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Journal of Failure Analysis and Prevention

, Volume 18, Issue 4, pp 782–790 | Cite as

Failure Analysis of Composite Mono Leaf Spring Using Modal Flexibility and Curvature Method

  • N. I. Jamadar
  • S. B. Kivade
  • Rakesh Raushan
Technical Article---Peer-Reviewed
  • 78 Downloads

Abstract

Post-failure analysis of composite structures by damage identification at pre-stage has gained considerable interest in recent years. In the paper, modal flexibility and modal curvature methods have been used for premature failure analysis of composite mono leaf spring through analytical and finite element approaches. Initially, finite element model of healthy and cracked spring is used to evaluate the eigenvalue and eigenvectors. Subsequently, change in flexibility and absolute curvature difference among both springs are evaluated after mass normalization. The presence, location and severity of crack in a spring are identified through differences in local flexibilities and change in absolute modal curvatures. The modal curvature method predicts location and severity of crack more precisely than the modal flexibility method.

Keywords

Failure analysis Modal flexibility Modal curvature Composite mono leaf spring Analytical Healthy and cracked spring 

List of symbols

Me

Elemental mass of healthy beam

Me*

Elemental mass of cracked beam

Ke

Elemental stiffness of healthy beam

Ke*

Elemental stiffness of cracked beam

le

Elemental length of beam

K

Assembled stiffness matrix of healthy beam

K*

Assembled stiffness matrix of cracked beam

M

Assembled mass matrix of healthy beam

M*

Assembled mass matrix of cracked beam

U

Eigenvector

[F]hx

Flexibility matrix of healthy beam at distance x

[F]dx

Flexibility matrix of cracked beam at distance x

Uxi

Mass normalized modal vector at distance x

Δ[F]

Change in flexibility

M(x)

Bending moment of healthy beam at distance x

M*(x)

Bending moment of cracked beam at distance x

K(x)

Curvature of healthy beam at distance x

K*(x)

Curvature of cracked beam at distance x

Δ[K]

Absolute modal curvature difference

Uh1, Uh2, Uh3 and Uh4

Are the normalized eigenvectors of healthy beam for 1st, 2nd, 3rd and 4th modes, respectively

Ud1, Ud2, Ud3 and Ud4

Are the normalized eigenvectors of cracked beam for 1st, 2nd, 3rd and 4th modes, respectively

Kh1, Kh2, Kh3 and Kh4

Are the modal curvatures of healthy beam for 1st, 2nd, 3rd and 4th modes, respectively

Kd1, Kd2, Kd3 and Kd4

Are the modal curvatures of cracked beam for 1st, 2nd, 3rd and 4th modes, respectively

References

  1. 1.
    M. He, Y. Tao Yang, Nondestructive identification of composite beams damage based on the curvature mode difference. J. Compos. Struct. (2017).  https://doi.org/10.1016/j.comp.struct.2017.05.040 Google Scholar
  2. 2.
    X. Zhoua, D. Wangb, M. Duana, J. Gua, Y. Liuaa, Numerical study on mode curvature for damage detection of a drilling riser using transfer matrix technique. J. Appl. Ocean Res. 2017(63), 65–75 (2017)CrossRefGoogle Scholar
  3. 3.
    Z.-B. Yang, M. Radzienski, P. Kudela, W. Ostachowicz, Fourier spectral-based modal curvature analysis and its application to damage detection in beams. J. Mech. Syst. Signal Process. (2016).  https://doi.org/10.1016/j.ymssp.2016.07.005 Google Scholar
  4. 4.
    Z.-B. Yang, M. Radzienski, P. Kudela, W. Ostachowicz, Scale-wave number domain filtering method for curvature modal damage detection. J. Compos. Struct. (2016).  https://doi.org/10.1016/j.compstruct.2016.07.074 Google Scholar
  5. 5.
    D. Dessi, G. Camerlengo, Damage identification techniques via modal curvature analysis: overview and comparison. J. Mech. Syst. Signal Process. 52–53, 181–205 (2015)CrossRefGoogle Scholar
  6. 6.
    V.B. Dawari, G.R. Vesmawala, Modal curvature and flexibility methods for honeycomb damage identification in reinforced concrete beams. Proc. Eng. 51, 119–124 (2013)CrossRefGoogle Scholar
  7. 7.
    S. Russo, Damage assessment of GFRP putruded structural elements. Compos. Struct. 96, 661–669 (2013)CrossRefGoogle Scholar
  8. 8.
    E. Ekinovic, S. Ekinovic, R. Sunulahpasic, A Glance to a mode shape based damage detection technique, in 17th International Research/Expert Conference TMT 2013, Istanbul, Turkey Google Scholar
  9. 9.
    W. Lestari, P. Qiao, Damage detection of fiber-reinforced polymer honeycomb sandwich beams. Compos. Struct. 67, 365–373 (2005)CrossRefGoogle Scholar
  10. 10.
    H.P. Zhu, Y.L. Xu, Damage detection of mono coupled periodic structures based on sensitivity analysis of modal parameters. J. Sound Vib. 285, 365–390 (2005)CrossRefGoogle Scholar
  11. 11.
    E.-T. Lee, H.-C. Eun, Damage detection approach based on the second derivative of flexibility estimated from incomplete mode shape data. Appl. Math. Model. (2017).  https://doi.org/10.1016/j.apm.2017.02.014 Google Scholar
  12. 12.
    S.H. Sung, K.Y. Koo, H.J. Jung, Modal flexibility-based damage detection of cantilever beam-type structures using baseline modification. J. Sound Vib. 333, 4123–4138 (2014)CrossRefGoogle Scholar
  13. 13.
    M.S. Gaith, Nondestructive health monitoring of cracked simply supported fiber-reinforced composite structures. J. Intell. Mater. Syst. Struct. 22(18), 2207–2214 (2011)CrossRefGoogle Scholar
  14. 14.
    E. Reynders, G. De Roeck, A local flexibility method for vibration- based damage localization and quantification. J. Sound Vib. 329, 2367–2383 (2010)CrossRefGoogle Scholar
  15. 15.
    L. Yu, T. Yin, Damage identification in frame structures based on FE model updating. J. Vib. Acoust. 132(5), 051007 (2010)CrossRefGoogle Scholar
  16. 16.
    M.A.B. Abdo, M. Hori, A numerical study of structural damage detection using changes in the rotation of mode shapes. J. Sound Vib. 251(2), 227–239 (2002)CrossRefGoogle Scholar
  17. 17.
    A.K. Pandey, M. Biswas, Experimental verification of flexibility difference method for locating damage in structures. J. Sound Vib. 184(2), 311–328 (1995)CrossRefGoogle Scholar
  18. 18.
    M.M.F. Yuen, A numerical study of the Eigen parameters of a damaged cantilever. J. Sound Vib. 103(3), 301–310 (1985)CrossRefGoogle Scholar
  19. 19.
    Society of Automotive Engineers, Inc. 400 Commonwealth Drive, Warrendale, PA, pp. 15096–0001.Google Scholar
  20. 20.
    Ansys Design nCode Manual, HBM, 2010Google Scholar

Copyright information

© ASM International 2018

Authors and Affiliations

  1. 1.Research Resource CenterVTUKalaburagi RegionIndia
  2. 2.Basavakalyan Engineering CollegeBasavakalyanIndia
  3. 3.Dr. D. Y. Patil Institute of TechnologyPimpri, PuneIndia

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