工程力学 ›› 2019, Vol. 36 ›› Issue (9): 32-39.doi: 10.6052/j.issn.1000-4750.2018.08.0443

• 基本方法 • 上一篇    下一篇

湿-热-机-弹耦合FGM梁的稳定性及振动特性

蒲育1,2, 周凤玺1   

  1. 1. 兰州理工大学土木工程学院, 兰州 730050;
    2. 兰州工业学院土木工程学院, 兰州 730050
  • 收稿日期:2018-08-05 修回日期:2019-05-09 出版日期:2019-09-25 发布日期:2019-05-17
  • 通讯作者: 周凤玺(1979-),男,甘肃会宁人,教授,博士,博导,主要从事岩土力学及新型材料结构的力学行为研究(E-mail:geolut@163.com). E-mail:geolut@163.com
  • 作者简介:蒲育(1984-),男,甘肃天水人,副教授,博士生,主要从事多场耦合新型材料结构的力学行为研究(E-mail:shifopuyu@126.com).
  • 基金资助:
    国家自然科学基金项目(51368038);兰州工业学院"启智"人才培养计划基金资助项目(2018QZ-05)

STABILITY AND VIBRATION BEHAVIOR OF FGM BEAMS UNDER HYGRO-THERMAL-MECHANICAL-ELASTIC LOADS

PU Yu1,2, ZHOU Feng-xi1   

  1. 1. School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China;
    2. College of Civil Engineering, Lanzhou Institute of Technology, Lanzhou 730050, China
  • Received:2018-08-05 Revised:2019-05-09 Online:2019-09-25 Published:2019-05-17

摘要: 研究了初始轴向机械载荷作用下Winkler-Pasternak弹性地基上功能梯度材料(FGM)梁在湿-热环境中的稳定性及振动特性。假设温度和湿度沿梁厚度方向稳态分布,材料的物性依赖于温度且按Voigt混合幂律模型连续分布。首先,基于一种扩展的n阶广义梁理论,应用Hamilton原理,统一建立了以轴向位移、弯曲变形项挠度及剪切变形项挠度为基本未知函数FGM梁的屈曲及自由振动方程,采用Navier解法获得了FGM简支梁静动态响应的精确解。其次,通过算例验证并给出了该广义梁理论阶次n的理想取值,丰富梁理论的同时,可供验证或改进其他各种剪切变形梁理论。最后,着重探讨了3种湿-热分布下湿度与温度增加、初始轴向机械载荷、跨厚比、地基刚度、梯度指标等诸多参数对FGM梁稳定性和振动特性的影响。

关键词: 功能梯度材料梁, 湿-热-机-弹耦合载荷, n阶广义梁理论, 精确解, 临界屈曲载荷, 固有频率

Abstract: The stability and vibration behavior of functionally graded material (FGM) beams resting on a Winkler-Pasternak elastic foundation under the action of initial axial mechanical load considering the hygro-thermal environment is investigated. Three hygro-thermal distributions through the thickness of the beams are assumed. The material properties are temperature-dependent and are distributed according to the Voigt mixture power law model. An n-th order generalized beam theory is proposed. The governing equations of buckling and free vibration are derived from the Hamilton's principle, in which the fundamental unknown functions are the axial displacement, bending and shear components of the transverse displacement. Applying the Navier method, the analytical solutions of the buckling and free vibration responses of FGM simply supported beams are obtained. The availability and accuracy of the n-th order generalized beam theory are tested and discussed through several numerical examples. The results show that it refines the beam theories and can be used as a benchmark to verify or modify other shear deformation beam theories. The effects of three types of hygro-thermal distribution, moisture and temperature rise, initial axial mechanical load, length-to-thickness ratio, elastic foundation stiffness and material graded index on the stability and vibration behavior of FGM beams are analyzed.

Key words: functionally graded material beam, hygro-thermal-mechanical-elastic load, n-th order generalized beam theory, exact solution, critical buckling load, natural frequency

中图分类号: 

  • TB34
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