Transverse Vibration and Stability of a Cracked Functionally Graded Rotating Shaft System

  • Debabrata GayenEmail author
  • Debabrata Chakraborty
  • Rajiv Tiwari
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Transverse vibration and stability of functionally graded (FG) shafts containing a transverse surface crack are studied considering material nonlinearity. Based on Timoshenko beam theory (TBT), a finite element (FE) model is developed for an FG shaft. Under thermal environment, material properties of radially graded FG shafts are considered using power law of material gradation. Stainless steel (SS), alumina (Al2O3) and zirconia (ZrO2) are used as constituent materials of FGM I (SS/Al2O3) and FGM II (SS/ZrO2). Local flexibility coefficients (LFCs) are computed as functions of temperature, size of crack and material gradient index based on linear elastic fracture mechanics. Influences of FGM type, material gradient, temperature gradient and crack size on dynamics of cracked FG rotors system are studied. Results show that beside the crack and geometric parameters, the choice of gradient index has importance on dynamics of the FG shaft for high-temperature applications.


FG cracked shaft Power law gradient index Temperature dependency material property Natural whirling frequency Stability threshold speed 


  1. 1.
    Reddy, J.N., Chin, C.D.: Thermoelastical analysis of functionally graded cylinders and plates. J. Therm. Stresses 21, 593–626 (1998)CrossRefGoogle Scholar
  2. 2.
    Gayen, D., Roy, T.: Finite element based vibration analysis of functionally graded spinning shaft system. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 228(18), 3306–3321 (2014)CrossRefGoogle Scholar
  3. 3.
    Nelson, H.D., Mcvaugh, J.M.: The dynamics of rotor bearing systems using finite elements. ASME Trans. J. Eng. Ind. 98, 593–600 (1976)CrossRefGoogle Scholar
  4. 4.
    Zorzi, E.S., Nelson, H.D.: Finite element simulation of rotor-bearing systems with internal damping. ASME Trans. J. Eng. Power 99(1), 71–76 (1977)CrossRefGoogle Scholar
  5. 5.
    Chen, L.W., Ku, D.M.: Finite element analysis of natural whirl speeds of rotating shafts. Comput. Struct. 40(3), 741–747 (1991)CrossRefGoogle Scholar
  6. 6.
    Sekhar, A.S., Dey, J.K.: Effects of cracks on rotor system instability. Mech. Mach. Theory 35(12), 1657–1674 (2000)CrossRefGoogle Scholar
  7. 7.
    Yang, J., Chen, Y.: Free vibration and buckling analyses of functionally graded beams with edge cracks. Compos. Struct. 83(1), 48–60 (2008)CrossRefGoogle Scholar
  8. 8.
    Gayen, D., Chakraborty, D., Tiwari, R.: Free vibration analysis of functionally graded shaft system with a surface crack. J. Vib. Eng. Technol. 6, 483–494 (2018)CrossRefGoogle Scholar
  9. 9.
    Gayen, D., Chakraborty, D., Tiwari, R.: Whirl frequencies and critical speeds of a rotor-bearing system with a cracked functionally graded shaft—finite element analysis. Eur. J. Mech. A Solids 61, 47–58 (2017)CrossRefGoogle Scholar
  10. 10.
    Gayen, D., Chakraborty, D., Tiwari, R.: Finite element analysis for a functionally graded rotating shaft with multiple breathing cracks. Int. J. Mech. Sci. 134, 411–423 (2017)CrossRefGoogle Scholar
  11. 11.
    Touloukian, Y.S.: Thermophysical Properties of High Temperature Solid Materials. McMillan, New York (1967)Google Scholar
  12. 12.
    Tada, H., Paris, P.C., Irwin, G.R.: The Stress Analysis of Cracks Handbook. Del Research Corporation, USA (1973)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Debabrata Gayen
    • 1
    Email author
  • Debabrata Chakraborty
    • 1
  • Rajiv Tiwari
    • 1
  1. 1.Department of Mechanical EngineeringIndian Institute of Technology GuwahatiGuwahatiIndia

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