Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T06:11:04.320Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-linear system identification of the dynamics of aeroelastic instability suppression based on targeted energy transfers

Published online by Cambridge University Press:  03 February 2016

Y. S. Lee ,
A. F. Vakakis ,
D. M. McFarland  and
L. A. Bergman
Y. S. Lee
Affiliation:
[email protected], Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, USA
A. F. Vakakis
Affiliation:
[email protected], Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
D. M. McFarland
Affiliation:
[email protected], Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, USA
L. A. Bergman
Affiliation:
[email protected], Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We revisit our earlier study of targeted energy transfer (TET) mechanisms for aeroelastic instability suppression by employing time-domain nonlinear system identification based on the equivalence between analytical and empirical slow flows. Performing multiscale partitions of the dynamics directly on measured (or simulated) time series without any presumptions regarding the type and strength of the system nonlinearity, we derive nonlinear interaction models (NIMs) as sets of intrinsic modal oscillators (IMOs). The eigenfre-quencies of IMOs are characterised by the ‘fast’ dynamics of the problem and their forcing terms represent slowly-varying nonlinear modal interactions across the different time scales of the dynamics. We demonstrate that NIMs not only provide information on modal energy exchanges under nonlinear resonant interactions, but also directly dictate robustness behaviour of TET mechanisms for suppressing aeroelastic instabilities. Finally, we discuss the usefulness of NIMs in constructing frequency-energy plots that reveal global features of the dynamics to distinguish between different TET mechanisms and to study robustness of aeroelastic instability suppression.

Type
Research Article
Information
The Aeronautical Journal , Volume 114 , Issue 1152 , February 2010 , pp. 61 - 82
Copyright
Copyright © Royal Aeronautical Society 2010 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Ljung, L., System Identification: Theory for the User, 2nd ed, Prentice Hall Information and System Sciences Series, 1999.Google Scholar
2. Ewins, D.J., Modal Testing: Theory and Practice, Research Studies Press, UK, 1990.Google Scholar
3. Ibrahim, S.R. and Mikulcik, E.C., A time domain modal vibration test technique, Shock and Vibration Bulletin, 1973, 43, pp 21–37.Google Scholar
4. Juang, J.-N. and Pappa, R., An eigensystem realisation algorithm for modal parameter identification and model reduction, J Guidance, Control, and Dynamics, 1985, 8, (5), pp 620–627.Google Scholar
5. Van Overschee, P. and De Moor, B., A unifying theorem for three subspace system identification algorithms, Automatica, 1995, 31, (12), pp 1853–1864.Google Scholar
6. Hermans, L. and Van Der Auweraer, H., Modal testing and analysis of structures under operational conditions: Industrial applications, Mechanical Systems and Signal Processing, 1999, 13, pp 193–216.Google Scholar
7. Batel, M., Operational modal analysis – Another way of doing modal testing, Sound and Vibration, 2002, pp 22–27.Google Scholar
8. Mohanty, P. and Rixen, D.J., Modified ERA method for operational modal analysis in the presence of harmonic excitations, Mechanical Systems and Signal Processing, 2006, 20, (1), pp 114–130.Google Scholar
9. Devriendt, C. and Guillaume, P., Identification of modal parameters from transmissibility measurements, J Sound and Vibration, 2008, 314, pp 343–356.Google Scholar
10. Kerschen, G., Worden, K., Vakakis, A.F. and Golinval, J.-C., Past, present and future of nonlinear system identification in structural dynamics, Mechanical Systems and Signal Processing, 2006, 20, (3), pp 505–592.Google Scholar
11. Marmarelis, V.Z., Identification of nonlinear systems by use of nonstationary white-noise inputs, Applied Mathematical Modelling, 1980, 4, pp 117–124.Google Scholar
12. Silva, W., Identification of nonlinear aeroelastic systems based on the Volterra theory: Progress and opportunities, Nonlinear Dynamics, 2005, 39, (1), pp 25–62.Google Scholar
13. Juditsky, A., Hjalmarsson, H., Benveniste, A., Delyon, B., Ljung, L., Sjöberg, J. and Zhang, Q., Nonlinear black-box models in system identification: Mathematical foundations, Automatica, 1995, 13, pp 1725–1750.Google Scholar
14. Jin, G., Sain, M.K., Pham, K.D., Spencer, J.B.F. and Ramallo, J.C., Modeling MR-dampers: A nonlinear blackbox approach, in: Proceedings of the American Control Conference, Arlington, VA, USA, 25-27 June 2001, pp 429–434.Google Scholar
15. Ma, X., Vakakis, A.F. and Bergman, L.A., Karhunen-Loeve analysis and order reduction of the transient dynamics of linear coupled oscillators with strongly nonlinear end attachments, J Sound and Vibration, 2008, 309, (3-5), pp 569–587.Google Scholar
16. Placzek, A., Tran, D.-M. and Ohayon, R., Hybrid proper orthogonal decomposition formulation for linear structural dynamics, J Sound and Vibration, 2008, 318, (4-5), pp 943–964.Google Scholar
17. Allison, T.C., Miller, A.K. and Inman, D.J., A time-varying identification method for mixed response measurements, J Sound and Vibration, 2009, 319, (3-5), pp 850–868.Google Scholar
18. Hasiewicz, Z., Pawlak, M. and Liwi Ski, P., Nonparametric identification of nonlinearities in block-oriented systems by orthogonal wavelets with compact support, IEEE Transactions on Circuits and Systems-I: Regular Papers, 2005, 52, (2), pp 427–441.Google Scholar
19. Masri, S. and Caughey, T., A nonparametric identification techanique for nonlinear dynamic systems, Transactions of the ASME, J Applied Mechanics, 1979, 46, pp 433–441.Google Scholar
20. Leontaritis, I.J. and Billings, S.A., Input-output parametric models for nonlinear systems. Part I. Deterministic nonlinear systems, Int J Control, 1985, 41, pp 303–328.Google Scholar
21. Leontaritis, I.J. and Billings, S.A., Input-output parametric models for nonlinear systems. Part II. stochastic nonlinear systems, International J Control, 1985, 41, pp 329–344.Google Scholar
22. Feldman, M., Non-linear system vibration analysis using Hilbert transform-I. Free vibration analysis method ‘FREEVIB’, Mechanical Systems and Signal Processing, 1994, 8, (2), pp 119–127.Google Scholar
23. Feldman, M., Non-linear system vibration analysis using Hilbert transform-II. Forced vibration analysis method ‘FORCEVIB’, Mechanical Systems and Signal Processing, 1994, 8, (3), pp 309–318.Google Scholar
24. Masri, S., Miller, R., Saud, A. and Caughey, T., Identification of nonlinear vibrating structures. I. Formulation, Transactions of the ASME, J Applied Mechanics, 1987, 54, (4), pp 918–922.Google Scholar
25. Masri, S., Miller, R., Saud, A. and Caughey, T., Identification of nonlinear vibrating structures. II. Applications, Transactions of the ASME, J Applied Mechanics, 1987, 54, (4), pp 923–950.Google Scholar
26. Masri, S.F., Caffrey, J.P., Caughey, T.K., Smyth, A.W. and Chassiakos, A.G., A general data-based approach for developing reduced-order models of nonlinear MDFO systems, Nonlinear Dynamics, 2005, 39, (1), pp 95–112.Google Scholar
27. Masri, S., Tasbihgoo, F. and Caffrey, J., Development of data-based model-free representation of non-conservative dissipative systems, International J Non-Linear Mechanics, 2007, 42, (1), pp 99–117.Google Scholar
28. Natke, H.G., Applications in aerospace and airplane engineering: Estimation of modal quantities and model improvement, in: Application of System Identification in Engineering, Natke, H.G. (Ed.), CISM Courses & Lectures No. 296, pp 391–419, 1988.Google Scholar
29. Plaetschke, E. and Weiss, S., Aircraft system identification – determination of flight mechanics parameters, in: Application of System Identification in Engineering, Natke, H.G. (Ed.), CISM Courses & Lectures No. 296, pp 42–447, 1988.Google Scholar
30. Lind, R., Snyder, K. and Brenner, M., Wavelet analysis to characterise non-linearities and predict limit cycles of an aeroelastic system, Mechanical Systems and Signal Processing, 2001, 15, pp 337–356.Google Scholar
31. Thothadri, M., Casas, R.A., Moon, F.C., D’andrea, R. and Johnson, C.R., Nonlinear system identification of multi-degree-of-freedom systems, Nonlinear Dynamics, 2003, 32, (3), pp 307–322.Google Scholar
32. Popescu, C.A., Wong, Y.S. and Lee, B.H.K., An expert system for predicting nonlinear aeroelastic behaviour of an airfoil, J Sound and Vibration, 2009, 319, pp 1312–1329.Google Scholar
33. Huang, N., Shen, Z., Long, S., Wu, M., Shih, H., Zheng, Q., Yen, N.C., Tung, C. and Liu, H., The empirical mode decompostion and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proceedings of the Royal Society of London, Series, A Mathematical and Physical Sciences, 1998, 454, pp 903–995.Google Scholar
34. Yang, J.N., Lei, Y., Pan, S. and Huang, N., System identification of linear structures based on Hilbert-Huang spectral analysis. Part 1: normal modes, Earthquake Engineering & Structural Dynamics, 2003, 32, (9), pp 1443–1467.Google Scholar
35. Yang, J.N., Lei, Y., Pan, S. and Huang, N., System identification of linear structures based on Hilbert-Huang spectral analysis. Part 2: Complex modes, Earthquake Engineering & Structural Dynamics, 2003, 32, (9), pp 1533–1554.Google Scholar
36. Pai, P.F., Nonlinear vibration characterisation by signal decomposition, J Sound and Vibration, 2007, 307, (3-5), pp 527–544.Google Scholar
37. Feldman, M., Identification of weakly nonlinearities in multiple coupled oscillators, J Sound and Vibration, 2007, 303, pp 357–370.Google Scholar
38. Chen, H.G., Yan, Y.J. and Jiang, J.S., Vibration-based damage detection in composite wingbox structures by HHT, Mechanical Systems and Signal Processing, 2007, 21, (1), pp 307–321.Google Scholar
39. Kerschen, G., Vakakis, A.F., Lee, Y.S., McFarland, D.M. and Bergman, L.A., Toward a fundamental understanding of the Hilbert-Huang transform in nonlinear structural dynamics, J Vibration and Control, 2008, 14, (1-2), pp 77–105.Google Scholar
40. Lee, Y.S., Vakakis, A.F., McFarland, D.M., Kerschen, G. and Bergman, L.A., Empirical mode decomposition in the reduced-order modeling of aeroelastic systems, in: 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Schaumburg, Illinois, USA, 7-10 April 2008.Google Scholar
41. Lee, Y.S., Tsakirtzis, S., Vakakis, A.F., Bergman, L.A. and McFarland, D.M., Physics-based foundation for empirical mode decomposition: Correspondence between intrinsic mode functions and slow flows, AIAA J, 47, (12), pp 2938–2963, 2009.Google Scholar
42. Lee, Y.S., Tsakirtzis, S., Vakakis, A.F., McFarland, D.M. and Bergman, L.A., A time-domain nonlinear system identification method based on multiscale dynamic partitions, Meccanica, in review.Google Scholar
43. Tsakirtzis, S., Lee, Y.S., Vakakis, A.F., Bergman, L.A. and McFarland, D.M., Modeling of Nonlinear Modal Interactions in the Transient Dynamics of an Elastic Rod with an Essentially Nonlinear Attachment, Communications in Nonlinear Science and Numerical Simulations, in press.Google Scholar
44. Vakakis, A.F., Gendelman, O., Bergman, L.A., McFarland, D.M., Kerschen, G. and Lee, Y.S., Passive Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems: I and II, Springer-Verlag, Berlin and New York, 2008.Google Scholar
45. Lee, Y.S., Vakakis, A.F., Bergman, L.A., McFarland, D.M. and Kerschen, G., Suppressing aeroelastic instability using broadband passive targeted energy transfers. Part 1: Theory, AIAA J, 2007, 45, (3), pp 693–711.Google Scholar
46. Lee, Y.S., Kerschen, G., McFarland, D.M., Hill, W.J., Nichkawde, C., Strganac, T.W., Bergman, L.A. and Vakakis, A.F., Suppressing aeroelastic instability using broadband passive targeted energy transfers. Part 2: Experiments, AIAA J, 2007, 45, (10), pp 2391–2400.Google Scholar
47. Lee, Y.S., Vakakis, A.F., Bergman, L.A., McFarland, D.M. and Kerschen, G., Enhancing robustness of aeroelastic instability suppression using multi-degree-of-freedom nonlinear energy sinks, AIAA J, 2008, 46, (6), pp 1371–1394.Google Scholar
48. Manevitch, L., The description of localised normal modes in a chain of nonlinear coupled oscillators using complex variables, Nonlinear Dynamics, 2001, 25, pp 95–109.Google Scholar
49. Lochak, P. and Meunier, C., Multiphase Averaging for Classical Systems: With Applications to Adiabatic Theorems, Springer-Verlag, 1988.Google Scholar
50. Rilling, G., Flandrin, P. and Gon Alvès, P., On empirical mode decomposition and its algorithms, in: IEEE-Eurasip Workshop on Nonlinear Signal and Image Processing, Grado, Italy, June 2003.Google Scholar
51. Vakakis, A., Manevitch, L., Mikhlin, Y., Pilipchuk, V. and Zevin, A., Normal Modes and Localisation in Nonlinear Systems, John Wiley & Sons, Inc., 1996.Google Scholar
52. Lee, Y.S., Vakakis, A. F., Bergman, L.A., McFarland, D.M. and Kerschen, G., Triggering mechanisms of limit cycle oscillations due to aeroelastic instability, J Fluids and Structures, 2005, 21, (5-7), pp 485–529.Google Scholar
53. Deering, R. and Kaiser, J.F., The Use of a Masking Signal to Improve Empirical Mode Decomposition, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing – Proceedings, Vol. I, Institute of Electrical and Electronics Engineers Inc., Piscataway, NJ 08855-1331, United States, Philadelphia, PA, USA, 2005, pp 485–488.Google Scholar
54. Lee, Y.S., Nucera, F., Vakakis, A.F., McFarland, D.M. and Bergman, L. A., Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments, Physical D, 2009, 238, pp 1868–1896.Google Scholar
55. Vakakis, A.F. and Gendelman, O., Energy pumping in nonlinear mechanical oscillators: Part II-Resonance capture, Transactions of the ASME, J Applied Mechanics, 2001, 68, pp 42–48.Google Scholar