摘要
采用弹性理论建立了功能梯度材料板的静力平衡方程,利用静力平衡方程确定了功能梯度材料板的中性面位置,在此基础上推导出了功能梯度材料板在均匀温度场中的非线性振动及屈曲微分方程组,求得了功能梯度材料椭圆板的非线性振动及屈曲的近似解,讨论分析了中性面位置、梯度指数、温度等因素对功能梯度材料椭圆板非线性振动及屈曲的影响.把该方法计算结果与有限元计算结果进行了比较,验证了该方法的计算结果是可靠的.算例分析表明,中性面位置对均匀温度场中功能梯度材料椭圆板的非线性振动及屈曲有一定影响.
The static equilibrium equation of functionally graded circular plate was established by using elastic theory, and the neutral plane site of functionally graded elliptical plate was determined. On the basis, the nonlinear vibration and buckling differential equations for the functionally graded elliptical plate in uniform temperature field were derived, the approximate solution to nonlinear thermal vibration and buckling of functionally graded circular plate was obtained, and the effect of neutral plane site, gradient index and temperature on nonlinear thermal vibration and buckling of functionally graded elliptical plate was discussed and analyzed. The calculation resuits agreed well with the results, which verified the method. Analysis of examples indicates that the neutral plane site has certain influence on nonlinear thermal vibration and buckling of functionally graded elliptical plate in uniform temperature field.
出处
《动力学与控制学报》
2013年第2期165-171,共7页
Journal of Dynamics and Control
基金
湖南省"十二五"重点建设学科(机械设计及理论)
湖南省教育厅项目(11A081)~~
关键词
功能梯度
材料
椭圆板
非线性
振动
屈曲
functionally graded
materials
elliptical plate
nonlinear
vibration
buckling
