Vibration Analysis of a Three-Layered FGM Cylindrical Shell including the Effect of Ring Support

Madiha Ghamkhar, Muhammad Nawaz Naeem, Muhammad Imran, Constantinos Soutis

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In this work, we study vibrations of three-layered cylindrical shells with one ring support along its length. Nature of material of the central layer is a functionally graded material (FGM) type. The considered FGM is of stainless steel and nickel. The internal and external layers are presumed to be made of isotropic material i.e., aluminum. The functionally graded material composition of the center layer is assorted by three volume fraction laws (VFL) which are represented by mathematical expressions of polynomial, exponential and trigonometric functions. The implementation of Rayleigh-Ritz method has been done under the Sanders' shell theory to obtain the shell frequency equation. Natural frequencies (NFs) are attained for the present model problem under six boundary conditions. Use of characteristic beam functions is made for the estimation of the dependence of axial modals. The impact of layer material variations with ring support is considered for many ring positions. Also the effect of volume fraction laws is investigated upon vibration characteristics. This investigation is performed for various physical parameters. Numerous comparisons of values of shell frequencies have been done with available models of such types of results to verify accuracy of the present formulation and demonstrate its numerical efficiency.

Original languageEnglish
Pages (from-to)587-600
Number of pages14
JournalOpen Physics
Issue number1
Early online date6 Oct 2019
Publication statusPublished - 2019


  • cylindrical shell
  • functionally graded material
  • isotropic material
  • Rayleigh-Ritz method
  • ring support
  • Sanders' shell theory


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