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热环境中粘贴压电层功能梯度材料梁的自由振动

李世荣 苏厚德 程昌钧

李世荣, 苏厚德, 程昌钧. 热环境中粘贴压电层功能梯度材料梁的自由振动[J]. 应用数学和力学, 2009, 30(8): 907-918. doi: 10.3879/j.issn.1000-0887.2009.08.003
引用本文: 李世荣, 苏厚德, 程昌钧. 热环境中粘贴压电层功能梯度材料梁的自由振动[J]. 应用数学和力学, 2009, 30(8): 907-918. doi: 10.3879/j.issn.1000-0887.2009.08.003
LI Shi-rong, SU Hou-de, CHENG Chang-jun. Free Vibration of Functionally Graded Material Beams With Surface-Bonded Piezoelectric Layers in Thermal Environment[J]. Applied Mathematics and Mechanics, 2009, 30(8): 907-918. doi: 10.3879/j.issn.1000-0887.2009.08.003
Citation: LI Shi-rong, SU Hou-de, CHENG Chang-jun. Free Vibration of Functionally Graded Material Beams With Surface-Bonded Piezoelectric Layers in Thermal Environment[J]. Applied Mathematics and Mechanics, 2009, 30(8): 907-918. doi: 10.3879/j.issn.1000-0887.2009.08.003

热环境中粘贴压电层功能梯度材料梁的自由振动

doi: 10.3879/j.issn.1000-0887.2009.08.003
基金项目: 国家自然科学基金资助项目(10872083;10602021);教育部博士点基金资助项目(200807310002)
详细信息
    作者简介:

    李世荣(1957- ),男,甘肃人,教授,博士(联系人.E-mail:lisr@lut.cn).

  • 中图分类号: O343

Free Vibration of Functionally Graded Material Beams With Surface-Bonded Piezoelectric Layers in Thermal Environment

  • 摘要: 研究了上下表面粘贴压电层的功能梯度材料Euler-Bernoulli梁在升温及电场作用下的屈曲和自由振动行为.在精确考虑轴线伸长基础上,建立了压电功能梯度材料层合梁在热-电-机载荷作用下的几何非线性动力学控制方程.其中,假设功能梯度材料性质沿厚度方向按照幂函数连续变化,上下压电层为各向同性均匀材料.在小振幅和谐振动假设下,上述非线性偏微分方程组被转化为两套相互耦合的常微分方程组,即过屈曲问题的控制方程和过屈曲构形附近的线性振动控制方程.采用打靶法数值求解上述两个耦合的常微分方程边值问题,获得了在均匀电场和横向非均匀升温场作用下两端固定压电-功能梯度材料层合梁在屈曲前和过屈曲构型附近的自由振动响应.绘出了梁的过屈曲平衡路径以及前3阶固有频率随热、电载荷及材料梯度参数变化的特性曲线.结果表明,梁的前3阶频率在屈曲前随着温度升高而减小,在进入过屈曲后它们却随着温度升高而增加.通过施加电压在压电层产生拉应力可有效地提高粱的热屈曲临界载荷,从而提高其固有频率.
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出版历程
  • 收稿日期:  2009-03-12
  • 修回日期:  2009-07-01
  • 刊出日期:  2009-08-15

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