热环境下弹性地基板屈曲路径和振动特性研究
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O326

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国家自然科学基金(11702033,52108133);长安大学中央高校基本科研业务经费(300102250110);河海大学中央高校基本科研业务经费(B210201019)


Post-buckling paths and vibration characteristics of a plate resting on the elastic foundation in thermal environment
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    摘要:

    气候炎热地区,热应力的产生会使得道路结构的刚度发生改变,甚至引发屈曲隆起的现象。为了揭示道路结构热屈曲机理及其对动力学特性的影响,本文以Winkler地基板为对象,对其在热环境下的后屈曲路径和振动特性演化规律进行了理论研究。首先,考虑热应力的影响,基于三阶剪切变形理论、von Karman几何非线性关系以及Hamilton原理得到Winkler地基板的非线性振动控制方程。然后,发展了两步求解方法,即先通过非线性静力分析得到地基板的热屈曲构型,而后以此屈曲构型为平衡位置计算固有频率和模态形状。基于此,针对典型算例,计算分析了不同基床系数下地基板的后屈曲路径和固有特性随温度的演化规律,揭示了基床系数对屈曲温度、屈曲构型、固有频率和模态形状的影响机理。

    Abstract:

    In hot area, the stiffness of the pavement will be changed under thermal stress, and even the buckling deformation may appear. To reveal the thermal buckling mechanism of the pavement and the effect on the dynamic characteristic, the post-buckling paths and vibration characteristics of a plate resting on the Winkler elastic foundation in thermal environment are studied theoretically. Firstly, considering the effect of thermal stress, the nonlinear vibration governing equation of the plate is formulated based on the third order shear deformation theory, von Karman nonlinear displacement-strain relationship and Hamilton’s principle. Secondly, a two-step theoretical method is developed: the nonlinear static thermal buckling displacement is solved firstly and the linear vibration characteristics are calculated at the reference buckling deflection. With the increment of the temperature, the variation trends of the post buckling paths and vibration characteristics of the plate resting on Winkler foundation with different stiffness coefficients are analyzed. The influences of foundation stiffness on the buckling temperature, buckling deflection, natural frequencies and mode shapes are revealed.

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薛治国,张博,孙宝印,等. 热环境下弹性地基板屈曲路径和振动特性研究[J]. 科学技术与工程, 2022, 22(16): 6393-6399.
Xue Zhiguo, Zhang Bo, Sun Baoyin, et al. Post-buckling paths and vibration characteristics of a plate resting on the elastic foundation in thermal environment[J]. Science Technology and Engineering,2022,22(16):6393-6399.

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历史
  • 收稿日期:2021-09-07
  • 最后修改日期:2022-05-16
  • 录用日期:2021-12-26
  • 在线发布日期: 2022-06-22
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