热环境下功能梯度矩形和斜板的非线性自由弯曲振动
Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments
AI总结：
基于von Karman假设的非线性公式，采用有限元法和直接迭代技术，研究了温度场和梯度指数对功能梯度板非线性振动频率比的影响。
摘要：
采用基于von Karman假设的非线性公式，研究了功能梯度材料（FGM）板在热环境下的自由振动特性。假设温度场在板表面均匀分布，并沿厚度方向变化。材料属性假设为温度相关，并沿厚度方向根据组分的体积分数按幂律分布梯度变化。利用Mori-Tanaka均匀化方法，根据组分的体积分数和材料属性估算有效材料属性。通过拉格朗日运动方程得到非线性控制方程，采用有限元程序结合直接迭代技术求解。重点考虑了梯度指数、温度、厚度、长宽比和斜角等参数对非线性频率比随振幅变化的影响。数值示例中，以氮化硅/不锈钢作为功能梯度材料。结果表明，温度场和梯度指数对功能梯度板的非线性振动有显著影响。
英文摘要：
The nonlinear formulation developed based on von Karman's assumptions is employed to study the free vibration characteristics of functionally graded material (FGM) plates subjected to thermal environment. Temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction. The material is assumed to be temperature dependent and graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents. The effective material properties are estimated from the volume fractions and the material properties of the constituents using Mori-Tanaka homogenization method. The nonlinear governing equations obtained using Lagrange's equations of motion are solved using finite element procedure coupled with the direct iteration technique. The variation of nonlinear frequency ratio with amplitude is highlighted considering various parameters such as gradient index, temperature, thickness and aspect ratios, and skew angle. For the numerical illustrations, silicon nitride/stainless steel is considered as functionally graded material. The results obtained here reveal that the temperature field and gradient index have significant effect on the nonlinear vibration of the functionally graded plate.
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