Amplitude-dependent characteristics; Digital Image Correlation (DIC); Energy-dependent characteristics; Jointed structures; Nonlinear system identification; Amplitude-dependent characteristic; Dependent characteristics; Digital image correlation; Digital image correlations; Energy dependent; Energy-dependent characteristic; Field data; Jointed structure; Non-linear system identification; Control and Systems Engineering; Signal Processing; Civil and Structural Engineering; Aerospace Engineering; Mechanical Engineering; Computer Science Applications
Abstract :
[en] The dynamic responses of assembled structures are greatly affected by the mechanical joints, which are often the cause of nonlinear behavior. To better understand and, in the future, tailor the nonlinearities, accurate methods are needed to characterize the dynamic properties of jointed structures. In this paper, the nonlinear characteristics of a jointed beam is studied with the help of multiple identification methods, including the Hilbert Transform method, Peak Finding and Fitting method, Dynamic Mode Decomposition method, State-Space Spectral Submanifold, and Wavelet-Bounded Empirical Mode Decomposition method. The nonlinearities are identified by the responses that are measured via accelerometers in a series of experiments that consist of hammer testing, shaker ringdown testing, and response/force-control stepped sine testing. In addition to accelerometers, two high-speed cameras are used to capture the motion of the whole structure during the shaker ringdown testing. Digital Image Correlation (DIC) is then adopted to obtain the displacement responses and used to determine the mode shapes of the jointed beam. The accuracy of the DIC data is validated by the comparison between the identification results of acceleration and displacement signals. As enabled by full-field data, the energy-dependent characteristics of the structure are also presented. The setup of the different experiments is described in detail in Part I (Chen et al., 2021) of this research. The focus of this paper is to compare nonlinear system identification methods applied to different measurement techniques and to exploit the use of high spatial resolution data.
Jin, Mengshi ✱; AECC Shanghai Commercial Aircraft Engine Manufacturing Co. LTD., Shanghai, China ; School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China
Kosova, Giancarlo ✱; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M) ; Siemens Industry Software, Leuven, Belgium
Cenedese, Mattia ✱; Institute for Mechanical Systems, ETH Zürich, Zürich, Switzerland
Chen, Wei ✱; AECC Shanghai Commercial Aircraft Engine Manufacturing Co. LTD., Shanghai, China ; School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China
Singh, Aryan ✱; Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, United States
Jana, Debasish ✱; Department of Civil and Environmental Engineering, Rice University, Houston, United States
Brake, Matthew R.W. ; Department of Mechanical Engineering, Rice University, Houston, United States
Schwingshackl, Christoph W. ; Imperial College London, Mechanical Engineering, London, United Kingdom
Nagarajaiah, Satish ; Department of Civil and Environmental Engineering, Rice University, Houston, United States ; Department of Mechanical Engineering, Rice University, Houston, United States
Moore, Keegan J. ; Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, United States
Noël, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique ; Control Systems Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology, Netherlands
✱ These authors have contributed equally to this work.
Language :
English
Title :
Measurement and identification of the nonlinear dynamics of a jointed structure using full-field data; Part II - Nonlinear system identification
This work presents the results of the Tribomechadynamics Research Camp (2019) at Rice University, Houston, Texas, USA (http://tmd.rice.edu). The authors appreciate the chance to work together. The authors are also grateful to the SIEMENS and South Central Imaging for their sponsorship. Wei Chen and Mengshi Jin thank China Scholarship Council (CSC) for their financial support at Rice University. Giancarlo Kosova has been supported by the European Union's Horizon 2020 research and innovation program under the Marie Sk?odowska-Curie grant agreement No 764547. Debasish Jana and Satish Nagarajaiah acknowledge the grant from the Science and Engineering Research Board of India (SERB). The data used in the paper is available at https://github.com/mattiacenedese/BRBtesting.This work presents the results of the Tribomechadynamics Research Camp (2019) at Rice University, Houston, Texas, USA ( http://tmd.rice.edu ). The authors appreciate the chance to work together. The authors are also grateful to the SIEMENS and South Central Imaging for their sponsorship. Wei Chen and Mengshi Jin thank China Scholarship Council (CSC) for their financial support at Rice University. Giancarlo Kosova has been supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 764547 . Debasish Jana and Satish Nagarajaiah acknowledge the grant from the Science and Engineering Research Board of India (SERB) .
Brake, M.R.W., (eds.) The Mechanics of Jointed Structures: Recent Research and Open Challenges for Developing Predictive Models for Structural Dynamics, 2017, Springer, Cham, Switzerland.
Gaul, L., Lenz, J., Nonlinear dynamics of structures assembled by bolted joints. Acta Mech. 125:1–4 (1997), 169–181.
Alamdari, M.M., Li, J., Samali, B., Ahmadian, H., Naghavi, A., Nonlinear joint model updating in assembled structures. J. Eng. Mech., 140(7), 2014.
Fantetti, A., Tamatam, L.R., Volvert, M., Lawal, I., Liu, L., Salles, L., Brake, M.R.W., Schwingshackl, C.W., Nowell, D., The impact of fretting wear on structural dynamics: Experiment and simulation. Tribol. Int. 138 (2019), 111–124.
Chen, W., Jin, M., Lawal, I., Brake, M.R.W., Song, H., Measurement of slip and separation in jointed structures with non-flat interfaces. Mech. Syst. Signal Process., 134, 2019, 106325.
Noël, J.P., Renson, L., Kerschen, G., Complex dynamics of a nonlinear aerospace structure: Experimental identification and modal interactions. J. Sound Vib. 333:12 (2014), 2588–2607.
Worden, K., Hickey, D., Haroon, M., Adams, D.E., Nonlinear system identification of automotive dampers: A time and frequency-domain analysis. Mech. Syst. Signal Process. 23:1 (2009), 104–126.
Jerome, T.W., Shepherd, M.R., Hambric, S.A., Acoustic excitation of a flanged joint. Nonlinear Dynamics, Vol. 1 Conference Proceedings of the Society for Experimental Mechanics Series, 2019, Springer International Publishing Ag, Cham, 211–224.
Kerschen, G., Worden, K., Vakakis, A.F., Golinval, J.C., Past, present and future of nonlinear system identification in structural dynamics. Mech. Syst. Signal Process. 20:3 (2006), 505–592.
Londoño, J.M., Neild, S.A., Cooper, J.E., Identification of backbone curves of nonlinear systems from resonance decay responses. J. Sound Vib. 348 (2015), 224–238.
Breunung, T., Haller, G., Explicit backbone curves from spectral submanifolds of forced-damped nonlinear mechanical systems. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 474(2213), 2018, 20180083.
J.M. Londoño, S.A. Neild, J.E. Cooper, Systems with bilinear stiffness: Extraction of backbone curves and identification, in: IMAC XXXIII A Conference and Exposition on Structural Dynamics, Orlando, FL, February, 2015.
Ewins, D.J., Weekes, B., delli Carri, A., Modal testing for model validation of structures with discrete nonlinearities. Phil. Trans. R. Soc. A, 373(2051), 2015, 20140410.
Ewins, D.J., Exciting vibrations: the role of testing in an era of supercomputers and uncertainties. Meccanica 51 (2016), 3241–3258.
Smith, S.A., Brake, M.R.W., Schwingshackl, C.W., On the characterization of nonlinearities in assembled structures. J. Vib. Acoust., 142(5), 2020, 11.
D. Roettgen, M.S. Allen, D. Kammer, R.L. Mayes, Substructuring of a nonlinear beam using a modal Iwan framework, Part I: Nonlinear modal model identification, in: IMAC XXXV A Conference and Exposition on Structural Dynamics, Garden Grove, CA, January, 2017.
Akay, A., Research Needs and Open Questions in Vibration Energy Transport and Dissipation: Technical Report., 2015, National Science Foundation, Arlington, VA, (Grant No: 0940347).
Brake, M.R.W., Schwingshackl, C.W., Reuss, P., Observations of variability and repeatability in jointed structures. Mech. Syst. Signal Process. 129 (2019), 282–307.
Schwarz, S., Kohlmann, L., Hartung, A., Gross, J., Scheel, M., Krack, M., Validation of a turbine blade component test with frictional contacts by phase-locked-loop and force-controlled measurements. J. Eng. Gas Turbines Power, 142(5), 2020, 051006.
Heinze, T., Panning-von Scheidt, L., Wallaschek, J., Global detection of detached periodic solution branches of friction-damped mechanical systems. Nonlinear Dynam. 99 (2020), 1841–1870.
Krack, M., Extension of the single-nonlinear-mode theory by linear attachments and application to exciter-structure interaction. 2020, 116120.
Feldman, M., Non-linear system vibration analysis using Hilbert transform—I. Free vibration analysis method ’Freevib’. Mech. Syst. Signal Process. 8:2 (1994), 119–127.
Feldman, M., Hilbert transform in vibration analysis. Mech. Syst. Signal Process. 25:3 (2011), 735–802.
Jin, M., Brake, M.R.W., Song, H., Comparison of nonlinear system identification methods for free decay measurements with application to jointed structures. J. Sound Vib. 453 (2019), 268–293.
Jin, M., Chen, W., Brake, M.R.W., Song, H., Identification of instantaneous frequency and damping from transient decay data. J. Vib. Acoust., 142(5), 2020, 051111.
Schmid, P.J., Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656 (2010), 5–28.
Arbabi, H., Mezic, I., Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the Koopman operator. SIAM J. Appl. Dyn. Syst. 16:4 (2017), 2096–2126.
Tu, J.H., Rowley, C.W., Luchtenburg, D.M., Brunton, S.L., Kutz, J.N., On dynamic mode decomposition: Theory and applications. Physics 1:2 (2014), 391–421.
Kerschen, G., Peeters, M., Golinval, J.C., Vakakis, A.F., Nonlinear normal modes, Part I: A useful framework for the structural dynamicist. Mech. Syst. Signal Process. 23:1 (2009), 170–194.
Haller, G., Ponsioen, S., Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction. Nonlinear Dynam. 86:3 (2016), 1493–1534.
Ponsioen, S., Pedergnana, T., Haller, G., Automated computation of autonomous spectral submanifolds for nonlinear modal analysis. J. Sound Vib. 420 (2018), 269–295.
Haller, G., Ponsioen, S., Exact model reduction by a slow–fast decomposition of nonlinear mechanical systems. Nonlinear Dynam. 90:1 (2017), 617–647.
Szalai, R., Ehrhardt, D., Haller, G., Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations. Proc. R. Soc. A, 473(2202), 2017.
Huang, N.E., Shen, Z., Long, S.R., Wu, M.L.C., Shih, H.H., Zheng, Q.N., Yen, N.C., Tung, C.C., Liu, H.H., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. A 454:1971 (1998), 903–995.
Moore, K.J., Kurt, M., Eriten, M., McFarland, D.M., Bergman, L.A., Vakakis, A.F., Wavelet-bounded empirical mode decomposition for vibro-impact analysis. Nonlinear Dynam. 93:3 (2018), 1559–1577.
Balaji, N.N., Brake, M.R.W., The surrogate system hypothesis for joint mechanics. Mech. Syst. Signal Process. 126 (2019), 42–64.
Noël, J.P., Kerschen, G., Nonlinear system identification in structural dynamics: 10 more years of progress. Mech. Syst. Signal Process. 83 (2017), 2–35.
Peeters, M., Viguie, R., Serandour, G., Kerschen, G., Golinval, J.C., Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques. Mech. Syst. Signal Process. 23:1 (2009), 195–216.
Reu, P., Introduction to digital image correlation: Best practices and applications. Exp. Tech. 36:1 (2012), 3–4.
Reu, P.L., Rohe, D.P., Jacobs, L.D., Comparison of DIC and LDV for practical vibration and modal measurements. Mech. Syst. Signal Process. 86 (2017), 2–16.
Brøns, M., Kasper, T.A., Chauda, G., Klaassen, S.W.B., Schwingshackl, C.W., Brake, M.R.W., Experimental investigation of local dynamics in a bolted lap joint using digital image correlation. J. Vib. Acoust., 142(5), 2020.
Ehrhardt, D.A., Allen, M.S., Measurement of nonlinear normal modes using multi-harmonic stepped force appropriation and free decay. Mech. Syst. Signal Process. 76–77 (2016), 612–633.
Peter, S., Scheel, M., Krack, M., Leine, R.I., Synthesis of nonlinear frequency responses with experimentally extracted nonlinear modes. Mech. Syst. Signal Process. 101 (2018), 498–515.
Renson, L., Gonzalez-Buelga, A., Barton, D.A.W., Neild, S.A., Robust identification of backbone curves using control-based continuation. J. Sound Vib. 367 (2016), 145–158.
Peeters, M., Kerschen, G., Golinval, J.C., Dynamic testing of nonlinear vibrating structures using nonlinear normal modes. J. Sound Vib. 330:3 (2011), 486–509.
Peeters, M., Kerschen, G., Golinval, J.C., Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration. Mech. Syst. Signal Process. 25:4 (2011), 1227–1247.
Chen, W., Jana, D., Singh, A., Jin, M., Cenedese, M., Kosova, G., Brake, M.W.R., Schwingshackl, C.W., Nagarajaiah, S., Moore, K., Noël, J.P., Measurement and identification of the nonlinear dynamics of a jointed structure using full-field data; Part I - Measurement of nonlinear dynamics. Mech. Syst. Signal Process., 2021, 108401.
Roettgen, D.R., Allen, M.S., Nonlinear characterization of a bolted, industrial structure using a modal framework. Mech. Syst. Signal Process. 84 (2017), 152–170.
Feldman, M., Hilbert transform methods for nonparametric identification of nonlinear time varying vibration systems. Mech. Syst. Signal Process. 47:1–2 (2014), 66–77.
T. Dossogne, T.W. Jerome, D.P.T. Lancereau, S.A. Smith, M.R.W. Brake, B.R. Pacini, P. Reuss, C.W. Schwingshackl, Experimental assessment of jointed configuration, in: IMAC XXXV A Conference and Exposition on Structural Dynamics, Garden Grove, CA, January, 2017.
Pai, P.F., Palazotto, A.N., HHT-based nonlinear signal processing method for parametric and non-parametric identification of dynamical systems. Int. J. Mech. Sci. 50:12 (2008), 1619–1635.
Cenedese, M., Haller, G., Constructing backbone curves from free-decay vibrations data in multi-degrees of freedom oscillatory systems. Kerschen, G., Brake, M.R.W., Renson, L., (eds.) Nonlinear Structures and Systems, Vol. 1, 2020, Springer International Publishing, Cham, 221–223.
Juang, J.N., Pappa, R.S., An eigensystem realization-algorithm for modal parameter-identification and model-reduction. J. Guid. Control Dyn. 8:5 (1985), 620–627.
Moore, K.J., Mojahed, A., Kurt, M., Eriten, M., McFarland, D.M., Bergman, L.A., Vakakis, A.F., Advanced nonlinear system identification for modal interactions in nonlinear structures: A review. Problems of Nonlinear Mechanics and Physics of Materials, 2019, Springer International Publishing, Cham, Switzerland, 101–118.
Huang, N.E., Wu, M.C., Long, S.R., Shen, S.S.P., Qu, W., Gloersen, P., Fan, K.L., A confidence limit for the empirical mode decomposition and Hilbert spectral analysis. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 459:2037 (2003), 2317–2345.
Moore, K.J., Kurt, M., Eriten, M., McFarland, D.M., Bergman, L.A., Vakakis, A.F., Wavelet-bounded empirical mode decomposition for measured time series analysis. Mech. Syst. Signal Process. 99 (2018), 14–29.
H.G.D. Goyder, D.P.T. Lancereau, Extracting natural frequencies and damping from time histories. Better than the frequency domain? in: ISMA International Conference on Noise and Vibration Engineering, KU Leuven, 2018.
C.W. Schwingshackl, C. Joannin, L. Pesaresi, J.S. Green, N. Hoffmann, Test method development for nonlinear damping extraction of dovetail joints, in: IMAC XXXII A Conference and Exposition on Structural Dynamics, Orlando, FL, February, 2014.
Noël, J.P., Renson, L., Grappasonni, C., Kerschen, G., Identification of nonlinear normal modes of engineering structures under broadband forcing. Mech. Syst. Signal Process. 74 (2016), 95–110.
Cenedese, M., Haller, G., How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proc. R. Soc. A, 476, 2020, 20190494.
Cenedese, M., Haller, G., Stability of forced–damped response in mechanical systems from a melnikov analysis. Chaos, 30(8), 2020, 083103.
Krack, M., Nonlinear modal analysis of nonconservative systems: Extension of the periodic motion concept. Comput. Struct. 154 (2015), 59–71.
Sun, Y., Vizzaccaro, A., Yuan, J., Salles, L., An extended energy balance method for resonance prediction in forced response of systems with non-conservative nonlinearities using damped nonlinear normal mode. Nonlinear Dynam. 103:4 (2021), 3315–3333.
Brøns, M., Kasper, T.A., Chauda, G., Klaassen, S.W.B., Schwingshackl, C.W., Brake, M.R.W., Experimental investigation of local dynamics in a bolted lap joint using digital image correlation. J. Vib. Acoust., 142(5), 2020, 051114.
Rosenberg, R.M., The normal modes of nonlinear n-degree-of-freedom systems. J. Appl. Mech. 29 (1962), 7–14.
Brunton, S.L., Kutz, J.N., Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control. 2019, Cambridge University Press, Cambridge, UK.
