摘要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，本文提出了一种高阶非线性振子模型。首先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；然后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；最后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，验证了本文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。
Abstract：To predict the amplitude response and other important characters of the vortex-induced vibration of a cylinder quickly and accurately, a high order nonlinear oscillator model was proposed.Based on the Lagrange second dynamic equations and the Taylor expansion formula, the vibration equation of the cylinder fixed by four symmetrical springs was derived, where the axial tensile nonlinearity and coupling nonlinearity were considered.Then, the fluctuating lift and drag in the vortex-induced vibration were obtained in accordance with the discrete point vortex theory, and the mathematical quantified relationship between the fluid forces was established.The improved Van der Pol equation was used to simulate the fluid oscillator, and then the coupling equations of the nonlinear structure and fluid oscillators were established.On this basis, the vortex-induced vibration for cylinders with different mass ratio and damping ratio was predicated, and the results were compared with testing data to verify the correctness and universality of the model.Finally the sensitivity of the parameters in model was analysed.
康庄，张橙，付森，徐祥. 圆柱体涡激振动的高阶非线性振子模型研究[J]. 振动与冲击, 2018, 37(18): 48-58.
KANG Zhuang,ZHANG Cheng,FU Sen,XU Xiang. Nonlinear oscillator model for the vortex-induced vibration of a cylinder. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(18): 48-58.
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