究对象,进一步通过数值模拟验证多尺度法定性讨论结果的准确性.结果除了质量块与拉索第一阶模态发生1∶1主共振、2∶1参数共振外,第二阶模态也将与质量块发生2∶1参数共振,但不发生1∶1主共振,同时共振拉索的位移响应均出现大幅“拍”振现象,此时的动态索力增量也有很大幅度的增长,已达到不可忽视的程度.结论实际工程拉索发生大幅参数共振的可能性很高,避免参数共振的频比关系是解决参数共振问题的有效途径,对保证桥梁结构的安全服役具有重要理论价值和实际意义.
Aim To accurately grasp the nonlinear resonance nature of cable-bridge coupling, the vibration control strategy and control method are proposed to solve the nonlinear dynamic characteristics of cable stayed bridge under the excitement of the bridge deck.Methods Considering the first two modes The nonlinear dynamic equations of cable-bridge coupling are established. The approximate analytical solution of multi-scale method is used to discuss the dynamic response characteristics of coupled system when the frequency ratios of bridge deck mass and cable are different. Taking the actual engineering cable as the research object, the accuracy of the multiscale statutory discussion was verified by numerical simulation.Results In addition to the 1: 1 primary resonance and the 2: 1 parameter resonance in the first mode of the mass and the cable, The second-order mode will also resonate with the mass at a 2: 1 parameter, but no 1: 1 primary resonance will occur, and the displacement response of the resonant cable will all show a sharp “beat” vibration. At this time, the dynamic cable force Increment also has a very large increase, has reached a degree that can not be ignored.Conclusion There is a high probability of substantial parametric resonance of the actual engineering cable, to avoid frequency-ratio relationship of parametric resonance is an effective way to solve the parametric resonance problem, Security service beam structure has important theoretical and practical significance.