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

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

阿贝斯思迪贝尔大学流体材料实验室,阿贝斯思迪贝尔 22000,阿尔及利亚;
伊本卡尔顿大学土木工程系,扎鲁拉 BP 78,提亚雷特 14000,阿尔及利亚;

详细信息

中图分类号: O323
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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

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

Laboratoire des Matériaux et Hydrologie, Université de Sidi Bel Abbes, BP 89 Cité Ben M'hidi 22000 Sidi Bel Abbes, Algérie;
Département de génie civil, Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie;
Département de génie civil, Faculté des Sciences de l'Ingénieur, Univesité Hassiba Benbouali de Chlef, Algérie

摘要

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．
- 功能梯度材料(FGMs) /
- 自由振动 /
- 复合板 /
- 精确平板理论 /
- Navier解
Abstract: The novelty of this paper was the use of four variable refined plate theory for freevibration analysis of functionally graded material sand wich rectangular plates. Unlike any other theories, the numbe rofunknown functions involved was only four, as a gainst five in case of other shearde formation theories. The theory presented was variationally consistent, had strong smiilarity with classical plate theory in many a spects, did not require shear correction factor, and gave rise to tran sverse shear stress variation such that the trans verse shear stresses vary parabolically a cross the thickness satisfying shear stress free surface conditions. Two commonty pes of FGM sand wich plates, namely, the sand wich with FGM face sheet and homogeneouscore and the sandwich with homogeneous faceshee tand FGM core, were considered. The equation of motion for FGM sandwich plates was obtained through Hamilton. sprinciple. The closed form solutions were obtained by using Navierte chnique, and then fundamental frequencies were found by solving the results of eigenvalue problems. The validity of the present theory was investigated by comparing some of the present results with those of the classical, the firstorder and the other higherorder theories. It can be concluded that the proposed theory is a ccurate and simple in solving the free vibration beha vior of FGM sandwich plates.
- functionally graded materials /
- free vibration, sandwich plate /
- refined plate theory /
- Navier solution /

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