×

Estimation of modal parameters for structurally damped systems using wavelet transform. (English) Zbl 1406.74351

Summary: In this paper, a procedure is presented to determine the modal parameters of a system with proportional structural damping exited by an impact force. A Morlet wavelet transform with an adjusting parameter is used to estimate the natural frequencies and damping factors from free-decay responses of structure. Also a method is used for identification of mode shapes from the estimated natural frequencies of wavelet transform and the free responses of structure. It is shown that the mode shape identification method can average the data in the noisy environments and reduce the effect of noise. A numerical example as well as two experimental case studies on a beam and a trapezoidal concrete plate demonstrates the validity of method.

MSC:

74J10 Bulk waves in solid mechanics
70J50 Systems arising from the discretization of structural vibration problems
Full Text: DOI

References:

[1] Allemang, R. J., The modal assurance criterion - twenty years of use and abuse, Sound Vib., 37, 14-21, (2003)
[2] Argoul, P.; Le, T.-P., Wavelet analysis of transient signals in civil engineering, (Friemond, M.; Maceri, F., Novel Approaches in Civil Engineering, Lecture Notes in Applied and Computational Mechanics, (2003), Springer Berlin), 14
[3] Argoul, P.; Le, T.-P., Instantaneous indicators of structural behaviour based on continuous Cauchy wavelet analysis, Mech. Syst. Signal Process., 17, 1, 243-250, (2003)
[4] Argoul, P.; Hans, S.; Conti, F.; Boutin, C., Time-frequency analysis of free oscillations of mechanical structures, application to the identification of the mechanical behavior of buildings under shocks, (Proceedings of the COST F3 Conference: System Identification and Structural Health Monitoring, Madrid, Spain, (2000)), 283-292
[5] Ashory, M. R.; Khatibi, M. M.; Jafari, M.; Malekjafarian, A., Determination of mode shapes using wavelet transform of free vibration data, Arch. Appl. Mech., 83, 6, 907-921, (2013) · Zbl 1293.74159
[6] Brüel&Kjær, PULSE, version 8.0, sound & vibration measurement A/S, (1996-2003)
[7] Chui, C., An introduction to wavelets, (1992), Academic Press New York · Zbl 0925.42016
[8] Crandall, S. H., The role of damping in vibration theory, Sound Vib., 11, 1, 3-18, (1970) · Zbl 0187.21901
[9] Ewins, D. J., Modal testing: theory, practice and application, (2000), Research Studies Press Ltd Baldock, Hertfordshire, England
[10] Feng, M. Q.; Kim, J. M.; Xue, H., Identification of a dynamic system using ambient vibration measurements, J. Appl. Mech., 65, 4, 1010-1021, (1998)
[11] Gaul, L.; Bohlen, S.; Kempfle, S., Transient and forced oscillations of systems with constant hysteretic damping, Mech. Res. Commun., 12, 4, 187-201, (1985) · Zbl 0588.70016
[12] Gaul, L.; Klein, P.; Kempfle, S., Transient and forced oscillations of systems with constant hysteretic damping, Mech. Res. Commun, 16, 5, 297-305, (1989)
[13] Hollkamp, J. J.; Batill, S. M., Automated parameter identification and order reduction for discrete time series models, AIAA J., 29, 1, 96-103, (1991)
[14] Ibrahim, S. R.; Mikulcik, E. C., A method for direct identification of vibration parameters from the free response, Shock Vib. Bull., 47, 4, 183-198, (1977)
[15] Khatibi, M. M.; Ashory, M. R.; Malekjafarian, A.; Brincker, R., Mass-stiffness change method for scaling of operational mode shapes, Mech. Syst. Signal Process., 26, 34-59, (2012)
[16] Lardies, J.; Gouttebroze, S., Identification of modal parameters using wavelet transform, J. Mech. Sci., 44, 11, 2263-2283, (2002) · Zbl 1025.74015
[17] Lardies, J.; Ta, M.-N., Modal parameter identification of stay cables from output-only measurements, Mech. Syst. Signal Process., 25, 133-150, (2011)
[18] Le, T.-P.; Argoul, P., Continuous wavelet transform for modal identification using free decay response, J. Sound. Vib., 277, 1-2, 73-100, (2004)
[19] Liu, G. R.; Quek, S. S., The finite element method: a practical course, (2003), Butterworth- Heinemann Oxford, England · Zbl 1027.74001
[20] López-Aenlle, M.; Brincker, R.; Pelayo, F.; Fernandez Canteli, A., On exact and approximated formulations for scaling-mode shapes in operational modal analysis by mass and stiffness change, J. Sound Vib., 331, 3, 622-637, (2012)
[21] Meyer, Y., Wavelets: algorithms and applications, (1993), Society for Industrial and Applied Mathematics Translation, SIMA Philadelphia · Zbl 0821.42018
[22] Miranda, F. J., Wavelet analysis of lightning return stroke, J. Atmos. Solar-Terr. Phys., 70, 11-12, 1401-1407, (2008)
[23] MODPLAN, Integrated software for structural dynamics, ICATS, (1988-2000), Imperial College of Science, Technology and Medicine, University of London UK
[24] Ruzzene, M.; Fasana, A.; Garibaldi, L.; Piombo, B., Natural frequencies and dampings identification using wavelet transform: application to real data, Mech. Syst. Signal Process., 11, 2, 207-218, (1997)
[25] Smith, W. R., Least-squares time-domain method for simultaneous identification of vibration parameters from multiple free-response records, (Proc of 22nd Structural Dynamics and Materials Conference, (1981)), 194-201
[26] Staszewski, W. J., Identification of damping in MDOF systems using time - scale decomposition, J. Sound Vib., 203, 2, 283-305, (1997)
[27] Sun, C. T.; Lu, Y. P., Vibration damping of structural elements, (1995), Prentice Hall International (UK) Limited London · Zbl 0840.73001
[28] Torresani, B., Analyse continue par ondelettes, (1995), CNRS Editions Paris · Zbl 0918.42025
[29] Yin, H. P.; Duhamel, D., Finite difference formulation for modal parameter estimation, J. Sound Vib., 231, 2, 259-275, (2000) · Zbl 1237.74201
[30] Yu, K.; Ye, J.; Zou, J.; Yang, B.; Yang, H., Missile flutter experiment and data analysis using wavelet transform, J. Sound Vib., 269, 3-5, 899-912, (2004)
[31] Zhang, L.; Yao, Y.; Lu, M., An improved time domain polyreference method for modal identification, Mech. Syst. Signal Process., 1, 4, 399-413, (1987) · Zbl 0669.93016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.