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Journal of Vibration Engineering & Technologies

, Volume 6, Issue 6, pp 483–494 | Cite as

Free Vibration Analysis of Functionally Graded Shaft System with a Surface Crack

  • Debabrata Gayen
  • Debabrata ChakrabortyEmail author
  • Rajiv Tiwari
Original Paper
  • 10 Downloads

Abstract

Background

Free vibration analysis of functionally graded (FG) non-spinning simply supported shaft having a transverse surface crack has been carried out. Material properties of the FG shaft are assumed to be graded radially following the power law of material gradation.

Method

Local flexibility coefficients as a function of depth of crack are computed with the help of Paris’ equation along with Castigliano’s theorem. Finite element (FE) formulation has been done using Timoshenko beam elements with two nodes and having four degrees of freedom per node. Based on the formulation, FE analysis has been performed to understand the effects of shaft’s slenderness, crack’s depth and location, gradient parameter and thermal gradient on the free vibration response of the cracked FG shaft.

Results

FE analysis show that for a cracked FG shaft, both gradation parameter and crack parameters have significant influence on the free vibration response.

Conclusions

Gradation parameter could be suitably chosen in the design of FG shafts so as to minimize the increase in flexibility due to appearance of cracks.

Keywords

Functionally graded material Material gradient index Flexibility coefficient Cracked shaft Temperature effects 

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Copyright information

© Krishtel eMaging Solutions Private Limited 2018

Authors and Affiliations

  • Debabrata Gayen
    • 1
  • Debabrata Chakraborty
    • 1
    Email author
  • Rajiv Tiwari
    • 1
  1. 1.Mechanical Engineering DepartmentIndian Institute of Technology GuwahatiGuwahatiIndia

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