移动简谐荷载作用下Kerr地基梁的稳态响应研究

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摘要利用双重Fourier变换以及围道积分方法得到了移动简谐荷载作用下Kerr地基梁的稳态响应解答。梁为Euler-Bernoulli梁，利用频散曲线分析了地基梁的共振频率和临界速度。分析了列车运行速度、荷载频率、地基压缩系数和剪切刚度对梁挠度响应的影响，分析地基阻尼对地基梁临界速度和共振频率的影响。最后，建立地基-梁有限元模型，计算了静载和简谐荷载作用下梁挠度响应，与Kerr地基梁、Pasternak地基梁和Winkler地基梁的解析计算结果进行对比，发现静载作用下Kerr地基梁计算结果最为接近，Pasternak地基模型次之，Winkler地基梁误差最大，动载作用下地基梁模型仅在近处与有限元挠度时程响应结果较为接近。

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关键词 ： Kerr地基模型, 地基梁挠度, 频散曲线, 地基阻尼, 移动简谐荷载

Abstract：By double Fourier transform and contour integration technique, a closed-form solution to the steady-state response of a uniform beam placed on Kerr foundation and subjected to a moving harmonic load was obtained. The beam was described as a Euler-Bernoulli beam, and the cut-on frequency and critical velocity of the foundation beam were determined based on the dispersive curve of Kerr foundation beam. The influences of the train speed, load frequency, coefficient of subgrade reaction and foundation shear coefficient on the deflection of foundation beam were investigated and the influence of foundation damping on the critical velocity and resonant frequency was also studied. Moreover, a two-dimensional beam-soil model was established to calculate the deflection of foundation beam under non-moving constant load and simple harmonic load. The numerical results were compared with the analytical solutions of Kerr foundation, Pasternak foundation, and the Winkler foundation. It is concluded that the Kerr foundation model can give best agreement with the FEM results, while the Winkler foundation model presents greatest discrepancy in static calculations. As for dynamic calculation, the time history responses base on different types of foundation beam models are only close to the numerical results at the places near the applied load.

Key words： Kerr foundation model deflection of foundation beam dispersive curve foundation damping moving oscillating load

收稿日期: 2016-08-08 出版日期: 2017-12-28

引用本文:

黄强1,2，黄宏伟1,2，张冬梅1,2，黄栩3. 移动简谐荷载作用下Kerr地基梁的稳态响应研究[J]. 振动与冲击, 2018, 37(1): 14-20.
Huang Qiang1,2 Huang Hong-wei1,2 Zhang Dong-mei1,2 Huang Xu3. Steady-state response of an infinite Euler-Bernoulli beam on Kerr foundation subjected to a moving oscillating load. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(1): 14-20.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2018/V37/I1/14

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