[en] In the virtual prototyping era, it remains crucial to validate the simulation results using experimental tests. In this context, one important assumption at the root of experimental modal analysis, the dominant method used in aerospace, civil and mechanical engineering, is that the structural system behaves linearly. To address this limitation, the idea of control-based nonlinear vibration testing (CBNVT) has recently emerged in the structural dynamics community. CBNVT combines (i) feedback control to stabilize unstable orbits and (ii) path-following techniques to explore - in a systematic and effective manner - the dynamics of the system directly during the experiment, i.e., without the need for a mathematical model of the system. The objective of this paper is twofold, namely (i) to present the existing methods in a unified manner and (ii) to introduce a novel, fully online and derivative-less experimental arclength continuation method.
D. J. Ewins, Modal Testing: Theory, Practice and Application. John Wiley & Sons, 2009.
K. Worden and G. R. Tomlinson, Nonlinearity in Structural Dynamics. IOP Publishing Ltd, 2001. [Online]. Available: http://stacks.iop.org/0750303565
J. Sieber and B. Krauskopf, “Control based bifurcation analysis for experiments,” Nonlinear Dynamics, vol. 51, no. 3, pp. 365-377, feb 2008. [Online]. Available: http://link.springer.com/10.1007/s11071-007-9217-2
S. Peter and R. I. Leine, “Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation,” Mechanical Systems and Signal Processing, vol. 96, pp. 139-158, nov 2017. [Online]. Available: https://linkinghub.elsevier.com/retrieve/pii/S0888327017302005
T. Karaağaçlı and H. N. Özgüven, “Experimental modal analysis of nonlinear systems by using response-controlled stepped-sine testing,” Mechanical Systems and Signal Processing, vol. 146, p. 107023, jan 2021. [Online]. Available: https://linkinghub.elsevier.com/retrieve/pii/S088832702030409X
G. Abeloos, F. Müller, E. Ferhatoglu, M. Scheel, C. Collette, G. Kerschen, M. Brake, P. Tiso, L. Renson, and M. Krack, “A consistency analysis of phase-locked-loop testing and control-based continuation for a geometrically nonlinear frictional system,” Mechanical Systems and Signal Processing, vol. 170, no. October 2021, p. 108820, may 2022. [Online]. Available: https://linkinghub.elsevier.com/retrieve/pii/S0888327022000188
T. Detroux, L. Renson, L. Masset, and G. Kerschen, “The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems,” Computer Methods in Applied Mechanics and Engineering, vol. 296, pp. 18-38, nov 2015. [Online]. Available: https://linkinghub.elsevier.com/retrieve/pii/S0045782515002297
D. A. W. Barton and J. Sieber, “Systematic experimental exploration of bifurcations with noninvasive control,” Physical Review E, vol. 87, no. 5, p. 052916, may 2013. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevE.87.052916
G. Abeloos, L. Renson, C. Collette, and G. Kerschen, “Stepped and swept control-based continuation using adaptive filtering,” Nonlinear Dynamics, vol. 104, no. 4, pp. 3793-3808, jun 2021. [Online]. Available: https://link.springer.com/10.1007/s11071-021-06506-z
S. Tatzko, G. Kleyman, and J. Wallaschek, “Continuation methods for lab experiments of nonlinear vibrations,” GAMM-Mitteilungen, vol. 46, no. 2, pp. 1-13, jun 2023. [Online]. Available: https://onlinelibrary.wiley.com/doi/10.1002/gamm.202300009
V. Babitsky, “Autoresonant mechatronic systems,” Mechatronics, vol. 5, no. 5, pp. 483-495, aug 1995. [Online]. Available: https://linkinghub.elsevier.com/retrieve/pii/0957415895000262
S. Mojrzisch, J. Wallaschek, and J. Bremer, “An Experimental Method for the Phase Controlled Frequency Response Measurement of Nonlinear Vibration Systems,” PAMM, vol. 12, no. 1, pp. 253-254, dec 2012. [Online]. Available: https://onlinelibrary.wiley.com/doi/10.1002/pamm.201210117
M. Link, M. Boeswald, S. Laborde, M. Weiland, and A. Calvi, “Non-linear experimental modal analysis and application to satellite vibration test data,” ECCOMAS Thematic Conference - COMPDYN 2011: 3rd International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering: An IACM Special Interest Conference, Programme, no. May 2014, 2011.
A. Carrella, “Introduction to Environmental Testing,” 2020. [Online]. Available: https://community.sw.siemens.com/s/article/simcenter-testlab-vibration-control
L. Renson, D. A. Barton, and S. A. Neild, “Experimental tracking of limit-point bifurcations and backbone curves using control-based continuation,” International Journal of Bifurcation and Chaos, vol. 27, no. 1, pp. 1-19, 2017. [Online]. Available: https://www.worldscientific.com/doi/abs/10.1142/S0218127417300026
G. Abeloos, “Control-based methods for the identification of nonlinear structures,” Ph.D. dissertation, University of Liège, 2022. [Online]. Available: https://hdl.handle.net/2268/295414
L. Woiwode and M. Krack, “Experimentally uncovering isolas via backbone tracking.” Journal of Structural Dynamics, pp. 122-143, 2024. [Online]. Available: https://popups.uliege.be/2684-6500/index.php?id=180
G. Raze, “An electronic Duffing oscillator,” 2024. [Online]. Available: https://github.com/GhislainRaze/Electronic-Duffing