Modal frequency analysis of metallic-ceramic functionally graded plates
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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。Abstract: Metallic-ceramic functionally graded materials have potential application value in the design of thermal barrier systems for aircraft panels due to their ultrahigh temperature resistant and high strength properties. In this article, the FGMs plate was used as the object to study the influence of parameters such as the volume fraction index, the geometric size of the plate and the thermal environment on the modal frequencies of a FGMs plate. Firstly, the power law distribution function was employed to discuss the influence of thermal environment on the physical properties of FGMs plates. Thereafter, the FGMs linear layered model dependent on temperature field was established by using the temperature continuously changing with the spatial position trait in the finite element, and the validity of this model in dynamic analysis was verified. Finally, the effects of ceramic volume fraction index, FGMs plate length-to-width ratio, temperature gradient and other variables on the modal frequencies of a FGMs plate were comprehensively analyzed and discussed. Results indicate that the higher order modes are mostly impacted by the uniform temperature field, while the linear and nonlinear temperature fields have the greatest impact on the first-order modes. In linear and nonlinear temperature fields, the volume fraction index is the most sensitive one to the effects of modal frequency drop ratio, while the modal frequency drop ratio is mainly affected by the coupling effect of the volume fraction index and the temperature gradient in uniform temperature field.
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Key words:
- functionally graded material /
- modal frequency /
- linear-layered /
- thermal environment
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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 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
Parameter Material α-1，α3 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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