Applied Mathematics and Mechanics

, Volume 29, Issue 12, pp 1601–1616 | Cite as

Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders

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Abstract

Analytical solutions to rotating functionally graded hollow and solid long cylinders are developed. Young’s modulus and material density of the cylinder are assumed to vary exponentially in the radial direction, and Poisson’s ratio is assumed to be constant. A unified governing equation is derived from the equilibrium equations, compatibility equation, deformation theory of elasticity and the stress-strain relationship. The governing second-order differential equation is solved in terms of a hypergeometric function for the elastic deformation of rotating functionally graded cylinders. Dependence of stresses in the cylinder on the inhomogeneous parameters, geometry and boundary conditions is examined and discussed. The proposed solution is validated by comparing the results for rotating functionally graded hollow and solid cylinders with the results for rotating homogeneous isotropic cylinders. In addition, a viscoelastic solution to the rotating viscoelastic cylinder is presented, and dependence of stresses in hollow and solid cylinders on the time parameter is examined.

Key words

rotating hollow cylinder solid shaft functionally graded materials 

Chinese Library Classification

O343 

2000 Mathematics Subject Classification

74B05 74D05 
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Copyright information

© Shanghai University and Springer-Verlag GmbH 2008

Authors and Affiliations

  • A. M. Zenkour
    • 1
    • 2
  • K. A. Elsibai
    • 3
  • D. S. Mashat
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of Mathematics, Faculty of EducationKafr El-Sheikh UniversityKafr El-SheikhEgypt
  3. 3.Department of Mathematics, Faculty of ScienceMansoura UniversityjMansouraEgypt

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