Vibrations of FGM Thin Cylindrical Shells With Exponential Volume Fraction Law

Abdul Ghafar Shah; Tahir Mahmood; Muhammad Nawaz Naeem

doi:10.3879/j.issn.1000-0887.2009.05.007

Volume 30 Issue 5

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Abdul Ghafar Shah, Tahir Mahmood, Muhammad Nawaz Naeem. Vibrations of FGM Thin Cylindrical Shells With Exponential Volume Fraction Law[J]. Applied Mathematics and Mechanics, 2009, 30(5): 567-574. doi: 10.3879/j.issn.1000-0887.2009.05.007

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Vibrations of FGM Thin Cylindrical Shells With Exponential Volume Fraction Law

doi: 10.3879/j.issn.1000-0887.2009.05.007

1.
Department of Mathematics, the Islamia University of Bahawalpur, Pakistan;
Department of Mathematics, Government College University, Faisalabad, Pakistan

Received Date: 2008-10-09
Rev Recd Date: 2009-01-03
Publish Date: 2009-05-15

Abstract

Abstract

The influence of an exponential volume fraction law on the vibration frequencies of thin functionally graded cylindrical shells was studied. Material properties in the shell thickness direction were graded in a ccordance with the exponential law. Expressions for the strain-displacement and curvature-displacement relationships were taken from Love.s thin shell theory. The Rayleigh-Ritz approach was used to derive the shell eigenfr equency 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.
- exponential volume fraction law,
- functionally graded materials(FGM),
- cylindrical shells,
- vibrations,
- the Rayleigh-Ritz approach

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References(23)

References

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