Digital Image Correlation (DIC); Full-field measurements; Jointed structures; Modal interactions; Nonlinear system identification; Nonlinear system testing; Correlation data; Digital image correlation; Digital image correlations; Field data; Full-field measurement; Jointed structure; Non-linear system identification; System testing; Control and Systems Engineering; Signal Processing; Civil and Structural Engineering; Aerospace Engineering; Mechanical Engineering; Computer Science Applications
Abstract :
[en] Jointed structures are ubiquitous constituents of engineering systems; however, their dynamic properties (e.g., natural frequencies and damping ratios) are challenging to identify correctly due to the complex, nonlinear nature of interfaces. This research seeks to extend the efficacy of traditional experimental methods for linear system identification (such as impact testing, shaker ringdown testing, random excitation, and force or amplitude-control stepped sine testing) on nonlinear jointed systems, e.g., the half Brake–Reußbeam, by augmenting them with full-field data collected by high-speed videography. The full-field response is acquired using high-speed cameras combined with Digital Image Correlation (DIC), which enables studying the spatial–temporal dynamic characteristics of the system. As this is a video-based experiment, additional constraints are attached to the beam at the node points to remove the rigid body motion, which ensures that the beam is in the view of the camera during the entire test. The use of a video-based method introduces new sources of experimental error, such as noise from the high-speed camera's fan and electrical noise, and so the measurement accuracy of DIC is validated using accelerometer data. After validating the DIC data, the measurements are recorded for several types of excitation, including hammer testing, shaker ringdown testing, fixed sine testing, and stepped sine testing. Using the DIC data to augment standard nonlinear system identification techniques, modal coupling and the mode shapes’ evolution are investigated. The suitability of videography methods for nonlinear system identification of nonlinear beams is explored for the first time in this paper, and recommendations for techniques to facilitate this process are made. This article focuses on developing an accurate data collection methodology as well as recommendations for nonlinear testing with DIC, which paves the way for video-based investigation of nonlinear system identification. In Part-II (Jin et al., 2021) of this work, the same data set is used for a rigorous assessment of nonlinear system identification with full-field DIC data.
Chen, Wei ✱; AECC Shanghai Commercial Aircraft Engine Manufacturing Co. LTD., Shanghai, China ; School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China
Jana, Debasish ✱; Department of Civil and Environmental Engineering, Rice University, Houston, United States
Singh, Aryan ✱; Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, United States
Jin, Mengshi ✱; AECC Shanghai Commercial Aircraft Engine Manufacturing Co. LTD., Shanghai, China ; School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China
Cenedese, Mattia ✱; Institute for Mechanical Systems, ETH Zürich, Zürich, Switzerland
Kosova, Giancarlo ✱; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M) ; Siemens Industry Software, Leuven, Belgium
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 I: Measurement of nonlinear dynamics
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, USA . 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) .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, USA. 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).
Brake, M.R.W., The Mechanics of Jointed Structures: Recent Research and Open Challenges for Developing Predictive Models for Structural Dynamics. 2017, Springer.
Gaul, L., Nitsche, R., The role of friction in mechanical joints. Appl. Mech. Rev. 54:2 (2001), 5173–5184.
Schwingshackl, C.W., Di Maio, D., Sever, I., Green, J.S., Modeling and validation of the nonlinear dynamic behavior of bolted flange joints. J. Eng. Gas Turbines Power, 135(12), 2013, 122504.
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.
Noel, J.P., Kerschen, G., Nonlinear system identification in structural dynamics: 10 more years of progress. Mech. Syst. Signal Process. 83 (2017), 2–35.
Brunton, S.L., Proctor, J.L., Kutz, J.N., Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proc. Natl. Acad. Sci. 113:15 (2016), 3932–3937.
Lai, Z., Nagarajaiah, S., Sparse structural system identification method for nonlinear dynamic systems with hysteresis/inelastic behavior. Mech. Syst. Signal Process. 117 (2019), 813–842.
Worden, K., Barthorpe, R.J., Cross, E.J., Dervilis, N., Holmes, G.R., Manson, G., Rogers, T.J., On evolutionary system identification with applications to nonlinear benchmarks. Mech. Syst. Signal Process. 112 (2018), 194–232.
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.
Atkins, P.A., Wright, J.R., Worden, K., An extension of force appropriation to the identification of non-linear multi-degree of freedom systems. J. Sound Vib. 237:1 (2000), 23–43.
Peeters, M., Kerschen, G., Golinval, J., Modal testing of nonlinear vibrating structures based on nonlinear normal modes: experimental demonstration. Mech. Syst. Signal Process. 25:4 (2011), 1227–1247.
Schwingshackl, C.W., Joannin, C., Pesaresi, L., Green, J.S., Hoffmann, N., Test method development for nonlinear damping extraction of dovetail joints. Dynamics of Coupled Structures, Vol. 1, 2014, Springer, 229–237.
Catalfamo, S., Smith, S.A., Morlock, F., Brake, M.R.W., Reuß, P., Schwingshackl, C.W., Zhu, W., Effects of experimental methods on the measurements of a nonlinear structure. Dynamics of Coupled Structures, Vol. 4, 2016, Springer, 491–500.
Gloth, G., Sinapius, M., Influence and characterisation of weak non-linearities in swept-sine modal testing. Aerosp. Sci. Technol. 8:2 (2004), 111–120.
Wright, J.R., Cooper, J.E., Desforges, M.J., Normal-mode force appropriation—theory and application. Mech. Syst. Signal Process. 13:2 (1999), 217–240.
Lau, J., Peeters, B., Debille, J., Guzek, Q., Kahlmann, T., Ground Vibration Testing Master Class: Modern Testing and Analysis Concepts Applied to an F-16 Aircraft Advanced Aerospace Applications, vol. 1, 2011, Springer, New York.
Kerschen, G., Peeters, M., Golinval, J., Vakakis, A.F., Nonlinear normal modes, Part I: A useful framework for the structural dynamicist. Mech. Syst. Signal Process. 23:1 (2009), 170–194.
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.
Peter, S., Riethmüller, R., Leine, R.I., Tracking of Backbone Curves of Nonlinear Systems using Phase-Locked-Loops. 2016, Springer International Publishing.
Scheel, M., Peter, S., Leine, R.I., Krack, M., A phase resonance approach for modal testing of structures with nonlinear dissipation. J. Sound Vib. 435 (2018), 56–73.
Noël, J.P., Kerschen, G., Frequency-domain subspace identification for nonlinear mechanical systems. Mech. Syst. Signal Process. 40:2 (2013), 701–717.
Lacy, S.L., Bernstein, D.S., Subspace identification for non-linear systems with measured-input non-linearities. Internat. J. Control 78:12 (2005), 906–926.
Marchesiello, S., Garibaldi, L., A time domain approach for identifying nonlinear vibrating structures by subspace methods. Mech. Syst. Signal Process. 22:1 (2008), 81–101.
Noel, J.P., Esfahani, A.F., Kerschen, G., Schoukens, J., A nonlinear state-space approach to hysteresis identification. Mech. Syst. Signal Process. 84 (2017), 171–184.
Warren, C., Niezrecki, C., Avitabile, P., Pingle, P., Comparison of FRF measurements and mode shapes determined using optically image based, laser, and accelerometer measurements. Mech. Syst. Signal Process. 25:6 (2011), 2191–2202.
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.
Chen, W., Zang, X., Wu, S., Jin, M., Song, H., Gradient-based point tracking method and its application in the modal test of a solar array model. Measurement, 2020.
Bhowmick, S., Nagarajaiah, S., Lai, Z., Measurement of full-field displacement time history of a vibrating continuous edge from video. Mech. Syst. Signal Process., 144, 2020, 106847.
Bhowmick, S., Nagarajaiah, S., Identification of full-field dynamic modes using continuous displacement response estimated from vibrating edge video. J. Sound Vib., 489, 2020, 115657.
Chen, Wei, Jin, Mengshi, Huang, Jiasheng, Chen, Yuanchang, Song, Hanwen, A method to distinguish harmonic frequencies and remove the harmonic effect in operational modal analysis of rotating structures. Mech. Syst. Signal Process., 2021.
Chu, T.C., Ranson, W.F., Sutton, Michael A., Applications of digital-image-correlation techniques to experimental mechanics. Exp. Mech. 25:3 (1985), 232–244.
Pan, Bing, Qian, Kemao, Xie, Huimin, Asundi, Anand, Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas. Sci. Technol., 20(6), 2009, 062001.
Sutton, Michael A., Orteu, Jean Jose, Schreier, Hubert, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications. 2009, Springer Science & Business Media.
Baqersad, Javad, Poozesh, Peyman, Niezrecki, Christopher, Avitabile, Peter, Photogrammetry and optical methods in structural dynamics–a review. Mech. Syst. Signal Process. 86 (2017), 17–34.
Feng, D.M., Feng, M.Q., Experimental validation of cost-effective vision-based structural health monitoring. Mech. Syst. Signal Process. 88 (2017), 199–211.
Spencer, Billie F. Jr., Hoskere, Vedhus, Narazaki, Yasutaka, Advances in computer vision-based civil infrastructure inspection and monitoring. Engineering 5:2 (2019), 199–222.
Beberniss, T.J., Ehrhardt, D.A., High-speed 3D digital image correlation vibration measurement: Recent advancements and noted limitations. Mech. Syst. Signal Process. 86 (2017), 35–48.
Jana, Debasish, Nagarajaiah, Satish, Computer vision-based real-time cable tension estimation in Dubrovnik cable-stayed bridge using moving handheld video camera. Struct. Control Health Monit., 28(5), 2021, e2713.
Pan, B., Qian, K., Xie, H., Asundi, A., Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Meas. Sci. Technol., 20(6), 2009, 062001.
Ehrhardt, D.A., Allen, M.S., Yang, S.F., Beberniss, T.J., Full-field linear and nonlinear measurements using continuous-scan laser Doppler vibrometry and high speed three-dimensional digital image correlation. Mech. Syst. Signal Process. 86 (2017), 82–97.
Bregar, T., Zaletelj, K., Cepon, G., Slavic, J., Boltezar, M., Full-field FRF estimation from noisy high-speed-camera data using a dynamic substructuring approach. Mech. Syst. Signal Process., 150, 2021, 12.
Singh, A., Moore, K.J., Characteristic nonlinear system identification of local attachments with clearance nonlinearities. Nonlinear Dynam. 102:3 (2020), 1667–1684.
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, 22.
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.
Poozesh, P., Baqersad, J., Niezrecki, C., Avitabile, P., Harvey, E., Yarala, R., Large-area photogrammetry based testing of wind turbine blades. Mech. Syst. Signal Process. 86 (2017), 98–115.
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.
Dossogne, T., Jerome, T.W., Lancereau, D.P.T., Smith, S.A., Brake, M.R.W., Pacini, B.R., Reuss, P., Schwingshackl, C.W., Experimental assessment of the influence of interface geometries on structural dynamic response. Dynamics of Coupled Structures, Vol. 4, 2017, Springer, 255–261.
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.
Zhang, Z., A flexible new technique for camera calibration. IEEE Trans. Pattern Anal. Mach. Intell. 22 (2000), 1330–1334.
Urban, S., Leitloff, J., Hinz, S., Improved wide-angle, fisheye and omnidirectional camera calibration. ISPRS J. Photogramm. Remote Sens. 108 (2015), 72–79.
Reu, P., All about speckles: Speckle size measurement. Exp. Tech. 38:6 (2014), 1–2.
Turner, D.Z., Digital Image Correlation Engine (DICe) Reference Manual: Sandia Rep. SAND2015-10606 O., 2015, Sandia Nat. Lab., Livermore, CA, USA.
Mace, T., Taylor, J., Schwingshackl, C.W., A novel technique to extract the modal damping properties of a thin blade. Topics in Modal Analysis & Testing, Vol. 8, 2020, Springer, 247–250.
Jana, D., Mukhopadhyay, S., Ray-Chaudhuri, S., Fisher information-based optimal input locations for modal identification. J. Sound Vib., 459, 2019, 114833.
Chen, W., Jin, M.S., Song, H.W., Optimal configuration of shakers for phase resonance testing using modal parameters. Proc. Inst. Mech. Eng. C 233:16 (2019), 5676–5690.
Goyder, H., Signal processing methods for determining the properties of bolted joints. ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2015, American Society of Mechanical Engineers V008T13A024.
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.
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.
Jin, M., Kosova, G., Cenedese, M., Chen, W., Singh, A., Jana, D., Brake, M.R.W., 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 II - Nonlinear system identification. 2021, 10.1016/j.ymssp.2021.108402.
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.
Balaji, N.N., Chen, W., Brake, M.R.W., Traction-based multi-scale nonlinear dynamic modeling of bolted joints: Formulation, application, and trends in micro-scale interface evolution. Mech. Syst. Signal Process., 139, 2020, 32.
Krack, M., Nonlinear modal analysis of nonconservative systems: Extension of the periodic motion concept. Comput. Struct. 154 (2015), 59–71.
Moore, K.J., Kurt, M., Eriten, M., McFarland, D.M., Bergman, L.A., Vakakis, A.F., Direct detection of nonlinear modal interactions from time series measurements. Mech. Syst. Signal Process., 2017.