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应用4变量精确平板理论分析FG复合板的自由振动

L·哈吉 H·A·艾特阿特曼 A·杜尼斯 I·米查贝 N·茜安 E·A·A·贝迪亚

L·哈吉, H·A·艾特阿特曼, A·杜尼斯, I·米查贝, N·茜安, E·A·A·贝迪亚. 应用4变量精确平板理论分析FG复合板的自由振动[J]. 应用数学和力学, 2011, 32(7): 866-882. doi: 10.3879/j.issn.1000-0887.2011.07.010
引用本文: L·哈吉, H·A·艾特阿特曼, A·杜尼斯, I·米查贝, N·茜安, E·A·A·贝迪亚. 应用4变量精确平板理论分析FG复合板的自由振动[J]. 应用数学和力学, 2011, 32(7): 866-882. doi: 10.3879/j.issn.1000-0887.2011.07.010
Lazreg Hadji, Hassen Ait Atmane, Abdelouahed Tounsi, Ismail Mechab, Noureddine Ziane, El Abbas Adda Bedia. Free Vibration of Functionally Graded Sandwich Plates Using Four Variable Refined Plate Theory[J]. Applied Mathematics and Mechanics, 2011, 32(7): 866-882. doi: 10.3879/j.issn.1000-0887.2011.07.010
Citation: Lazreg Hadji, Hassen Ait Atmane, Abdelouahed Tounsi, Ismail Mechab, Noureddine Ziane, El Abbas Adda Bedia. Free Vibration of Functionally Graded Sandwich Plates Using Four Variable Refined Plate Theory[J]. Applied Mathematics and Mechanics, 2011, 32(7): 866-882. doi: 10.3879/j.issn.1000-0887.2011.07.010

应用4变量精确平板理论分析FG复合板的自由振动

doi: 10.3879/j.issn.1000-0887.2011.07.010
详细信息
  • 中图分类号: O323

Free Vibration of Functionally Graded Sandwich Plates Using Four Variable Refined Plate Theory

  • 摘要: 应用4变量的精确平板理论,对矩形功能梯度材料(FGM)复合板进行自由振动分析.与其它的理论不同,该理论的未知函数数量只有4个,而别的剪变形理论的未知函数为5个.提出的4变量精确平板理论,协调条件有了改变,与经典的薄板理论相比,许多方面有着惊人的相似,无需引入剪切修正因数——当横向剪应力越过板厚后,为了满足剪应力自由表面条件,出现抛物线状的改变,导致横向剪应力的变化.考虑了两种常见类型的FGM复合板,即,FGM表面层和各向同性夹芯层的复合板,以及各向同性表面层和FGM夹芯层的复合板.通过Hamilton原理,得到了FGM复合板的运动方程.得到闭式的Navier解,然后求解特征值问题,得到自由振动的基本频率.将该理论得到的结果,与经典理论,一阶的及其它更高阶的理论所得到的结果进行比较,检验了该理论的有效性.研究发现,该理论在求解FGM复合板自由振动性能方面,既精确又简单.
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出版历程
  • 收稿日期:  2010-10-18
  • 修回日期:  2011-04-17
  • 刊出日期:  2011-07-15

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