热环境下弹性地基板屈曲路径和振动特性研究  

Post-buckling Paths and Vibration Characteristics of a Plate Resting on the Elastic Foundation in Thermal Environment

作　　者：薛治国 张博 孙宝印 王迪 XUE Zhi-guo;ZHANG Bo;SUN Bao-yin;WANG Di(The No.5 Engineering Co., Ltd. Shanxi Road & Bridge Construction Group Co,. Ltd., Taiyuan 030012, China;School of Sciences, Chang’an University, Xi’an 710054, China;College of Civil and Transportation Engineering, Hohai University, Nanjing 210013, China;School of Construction Machinery, Chang’an University, Xi’an 710054)

机构地区：[1]山西路桥第五工程有限公司,太原030012 [2]长安大学理学院,西安710054 [3]河海大学土木与交通学院,南京210013 [4]长安大学工程机械学院,西安710054

出　　处：《科学技术与工程》2022年第16期6393-6399,共7页Science Technology and Engineering

基　　金：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)。

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,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。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 were studied theoretically.Firstly,considering the effect of thermal stress,the nonlinear vibration governing equation of the plate was 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 was developed.The nonlinear static thermal buckling displacement was solved firstly and the linear vibration characteristics were 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 were analyzed.The influences of foundation stiffness on the buckling temperature,buckling deflection,natural frequencies and mode shapes were revealed.

关 键 词：Winkler地基板 热环境 后屈曲路径 固有频率 模态形状 

分 类 号：O326[理学—一般力学与力学基础]