FGM中厚圆板轴对称自由振动的打靶法求解

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振动与冲击 ›› 2016, Vol. 35 ›› Issue (18) : 95-100.

论文

李清禄1，张靖华1，李世荣2

作者信息 +

Numerical Solution of the Free vibration of functionally graded material moderately thick circular plates by shooting method

LI Qinglu1, ZHANG Jinghua1, LI Shirong2

Author information +

文章历史 +

摘要

研究了由陶瓷和金属两种材料组成的功能梯度材料(FGM)中厚圆板的自由振动问题。基于考虑横向剪切变形中厚板的几何方程、物理方程及平衡方程,建立了以中面转角和横向位移为基本未知量的功能梯度中厚圆板轴对称自由振动问题的控制方程;假定功能梯度中厚圆板的材料性质方向按照幂函数连续变化规律;采用打靶法数值求解所得非线性两点边值问题出，获得了多种边界下功能梯度中厚圆板的无量纲自然频率以及振动模态。讨论了材料梯度指数、板的厚度以及边界条件对自然频率的影响。

Abstract

The free vibration of FGM moderately thick circular plates was investigated.A FGM plate consisting of metal and ceramic was considered in the study.Based on the geometric equation, physical equation and equilibrium equation of thick plates, taking into account the transverse shearing deformation, the free vibration equation of axisymmetric FGM thick circular plates was derived in terms of the middle surface angles of rotation and lateral displacement.The material properties of the plate were assumed to vary continuously in the thickness direction according to a power law.By using the shooting method to solve the coupled ordinary differential equations with different boundary conditions, the natural frequencies of FGM thick circular plates were obtained numerically.The effects of material gradient property, thickness ratio and boundary conditions on the natural frequencies were discussed in detail.

导出引用

李清禄1，张靖华1，李世荣2. FGM中厚圆板轴对称自由振动的打靶法求解[J]. 振动与冲击, 2016, 35(18): 95-100

LI Qinglu1, ZHANG Jinghua1, LI Shirong2. Numerical Solution of the Free vibration of functionally graded material moderately thick circular plates by shooting method[J]. Journal of Vibration and Shock, 2016, 35(18): 95-100

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