Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (5): 607-615.doi: https://doi.org/10.1007/s10483-009-0507-x

• Articles • 上一篇    下一篇

Vibrations of FGM thin cylindrical shells with exponential volume fraction law

Abdul Ghafar Shah1  Tahir Mahmood1  Muhammad Nawaz Naeem2   

  1. 1. Department of Mathematics, The Islamia University of Bahawalpur, Pakistan;
    2. Department of Mathematics, Government College University,Faisalabad, Pakistan
  • 收稿日期:2008-11-30 修回日期:2009-01-29 出版日期:2009-05-01 发布日期:2009-05-01

Vibrations of FGM thin cylindrical shells with exponential volume fraction law

Abdul Ghafar Shah1  Tahir Mahmood1  Muhammad Nawaz Naeem2   

  1. 1. Department of Mathematics, The Islamia University of Bahawalpur, Pakistan;
    2. Department of Mathematics, Government College University,Faisalabad, Pakistan
  • Received:2008-11-30 Revised:2009-01-29 Online:2009-05-01 Published:2009-05-01

摘要: In this paper, the influence of an exponential volume fraction law on the vibration frequencies of thin functionally graded cylindrical shells is studied. Material properties in the shell thickness direction are graded in accordance with the exponential law. Expressions for the strain-displacement and curvature-displacement relationships are taken from Love’s thin shell theory. The Rayleigh-Ritz approach is used to derive the shell eigenfrequency equation. Axial modal dependence is assumed in the characteristic beam functions. Natural frequencies of the shells are observed to be dependent on the constituent volume fractions. The results are compared with those available in the literature for the validity of the present methodology.

关键词: functionally graded material (FGM), vibration, cylindrical shell, Rayleigh- Ritz method, exponential volume fraction law

Abstract: In this paper, the influence of an exponential volume fraction law on the vibration frequencies of thin functionally graded cylindrical shells is studied. Material properties in the shell thickness direction are graded in accordance with the exponential law. Expressions for the strain-displacement and curvature-displacement relationships are taken from Love’s thin shell theory. The Rayleigh-Ritz approach is used to derive the shell eigenfrequency equation. Axial modal dependence is assumed in the characteristic beam functions. Natural frequencies of the shells are observed to be dependent on the constituent volume fractions. The results are compared with those available in the literature for the validity of the present methodology.

Key words: functionally graded material (FGM), vibration, cylindrical shell, Rayleigh- Ritz method, exponential volume fraction law

中图分类号: 

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals