| 基于二元耦联性解耦下多孔FGM梁的热-力耦合振动与屈曲特性 |
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| 引用本文： | 蒲育,周凤玺,任永忠,刘君. 基于二元耦联性解耦下多孔FGM梁的热-力耦合振动与屈曲特性[J]. 工程力学, 2020, 37(8): 10-19. DOI: 10.6052/j.issn.1000-4750.2019.09.0553 |
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| 作者姓名： | 蒲育 周凤玺 任永忠 刘君 |
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| 作者单位： | 1.兰州工业学院土木工程学院，兰州 730050 |
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| 基金项目： | 国家自然科学基金项目(51978320，11962016)；甘肃省高等学校创新能力提升项目(2019B-180)；兰州工业学院“启智”人才培养计划基金项目(2018QZ-05，2019QZ-05，2019QZ-08)；兰州工业学院校级重点学科项目(2019XK-04) |
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| 摘 要： | 采用一种改进型广义微分求积(MGDQ)法,数值研究了初始轴向机械力作用下含均匀孔隙的功能梯度材料(FGM)梁在热环境中的耦合振动及耦合屈曲特性。考虑了材料性质随温度的相关性,温度沿梁的厚度方向按不同类型稳态分布,采用含孔隙率修正的Voigt混合幂率模型来表征多孔FGM梁的材料属性。采用一种n阶广义梁理论(GBT),在Hamilton体系下统一建立描述该系统耦合振动及屈曲问题力学模型的控制方程。通过引入边界控制参数,可实施3种典型边界梁动态响应MGDQ法求解的MATLAB统一化编程。基于两种静动态力学行为之间的二元耦联性,编写循环子程序用来获得屈曲静态响应,该分析方法极大地简化了解耦过程并提高了计算效率。通过算例主要探究了梁理论、边界条件、温度分布、升温、初始轴向机械力、热-力耦合效应、孔隙率、梯度指标、跨厚比等诸多参数对多孔FGM梁振动及屈曲特性的影响,同时刻画并揭示了两种静动态力学行为之间的二元耦联性。
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| 关 键 词： | 多孔FGM梁 n阶广义梁理论 热-力耦合载荷 耦合振动 耦合屈曲 改进型广义微分求积法 |
| 收稿时间： | 2019-09-22 |
VIBRATION AND BUCKLING BEHAVIORS OF POROUS FGM BEAMS UNDER THERMAL-MECHANICAL LOADS BY DUALITY RELATION |
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| Affiliation: | 1.College of Civil Engineering, Lanzhou Institute of Technology, Lanzhou 730050, China2.School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China |
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| Abstract: | A modified generalized differential quadrature (MGDQ) method is utilized to investigate the coupling vibration and buckling characteristics of functionally graded material (FGM) beams with even porosity distribution in thermal environment and under the action of an initial axial mechanical force. Various types of temperature distributions are considered through the thickness direction, and the material properties are temperature-dependent according to modified Voigt mixture power-law model with porosity. Using an n-th order generalized beam theory (GBT), the free vibration and buckling governing equations for this system are derived by Hamiltonian principle as a unity. The control parameters for three different boundary conditions are proposed, and the MGDQ method can be utilized to solve the coupling vibration response with MATLAB computational procedure. Based on the duality between the static and dynamic behaviors of the structure, the buckling responses are obtained by writing loop subprogram, which can greatly simplify decoupling process and improve calculation efficiency. The effects of various beam theories, boundary conditions, different types of temperature rise, initial axial force, thermal-mechanical loads, porosity, material graded index and slenderness ratios on the vibration and buckling behaviors of FGM beams are discussed, and the significant duality for the two different mechanical behaviors of the structure are also revealed by several numerical examples. |
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