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Vibration analysis and crack identification of a rotor with open cracks

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Abstract

A finite element model is used for flexural vibration analysis of a static (non-rotating) rotor with open cracks; the stiffness matrices of the cracked elements are obtained using transfer matrix analysis and local flexibility theorem. Through numerical simulation, the effects of the slenderness ratio and the crack depth on the mode shapes and the changes in the eigenfrequencies of the cracked rotor are investigated; the variations of the changes in eigenfrequencies with crack location are studied; and the ratios of the changes in the first two eigenfrequencies are discussed for rotors with two cracks. Then, crack identification algorithms for one unknown crack case and for two unknown cracks case are proposed, and illustrative examples are demonstrated to verify the validity of the proposed algorithms.

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References

  1. Gasch R.: A survey of the dynamic behavior of a simple rotating shaft with a transverse crack. J. Sound Vib. 160(2), 313–332 (1993)

    Article  MATH  Google Scholar 

  2. Gasch R.: Dynamic behavior of a simple rotor with a cross-sectional crack. In: Vibrations in Rotating Machinery, pp. 123–128. IMechE Conference Publication, London (1976)

  3. Dimarogonas A.D.: Vibration of cracked structures: a state of the art review. Eng. Fracture Mech. 55(5), 831–857 (1996)

    Article  Google Scholar 

  4. Dimarogonas A.D., Paipetis S.A.: Analytical Methods in Rotor Dynamics. Applied Science Publisher, New York (1983)

    Google Scholar 

  5. Papadopoulos C.A.: Torsional vibrations of rotors with transverse surface cracks. Comput. Struct. 51(6), 713–718 (1994)

    Article  MATH  Google Scholar 

  6. Armon D., Haim Y.B., Braun S.: Crack detection in beams by rank-ordering of eigenfrequency shifts. Mech. Syst. Signal Process. 8(1), 81–91 (1994)

    Article  Google Scholar 

  7. Lee Y.S., Chung M.J.: A study on crack detection using eignenfrequency test data. Comput. Struct. 77(3), 327–342 (2000)

    Article  MathSciNet  Google Scholar 

  8. Dong G.M., Chen J., Zou J.: Parameter identification of a rotor with an open crack. Eur. J. Mech. A Solids 23, 325–333 (2004)

    Article  MATH  Google Scholar 

  9. Stubbs N., Broome T.H., Osegueda R.: Nondestructive construction error detection in large space structures. AIAA J. 28(1), 146–152 (1990)

    Article  Google Scholar 

  10. Ostachowicz W.M., Krawczuk M.: Analysis of the effect of cracks on the natural frequencies of a cantilever beam. J. Sound Vib. 150(2), 191–201 (1991)

    Article  Google Scholar 

  11. Hu J.L., Liang R.Y.: An integrated approach to detection of cracks using vibration characteristics. J. Franklin Inst. 330(5), 841–853 (1993)

    Article  MATH  Google Scholar 

  12. Ruotolo R., Surace C.: Damage assessment of multiple cracked beams: numerical results and experimental validation. J. Sound Vib. 206(4), 567–588 (1997)

    Article  Google Scholar 

  13. Sekhar A.S.: Vibration characteristics of a cracked rotor with two open cracks. J. Sound Vib. 223(4), 497–512 (1999)

    Article  Google Scholar 

  14. Gudmundson P.: The dynamic behavior of slender structures with cross-sectional cracks. J. Mech. Phys. Solids 31(4), 329–345 (1983)

    Article  MATH  Google Scholar 

  15. Gounaris G., Dimarogonas A.: A finite element of a cracked prismatic beam for structural analysis. Comput. Struct. 28(3), 309–313 (1988)

    Article  MATH  Google Scholar 

  16. Nikolakopoulos P.G., Katsareas D.E., Papadopoulos C.A.: Crack identification in frame structures. Comput. Struct. 64(1–4), 389–406 (1997)

    Article  MATH  Google Scholar 

  17. Qian G.L., Gu S.N., Jiang J.S.: The dynamic behavior and crack detection of a beam with a crack. J. Sound Vib. 138(2), 233–243 (1990)

    Article  Google Scholar 

  18. Dimarogonas A.D., Papadopoulos C.A.: Vibration of cracked shafts in bending. J. Sound Vib. 91(4), 583–593 (1983)

    Article  MATH  Google Scholar 

  19. Adams R.D., Cawley P., Pye C.J. et al.: A vibration technique for non-destructively assessing the integrity of structures. J. Mech. Eng. Sci. 20(2), 93–100 (1978)

    Article  Google Scholar 

  20. Cawley P., Adams R.D.: The location of defects in structures from measurements of natural frequencies. J. Strain Anal. Eng. Des. 14(2), 49–57 (1979)

    Article  Google Scholar 

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Authors and Affiliations

  1. The State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240, People’s Republic of China

    Guangming Dong & Jin Chen

Authors
  1. Guangming Dong
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  2. Jin Chen
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Correspondence to Jin Chen.

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Dong, G., Chen, J. Vibration analysis and crack identification of a rotor with open cracks. Japan J. Indust. Appl. Math. 28, 171–182 (2011). https://doi.org/10.1007/s13160-011-0031-3

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  • DOI: https://doi.org/10.1007/s13160-011-0031-3

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