为快速准确预报圆柱双自由度涡激振动幅值响应等重要特性,提出了一种高阶非线性振子模型。基于拉格朗日第二类动力学方程及二元函数的泰勒展开公式推导了四对称弹簧固定的圆柱振动方程,在其中计入了轴向拉伸非线性项和耦合非线性项;根据离散点涡理论推导了圆柱涡激振动中所受的脉动升力和脉动阻力,并得到了它们之间的数学量化关系;利用包含五阶气动阻尼项的改进Van der Pol方程来模拟流体振子,进而建立了非线性结构振子和流体振子的耦合方程组模型。在此基础上对不同质量比和阻尼比的圆柱进行涡激振动预报,并与试验数据进行对比分析,验证了该模型应用的正确性和广泛性,最后对模型中的各项参数进行了敏感性分析。
In the paper,an experiment investigation was conducted for one-and two-degree of freedom vortex-induced vibration(VIV) of a horizontally-oriented cylinder with diameter of 11 cm and length of 120 cm.In the experiment,the spring constants in the cross-flow and in-line flow directions were regulated to change the natural vibration frequency of the model system.It was found that,in the one-degree of freedom VIV experiment,a "double peak" phenomenon was observed in its amplitude within the range of the reduced velocities tested,moreover,a "2T" wake appeared in the vicinity of the second peak.In the two-degree of freedom VIV experiment,the trajectory of cylinder exhibited a reverse "C" shape,i.e.,a "new moon" shape.Through analysis of these data,it appears that,besides the non-dimensional in-line and cross-flow natural vibration frequency ratios,the absolute value of the natural vibration frequency of cylinder is also one of the important parameters affecting its VIV behavior.
