金属陶瓷功能梯度板的模态频率分析

刘超 刘文光

刘超, 刘文光. 金属陶瓷功能梯度板的模态频率分析[J]. 航空材料学报, 2020, 40(5): 88-95. doi: 10.11868/j.issn.1005-5053.2020.000087
引用本文: 刘超, 刘文光. 金属陶瓷功能梯度板的模态频率分析[J]. 航空材料学报, 2020, 40(5): 88-95. doi: 10.11868/j.issn.1005-5053.2020.000087
Chao LIU, Wenguang LIU. Modal frequency analysis of metallic-ceramic functionally graded plates[J]. Journal of Aeronautical Materials, 2020, 40(5): 88-95. doi: 10.11868/j.issn.1005-5053.2020.000087
Citation: Chao LIU, Wenguang LIU. Modal frequency analysis of metallic-ceramic functionally graded plates[J]. Journal of Aeronautical Materials, 2020, 40(5): 88-95. doi: 10.11868/j.issn.1005-5053.2020.000087

金属陶瓷功能梯度板的模态频率分析

doi: 10.11868/j.issn.1005-5053.2020.000087
基金项目: 国家自然科学基金(51965042);江西省自然科学基金(20181BAB206023)
详细信息
    通讯作者:

    刘文光(1978—),男,博士,副教授,主要从事结构动力学及疲劳寿命预测研究,E-mail:liuwg14@nchu.edu.cn

  • 中图分类号: TH212

Modal frequency analysis of metallic-ceramic functionally graded plates

  • 摘要: 金属陶瓷功能梯度材料因其良好的耐热特性和高强度性能,在飞行器壁板的热防护系统设计中具有潜在的应用价值。以功能梯度板为对象,研究陶瓷体积分数指数、板的几何尺寸和热环境等参数对功能梯度板模态频率的影响。首先,采用幂律分布函数材料模型,讨论热环境对功能梯度材料物理特性的影响;在此基础上,利用温度在有限元中随空间位置连续变化的特点,建立依赖温度场变化的功能梯度材料板线性分层有限元模型,并验证该模型在动力学分析中的有效性;最后,分析陶瓷体积分数指数、功能梯度板的长宽比、温度梯度等变量对功能梯度板模态频率的影响。结果表明:高阶模态频率受均匀温度场的影响最大,而第一阶模态频率受线性和非线性温度场的影响更大;线性和非线性温度场下,陶瓷体积分数指数对模态频率下降率的影响最为敏感;均匀温度场下模态频率下降率主要受体积分数指数和温度梯度耦合作用的影响。

     

  • 图  1  FGMs板模型

    Figure  1.  FGMs plate model

    图  2  FGMs板的分层建模方法

    Figure  2.  Modeling principle of FGMs plate

    图  3  三种温升下沿厚度方向温度场的分布

    Figure  3.  Distribution of temperature field along thickness direction under three temperature rises

    图  4  热环境对弹性模量的影响 (a)均匀温度场;(b)线性温度场;(c)非线性温度场

    Figure  4.  Effects of thermal environment on Young’s modulus (a) uniform temperature field;(b) linear temperature field;(c)nonlinear temperature field

    图  5  均匀温升下FGMs板前6阶模态频率对比 

    Figure  5.  Comparisons of the first six modal frequencies for FGMs plate subjected to uniform temperature rise

    图  6  模态频率的收敛性

    Figure  6.  Convergence of modal frequencies

    图  7  陶瓷体积分数指数和长宽比对模态频率的影响 (a)均匀温度场;(b)线性温度场;(c)非线性温度场

    Figure  7.  Effects of volume fraction index and aspect ratio on the modal frequencies (a)uniform temperature field;(b)linear temperature field;(c)nonlinear temperature field

    图  8  温度梯度和长宽比对模态频率的影响 (a)均匀温度场;(b)线性温度场;(c)非线性温度场

    Figure  8.  Effects of temperature gradient and aspect ratio on the modal frequencies (a)uniform temperature field;(b)linear temperature field;(c)nonlinear temperature field

    图  9  陶瓷体积分数指数和温度梯度对模态频率的影响 (a)均匀温度场;(b)线性温度场;(c)非线性温度场

    Figure  9.  Effects of volume fraction index and temperature gradient on the modal frequencies (a)uniform temperature field;(b)linear temperature field;(c)nonlinear temperature field

    图  10  热环境对模态下降率的影响 (a)均匀温度场;(b)线性温度场;(c)非线性温度场

    Figure  10.  Effects of thermal environment on the decrease ratio of modal frequencies (a)uniform temperature field;(b)linear temperature field;(c)nonlinear temperature field

    表  1  SUS304和Si3N4温敏特性系数[25]

    Table  1.   Temperature-dependent coefficients of SUS304 and Si3N4[25]

    Parameter Material α-1α3 α0 α1 α2
    Density,ρ SUS304 0 8166.00 0 0
    Si3N4 0 2370.00 0 0
    Young’s modulus,E SUS304 0 201.04 3.079 × 10-4 –6.534 × 10–7
    Si3N4 0 348.43 –3.070 × 10–4 2.160 × 10–7
    Heat transfer coefficient,β SUS304 0 12.04 0 0
    Si3N4 0 9.19 0 0
    Poisson’s ratio,ʋ SUS304 0 0.33 –2.002 × 10–4 0
    Si3N4 0 0.24 0 0
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出版历程
  • 收稿日期:  2020-05-19
  • 修回日期:  2020-06-16
  • 网络出版日期:  2020-08-28
  • 刊出日期:  2020-10-01

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