考虑土体质量的Winkler地基梁非线性自由振动分析

马建军, 聂梦强, 高笑娟, 秦紫果

马建军, 聂梦强, 高笑娟, 秦紫果. 考虑土体质量的Winkler地基梁非线性自由振动分析[J]. 工程力学, 2018, 35(S1): 150-155. DOI: 10.6052/j.issn.1000-4750.2017.06.S027
引用本文: 马建军, 聂梦强, 高笑娟, 秦紫果. 考虑土体质量的Winkler地基梁非线性自由振动分析[J]. 工程力学, 2018, 35(S1): 150-155. DOI: 10.6052/j.issn.1000-4750.2017.06.S027
MA Jian-jun, NIE Meng-qiang, GAO Xiao-juan, QIN Zi-guo. Nonlinear free vibration of a beam on Winkler foundation with a consideration of soil mass effect[J]. Engineering Mechanics, 2018, 35(S1): 150-155. DOI: 10.6052/j.issn.1000-4750.2017.06.S027
Citation: MA Jian-jun, NIE Meng-qiang, GAO Xiao-juan, QIN Zi-guo. Nonlinear free vibration of a beam on Winkler foundation with a consideration of soil mass effect[J]. Engineering Mechanics, 2018, 35(S1): 150-155. DOI: 10.6052/j.issn.1000-4750.2017.06.S027

考虑土体质量的Winkler地基梁非线性自由振动分析

基金项目: 国家自然科学基金项目(11502072,51474095)
详细信息
    作者简介:

    聂梦强(1992-),男,河南洛阳人,硕士生,主要从事弹性地基梁的非线性动力学研究(E-mail:594143157@qq.com);高笑娟(1973-),女,河南偃师人,副教授,博士,所长,主要从事岩土工程方面研究(E-mail:gaoxjly@163.com);秦紫果(1993-),女,河南洛阳人,硕士生,主要从事桩基的非线性动力学研究(E-mail:448080838@qq.com).

    通讯作者:

    马建军(1982-),男,河南孟州人,副教授,博士,主要从事桩基非线性动力响应研究(E-mail:majianjun@haust.edu.cn)

  • 中图分类号: TU348

Nonlinear free vibration of a beam on Winkler foundation with a consideration of soil mass effect

  • 摘要: 基于Winkler地基模型、Euler梁理论和弹性地基的运动方程,建立了考虑土体质量影响的Winkler地基上有限长梁的非线性动力学模型。利用特征值分析和多尺度方法,分别求得梁的线性和非线性固有频率及模态构型。进而通过数值分析,研究了土体质量对Winkler地基上有限长梁线性和非线性自由振动的影响。研究结果表明:若将土体质量对梁动力响应的影响引入Winkler地基上有限长梁的动力学模型,梁的固有频率降低;土体质量对梁的高阶非线性模态构型影响显著。
    Abstract: Based on the Winkler model, Euler beam theory, and the motion equation of elastic foundation, the nonlinear dynamics model of a finite-length beam on Winkler foundation with a consideration of the effect of soil mass is obtained. Applying the eigenvalue analysis and the method of multiple scales, the linear and nonlinear natural frequencies and mode shapes of the beam are obtained. By means of the numerical calculation, the effect of soil mass on the linear and nonlinear free vibrations of the finite-length beam on Winkler foundation are explored. The numerical results show that:the natural frequencies of beam decrease, when the effect of soil mass on the dynamic response of the beam is included in the nonlinear dynamic model of the finite-length beam on Winkler foundation. Moreover, it is significant for the effect of soil mass on the high-order nonlinear mode shapes of the beam.
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出版历程
  • 收稿日期:  2017-06-03
  • 修回日期:  2017-11-06
  • 刊出日期:  2018-06-29

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