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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (9): 1077-1082.doi: https://doi.org/10.1007/s10483-009-0901-x

• Articles •    下一篇

Free axisymmetric vibration of FGM circular plates

王云1,2 徐荣桥1 丁浩江1   

  1. 1. Department of Civil Engineering, Zijingang Campus, Zhejiang University,Hangzhou 310058, P. R. China;
    2. School of Mechanical Engineering, Hangzhou Dianzi University,Hangzhou 310018, P. R. China
  • 收稿日期:2009-04-26 修回日期:2009-06-30 出版日期:2009-09-01 发布日期:2009-09-01

Free axisymmetric vibration of FGM circular plates

WANG Yun1,2, XU Rong-Qiao1, DING Hao-Jiang1   

  1. 1. Department of Civil Engineering, Zijingang Campus, Zhejiang University,Hangzhou 310058, P. R. China;
    2. School of Mechanical Engineering, Hangzhou Dianzi University,Hangzhou 310018, P. R. China
  • Received:2009-04-26 Revised:2009-06-30 Online:2009-09-01 Published:2009-09-01

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摘要： Based on the three-dimensional theory, this work presents a direct displacement method to investigate the free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded and properties obey the exponential law along the thickness direction of the plate. Under two boundary conditions, the solution satisfies all basic equations and the corresponding boundary condition at every point. Thus, it is three-dimensional exact. Numerical examples are presented and compared with previous works. The present method can also be extended to the case of arbitrary distribution of the material properties along the thickness direction of the plate.

关键词: functionally graded material (FGM), circular plate, free vibration, axisymmetry

Abstract: Based on the three-dimensional theory, this work presents a direct displacement method to investigate the free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded and properties obey the exponential law along the thickness direction of the plate. Under two boundary conditions, the solution satisfies all basic equations and the corresponding boundary condition at every point. Thus, it is three-dimensional exact. Numerical examples are presented and compared with previous works. The present method can also be extended to the case of arbitrary distribution of the material properties along the thickness direction of the plate.

Key words: functionally graded material (FGM), circular plate, free vibration, axisymmetry

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