基于多尺度法索-桥耦合非线性动力响应分析

Nonlinear Dynamic Response Analysis of Cable-Bridge Coupling based on Multiple Scale Method

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.

In order to correctly hold essence of nonlinear resonance coupled cable and bridge, an approach for investigating the nonlinear dynamic characteristics of cable in cable-stayed bridge under bridge deck excita- tion is proposed in this paper. Firstly, the influence of first two modes of cable is considered, and the nonlin- ear vibration differential equations are derived in dimensionless style by considering the cable-bridge coupled effect. Then the nonlinear vibration differential equations are approximately solved via multiple scale meth- od. Meanwhile variation of coupled system dynamic response characteristics is discussed when the ratios of deck mass block and cable natural frequency are different. At last, multiple scale method is accurate via nu- merical simulation based on a real bridge. The results show that 2：1 parametric resonance,not but 1：1 prima- ry resonance, will occur between the second cable mode and mass block,besides 1：1 primary resonance and 2：1 parametric resonance occur between mass block and cable. Meanwhile the large amplitude beat vibration of resonant cable displacement responses will occur, increment of dynamic cable tension will increase with a large extent. Therefore, the possibility for cable occurring large amplitude parametric resonance is very high in practical engineering. To avoid frequency ratio relationship of parametric resonance is the effective way to solve the parametric resonance problem. Researching a sort of scientific test method is very important on the- ory and application to enhance safety working of bridge structure.