Sage Journals: Discover world-class research

Abstract

A new effective and efficient time domain modal analysis is presented in this paper. Based on the theoretical expansion of free decay response functions of damped structures, the method is formulated to utilize measured free-decay response data to efficiently form an equivalent derived eigensystem. Rigorous mathematical derivation will show that modal parameters (natural frequencies, damping ratios and mode shapes) of a damped test structure can be determined from the eigenvalues and eigenvectors of the derived equivalent eigensystem. Scaling of the resulting mode shapes so that they become so called A-normalized will be explored. General guidelines for selection of user-selectable algorithm parameters are also discussed to maximize the benefit of the proposed method. Another important theoretical development associated with the new method is a new concept of modal confidence factor (MCF) for the examination of identification results. The practical applicability and validity of the proposed method and the new MCF will be demonstrated through various numerical case studies. The concepts of equivalent derived eigensystem and MCF associated with the proposed method are new and have been demonstrated to be very effective. The identification results obtained are very accurate as compared with their exact counterparts and the method is very efficient in computational implementations.

Keywords

System identification time-domain modal analysis equivalent eigensystem modal parameter estimation damped vibration system

Get full access to this article

View all access options for this article.

References

Allemang RJ ( 1993) Modal analysis - where do we go from here? International Journal of Analytical and Experimental Modal Analysis 8(2): 80-91.

Brown D. , Allemang R. , Zimmerman R. and Mergeay M. ( 1988) Parameter estimation techniques for modal analysis. SAE Paper No. 790221, SAE Transaction 88(1): 828-846.

Burney FA , Pandit SM and Wu SM ( 1976) A stochastic approach to characterization of machine tool system dynamics under actual working conditions. ASME Series B 98(2): 614-619.

Chen CT ( 1984) Linear System Theory and Design. New York: CBS College Publishing.

Eman KF and Kim KJ ( 1983) Modal analysis of machine tool structures based on experimental data. Journal of Engineering for Industry 105(4): 159-165.

Gersch W. and Fouth DA ( 1974) Least squares estimates of structural system parameters using covariance function data. IEEE Transactions on Automatic Control AC- 19(6): 898-903.

Gersch W. and Luo S. ( 1972) Discrete time series synthesis of randomly excited structural system responses. Journal of Acoustics 51(1): 402-408.

Gersch W. , Nielsen NN and Akaike H. ( 1973) Maximum likelihood estimation of structural parameters from random vibration data. Journal of Sound and Vibration 31(3): 295-308.

Goldberg JL ( 1992) Matrix Theory with Applications. New York, USA: McGraw-Hill.

10.

Ibrahim SR ( 1977a) Random decrement technique for modal identification of structure. AIAA Journal of Spacecraft and Rockets 14(11): 696-700.

11.

Ibrahim SR ( 1977b) The use of random decrement technique for identification of structural modes of vibration. AIAA Paper No. 77-368.

12.

Ibrahim SR ( 1978) Modal confidence factor in vibration testing. Shock and Vibration Bulletin 48(1): 65-75.

13.

Ibrahim SR ( 1979) Application of random time domain analysis to dynamic flight measurement. Shock and Vibration Bulletin 49(2): 165-170.

14.

Ibrahim SR and Mikulcik EC ( 1973) A time modal vibration test technique. Shock and Vibration Bulletin 43(4): 21-37.

15.

Ibrahim SR and Mikulcik EC ( 1976) The experimental determination of vibration parameter from time responses. Shock and Vibration Bulletin 46(5): 187-196.

16.

Ibrahim SR and Mikulcik EC ( 1977) A method for the direct identification of vibration parameters from the free responses. Shock and Vibration Bulletin 47(4): 183-198.

17.

Juang JN ( 1987) Mathematical correlation of modal parameter identification methods via system realization theory. Journal of Modal Analysis 2: 1-18.

18.

Juang JN and Papa RS ( 1985) An eigensystem realization algorithm (ERA) for modal parameter identification and model reduction. Journal of Guidance, Control, and Dynamics 8(5): 620-627.

19.

Juang JN and Papa RS ( 1986) Effects of noise on modal parameters identified by the eigensystem realization algorithm. Journal of Guidance, Control, and Dynamics 9(3): 294-303.

20.

Lee A-C. and Chen J-H. ( 1990) Optimal extraction of structural characteristics from response measurements. Journal of Guidance 13(4): 675-683.

21.

Leuridan JM , Brown DL and Allemang RJ ( 1986) Time domain parameter identification methods for linear modal analysis: a unifying approach. Journal of Vibration, Acoustics, Stress, and Reliability in Design 108: 1-8.

22.

Longman RW and Juang JN ( 1989) Recursive form of the eigensystem realization algorithm for system identification. Journal of Guidance 12(5): 647-652.

23.

Mergeay M. ( 1983) Least squares complex exponential method and global system parameter estimation used by modal analysis, in Proceedings of the 8th International Seminar on Modal Analysis 3, 15-17 September, Leuven, Belgium, pp. 1-19.

24.

Pandit SM ( 1977) Analysis of vibration records by data dependent systems . Shock and Vibration Bulletin 47: 161-174.

25.

Pandit SM and Wu SM ( 1983) Time Series and System Analysis with Applications. New York: Wiley.

26.

Papa RS and Ibrahim SR ( 1981) A parametric study of the ITD modal identification algorithm . Shock and Vibration Bulletin 51(3): 43-72.

27.

Papa RS and Juang JN ( 1985) Galileo spacecraft modal identification using an eigensystem realization algorithm. Journal of the Astronautical Science 33(1): 15-33.

28.

Peterson LD and Bullock SJ ( 1991) A comparison of the eigensystem realization algorithm and the Q-Markov cover, in Proceedings of the 32nd AIAA/ASME/ASCE/ AHS/ASC Structure, Structural Dynamics, and Materials Conference , 6-9 April, Washington, DC, pp. 2169-2178.

29.

Peterson LD ( 1995) Efficient computation of the eigensystem realization algorithm . Journal of Guidance, Control, and Dynamics 18(3): 395-403.

30.

Vold H. , Kundrat J. , Rocklin T. and Russell R. ( 1982) A multi-input modal estimation algorithm for mini-computer . SAE Paper No. 820194, SAE Transactions 91(1): 815-821.

31.

Vold H. and Rocklin T. ( 1982) The numerical implementation of a multi-input modal estimation method for mini-computer, in Proceedings of the 1st International Modal Analysis Conference, 1-4 February, Orlando, FL, pp. 542-548.

32.

Vold H. and Russell R. ( 1983) Advanced analysis methods improve modal test results. Journal of Sound and Vibration 17(3): 36-40.

33.

Yang CD and Yeh FB ( 1990) Identification, reduction, and refinement of model parameters by the eigensystem realization algorithm. Journal of Guidance 13(6): 1051-1059.

34.

Zimmerman R. , Brown D. and Allemang R. ( 1982) Improved parameter estimation techniques for experimental modal analysis. Final Report, NASA Grant NGS-1486, NASA Langley Research Center 1-23.