Advertisement

Nonlinear Dynamics

, Volume 70, Issue 2, pp 1407–1420 | Cite as

Displacement modal identification method of elastic system under operational condition

  • Yunyu YinEmail author
  • Stana Živanović
  • Dongxu Li
Original Paper

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.

Keywords

Displacement modal identification Operational modal analysis (OMA) Structure dynamics 

Nomenclature

M,C,K

mass, damping and stiffness matrix

Open image in new window

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

jr

number of generalized displacements

Open image in new window

generalized displacement, velocity and acceleration vectors

Φj

jth shape function vector

Φ

shape function matrix

Φij

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

qj(tk)

jth generalized displacement value at time t k

qk

vector of generalized displacements at time t k

i

index of test point, i=1,2,…,m

k

index of time

xi

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

m

number of acceleration test points

f1

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. 1.
    Reynders, E.: System identification methods for (operational) modal analysis: review and comparison. Arch. Comput. Methods Eng. 19, 51–124 (2012) MathSciNetCrossRefGoogle Scholar
  2. 2.
    Živanović, S., Pavic, A., Reynolds, P.: Modal testing and FE model tuning of a lively footbridge structure. Eng. Struct. 28, 857–868 (2006) CrossRefGoogle Scholar
  3. 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) CrossRefGoogle Scholar
  4. 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) CrossRefGoogle Scholar
  5. 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. 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. 7.
    Wang, J., Hu, X.: The Application of MATLAB in Processing Vibration Signals, pp. 160–161. Water Power Press, Beijing (2006) Google Scholar
  8. 8.
    Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice Hall, Upper Saddle River (1999) Google Scholar
  9. 9.
    Pintelon, R., Schoukens, J.: System Identification. IEEE Press, New York (2001) CrossRefGoogle Scholar
  10. 10.
    Gevers, M.: A personal view of the development of system identification. IEEE Control Syst. Mag. 26(6), 93–105 (2006) CrossRefGoogle Scholar
  11. 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) CrossRefGoogle Scholar
  12. 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) MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Schoukens, J., Pintelon, R., Dobrowiecki, T., Rolain, Y.: Identification of linear system with nonlinear distortions. Automatica 41(3), 491–504 (2005) MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Yin, Y.: Theory of Structural Dynamics and Identification of Rocket’s Transverse Load. China Astronautic Publishing House (2011) Google Scholar
  15. 15.
    Ibrahim, S.R.: Random decrement technique for modal identification of structures. J. Spacecrt. 14(11) (1977) Google Scholar
  16. 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. 17.
    Masri, S.F., Caughey, T.K.: A nonparametric identification technique for nonlinear dynamic problems. J. Appl. Mech. 46, 433–447 (1979) zbMATHCrossRefGoogle Scholar
  18. 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) CrossRefGoogle Scholar
  19. 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) CrossRefGoogle Scholar
  20. 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) CrossRefGoogle Scholar
  21. 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) CrossRefGoogle Scholar
  22. 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) CrossRefGoogle Scholar
  23. 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) zbMATHCrossRefGoogle Scholar
  24. 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) zbMATHCrossRefGoogle Scholar
  25. 25.
    Mook, D.J.: Estimation and identification of nonlinear dynamic systems. AIAA J. 27, 968–974 (1989) MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Mohammad, K.S., Worden, K., Tomlinson, G.R.: Direct parameter estimation for linear and nonlinear structures. J. Sound Vib. 152, 471–499 (1992) zbMATHCrossRefGoogle Scholar
  27. 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) CrossRefGoogle Scholar
  28. 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. 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. 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 zbMATHGoogle Scholar
  31. 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. 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. 33.
    Yasuda, K., Kamiya, K.: Experimental identification technique of nonlinear beams in time domain. Nonlinear Dyn. 18, 185–202 (1999) MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Aerospace and Materials EngineeringNational University of Defense TechnologyChangshaP.R. China
  2. 2.Science and Technology on Space Physics LaboratoryBeijingP.R. China
  3. 3.School of EngineeringWarwick UniversityCoventryUK

Personalised recommendations