基于非线性涡激力广义模型的涡振幅值换算

节段模型测振风洞试验是研究涡激共振风速锁定区间和振动幅值的主要手段之一，但节段模型涡振振幅并不能由几何缩尺比直接换算至实桥，需要对测试结果进行修正。已有研究表明，涡激力具有强烈的非线性特性，因此基于线性涡激力模型的换算方法不再适用。此外，由于采用的非线性涡激力模型不准确，基于非线性涡激力模型的已有换算方法也不一定适用，并且目前基于非线性涡激力模型的换算方法也没有给出阻尼比的修正方法。为此，文章借鉴量纲分析方法，推导非线性涡激力广义模型，并给出计算涡振振幅的非线性涡激力简化广义模型，然后根据能量相等的原则推导节段模型与实桥的涡振幅值换算公式。研究表明：当节段模型与实桥结构阻尼比一致时，振幅换算关系仅与桥梁阵型函数值有关；当节段模型与实桥结构阻尼比不一致时，振幅换算关系还与涡振生长或衰变过程位移振幅变化率以及涡振稳定状态无量纲幅值有关；不同换算方法的结果对比表明本文换算结果与实测值最为接近。

Amplitude conversion of vortex-induced vibration based on #br#generalized model of nonlinear vortex-induced force

Wind tunnel test with a sectional model is one of the main methods to determine the lock-in region and the maximum amplitude of vortex-induced vibration (VIV). The amplitude of VIV obtained from the wind tunnel test should be modified and cannot be converted directly to its prototype bridge via the geometric scale ratio. Many researches have indicated that the vortex-induced force is characterized with the strong nonlinear behavior,and thus the conversion method based on a linear vortex-induced force model is no longer applicable. In addition,the existing conversion methods based on the nonlinear vortex-induced force model which is inaccurate may not be applicable,and they don’t provide the modification to the damping ratio. In view of the above,the generalized model of nonlinear vortex-induced force is derived by means of the dimensional analysis method. The simplified generalized model of vortex induced force,which is only useful for amplitude calculation,is also presented. The amplitude conversion method of VIV between a sectional model and its prototype bridge is deduced by applying the principle that the equal energy input should result in the equal amplitude. The analysis results show that,although the nonlinear vortex-induced force models may be different,the amplitude conversion relationship remains the same. If the damping ratio of the sectional model equals to that of its prototype bridge,the conversion relationship only relates to the structural model shapes. If they are not equal,the conversion relationship not only relates to the structural model shapes but also to the change rate of amplitude during the decay-to-resonance period or growth-to-resonance period of VIV as well as the stable dimensionless amplitude of VIV. Compared to other conversion methods,the results obtained from the proposed method have better agreements with the field measurement results.