Skip to main content
SpringerLink
Log in

Displacement modal identification method of elastic system under operational condition

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Modal identification of engineering structure in operation deals with the estimation of modal parameters from vibration data obtained in working conditions rather than laboratory conditions. After one structure destruction during a flight test, it was strongly required to carry out full-scale model testing to acquire the low-frequency vibration acceleration data of the investigated rocket (its structural dynamic properties could be represented by a beam). These vibration data were used to assess the modal properties of the modified structure. In this paper, a new modal identification method based on vibration displacement is suggested. The displacements of the measured points on the rocket are obtained by the integration of the low-frequency vibration accelerations during free flight test. In the method, the data are filtered through wavelet transform. For comparison, several methods are used to extract the modal frequencies of the investigated beam. In terms of the results of standard deviation of identified frequencies, it is believed that the generalized displacement-based modal identification method is more practicable in modal identification for similar problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26

Similar content being viewed by others

Abbreviations

M,C,K :

mass, damping and stiffness matrix

:

displacement, velocity and acceleration vector at time t

p :

linear external force vector at time t

N :

non-linear external force matrix

t :

time, s

j :

index of generalized displacement, j=1,2,…,j r

j r :

number of generalized displacements

:

generalized displacement, velocity and acceleration vectors

Φ j :

jth shape function vector

Φ :

shape function matrix

Φ ij :

the jth shape function value in the position of the ith test point

q j (t k ):

jth generalized displacement value at time t k

q k :

vector of generalized displacements at time t k

i :

index of test point, i=1,2,…,m

k :

index of time

x i :

x coordinate of the test point along the beam’s axis

m :

number of acceleration test points

f 1 :

first mode frequency, Hz

(•)T :

transpose of matrix

DMIM:

Displacement Modal Identification Method

GDMIM:

Generalized Displacement-based Modal Identification Method

Fre.:

Frequency

Int.:

Interval of time period, s

Std.:

Standard deviation

RDT:

Random Decrement Technique

Disp.:

Displacement

References

  1. Reynders, E.: System identification methods for (operational) modal analysis: review and comparison. Arch. Comput. Methods Eng. 19, 51–124 (2012)

    Article  MathSciNet  Google Scholar 

  2. Živanović, S., Pavic, A., Reynolds, P.: Modal testing and FE model tuning of a lively footbridge structure. Eng. Struct. 28, 857–868 (2006)

    Article  Google Scholar 

  3. Carne, T.G., James, G.H. III: The inception of OMA in the development of modal testing technology for wind turbines. Mech. Syst. Signal Process. 24(5), 1213–1226 (2010)

    Article  Google Scholar 

  4. Hermans, L., Van der Auweraer, H.: Modal testing and analysis of structures under operational conditions: industrial applications. Mech. Syst. Signal Process. 13(2), 193–216 (1999)

    Article  Google Scholar 

  5. James, G.H. III: Modal parameter estimation from space shuttle flight data. In: Proceedings of the 21st International Modal Analysis Conference, Kissimmee, FL (2003)

    Google Scholar 

  6. Clarke, H., Stainsby, J., Carden, E.P.: Operational modal analysis of resiliently mounted marine diesel generator/alternator. In: Proulx, T. (ed.) Rotating Machinery, Structural Health Monitoring, and Shock and Vibration Topics, Jacksonville, FL. Proceedings of the 29th International Modal Analysis Conference Series, vol. 5, pp. 1461–1473. Springer, Berlin (2011)

    Google Scholar 

  7. Wang, J., Hu, X.: The Application of MATLAB in Processing Vibration Signals, pp. 160–161. Water Power Press, Beijing (2006)

    Google Scholar 

  8. Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice Hall, Upper Saddle River (1999)

    Google Scholar 

  9. Pintelon, R., Schoukens, J.: System Identification. IEEE Press, New York (2001)

    Book  Google Scholar 

  10. Gevers, M.: A personal view of the development of system identification. IEEE Control Syst. Mag. 26(6), 93–105 (2006)

    Article  Google Scholar 

  11. Goethals, I., Pelckmans, J., Suykens, J.A.K., De Moor, B.: Subspace identification of Hammerstein systems using least squares support vector machines. IEEE Trans. Autom. Control 50(10), 1509–1519 (2005)

    Article  Google Scholar 

  12. Schoukens, J., Pintelon, R., Enqvist, M.: Study of the LTI relations between the outputs of two coupled Wiener systems and its application to the generation of initial estimates for Wiener-Hammerstein systems. Automatica 44(7), 1654–1665 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Schoukens, J., Pintelon, R., Dobrowiecki, T., Rolain, Y.: Identification of linear system with nonlinear distortions. Automatica 41(3), 491–504 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yin, Y.: Theory of Structural Dynamics and Identification of Rocket’s Transverse Load. China Astronautic Publishing House (2011)

  15. Ibrahim, S.R.: Random decrement technique for modal identification of structures. J. Spacecrt. 14(11) (1977)

  16. Maia, N.M.M., Silva, J.M.M., He, J., Lieven, N.A.J., Lin, R.M., Skingle, G.W., et al.: Theoretical and Experimental Modal Analysis. Wiley, New York (1997)

    Google Scholar 

  17. Masri, S.F., Caughey, T.K.: A nonparametric identification technique for nonlinear dynamic problems. J. Appl. Mech. 46, 433–447 (1979)

    Article  MATH  Google Scholar 

  18. Udwadia, F.E., Kuo, C.-P.: Non-parametric identification of a class of non-linear close-coupled dynamic systems. Earthquake Eng. Struct. Dyn. 9, 385–409 (1981)

    Article  Google Scholar 

  19. Kirshenboim, J., Ewins, D.J.: A method for recognizing structural nonlinearities in steady-state harmonic testing. J. Vib. Acoust. Stress Reliab. Des. 106, 49–52 (1984)

    Article  Google Scholar 

  20. Stanway, R., Sproston, J.L., Stevens, N.G.: A note on parameter estimation in non-linear vibrating systems. Proc. Inst. Mech. Eng. Part C 199(C1), 79–84 (1985)

    Article  Google Scholar 

  21. Yang, Y., Ibrahim, S.R.: A nonparametric identification technique for a variety of discrete nonlinear vibrating systems. J. Vib. Acoust. Stress Reliab. Des. 107, 60–66 (1985)

    Article  Google Scholar 

  22. Busby, H.R., Nopporn, C., Singh, R.: Experimental modal analysis of non-linear systems: A feasibility study. J. Sound Vib. 180, 415–427 (1986)

    Article  Google Scholar 

  23. Masri, S.F., Miller, R.K., Saud, A.F., Caughey, T.K.: Identification of nonlinear vibrating structures: Part I—formulation. J. Appl. Mech. 54, 918–922 (1987)

    Article  MATH  Google Scholar 

  24. Masri, S.F., Miller, R.K., Saud, A.F., Caughey, T.K.: Identification of nonlinear vibrating structures: Part II—application. J. Appl. Mech. 54, 923–929 (1987)

    Article  MATH  Google Scholar 

  25. Mook, D.J.: Estimation and identification of nonlinear dynamic systems. AIAA J. 27, 968–974 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  26. Mohammad, K.S., Worden, K., Tomlinson, G.R.: Direct parameter estimation for linear and nonlinear structures. J. Sound Vib. 152, 471–499 (1992)

    Article  MATH  Google Scholar 

  27. Masri, S.F., Chassiakos, A.G., Chaughey, T.K.: Identification of nonlinear dynamic systems using neural networks. J. Appl. Mech. 60, 123–133 (1993)

    Article  Google Scholar 

  28. Guglieri, G.: A comprehensive analysis of wing rock dynamics for slender delta wing configurations. Nonlinear Dyn. (2012). doi:10.1007/s11071-012-0369-3

    Google Scholar 

  29. Vidmar, B.J., Feeny, B.F., Shaw, S.W., Haddow, A.G., Geist, B.K., Verhanovitz, N.J.: The effects of Coulomb friction on the performance of centrifugal pendulum vibration absorbers. Nonlinear Dyn. (2012). doi:10.1007/s11071-011-0289-7

    Google Scholar 

  30. Juang, J.-N., Lee, Ch.-H.: Continuous-time bilinear system identification using single experiment with multiple pulses. Nonlinear Dyn. (2012). doi:10.1007/s11071-011-0323-9

    MATH  Google Scholar 

  31. Hizir, N.B., Phan, M.Q., Betti, R., Longman, R.W.: Identification of discrete-time bilinear systems through equivalent linear models. Nonlinear Dyn. (2012). doi:10.1007/s11071-012-0408-0

    Google Scholar 

  32. He, J., Xu, B., Masri, S.F.: Restoring force and dynamic loadings identification for a nonlinear chain-like structure with partially unknown excitations. Nonlinear Dyn. (2012). doi:10.1007/s11071-011-0260-7

    Google Scholar 

  33. Yasuda, K., Kamiya, K.: Experimental identification technique of nonlinear beams in time domain. Nonlinear Dyn. 18, 185–202 (1999)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aerospace and Materials Engineering, National University of Defense Technology, Changsha, Hunan, 410073, P.R. China

    Yunyu Yin & Dongxu Li

  2. Science and Technology on Space Physics Laboratory, Beijing, 100076, P.R. China

    Yunyu Yin

  3. School of Engineering, Warwick University, Coventry, CV4 7AL, UK

    Yunyu Yin & Stana Živanović

Authors
  1. Yunyu Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stana Živanović
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dongxu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yunyu Yin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yin, Y., Živanović, S. & Li, D. Displacement modal identification method of elastic system under operational condition. Nonlinear Dyn 70, 1407–1420 (2012). https://doi.org/10.1007/s11071-012-0543-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-012-0543-7

Keywords

Search

Navigation