Abstract
Background
Various nonlinear system identification methods applicable to distributed nonlinearities have been developed over the last decade. However, many of them are not eligible to accurately quantify a high degree of nonlinearity. Furthermore, there exist few studies that actually validate the identified nonlinear properties.
Objective
The main objective of this paper is the validation of a novel nonlinear system identification framework recently developed by the authors on a double-clamped thin beam structure that exhibits continuously distributed strong geometrical nonlinearity due to large amplitude oscillations and considerable damping nonlinearity due to micro-slip in the beam-base connections.
Methods
The identification framework consists of response-controlled stepped-sine testing (RCT) and the harmonic force surface (HFS) concept. The framework is implemented by using standard hardware and software in modal testing. The RCT approach is based on keeping the displacement amplitude of the driving point constant throughout the frequency sweep and its basic assumptions are well-separated modes and no internal resonance. Constant-force frequency response curves and backbone curves of the first nonlinear normal mode (NNM) are identified at multiple measurement points from HFSs constructed by using measured harmonic excitation force spectra. The NNM shapes of the first mode at various vibration levels are then constructed from the identified NNM backbone curves. On the other side, the response level-dependent modal parameters are identified by applying standard linear modal analysis techniques to frequency response functions (FRFs) measured at constant displacement amplitude levels throughout RCT.
Results
The RCT-HFS framework quantifies about a 20% shift of the natural frequency and an order of magnitude change of the modal damping ratio (from 0.5% to 4%) for the first mode of the double-clamped beam, which indicates a considerably high degree of stiffness and damping nonlinearities in the vibration range of interest. The identified nonlinear modal parameters are successfully validated by comparing near-resonant constant-force frequency response curves synthesized from these parameters with the ones measured by constant-force stepped-sine testing and with the ones extracted from the HFSs. The HFSs are determined for the first time in an experiment at multiple measurement points other than the driving point. The NNM shapes determined from HFSs are also validated by comparing them with the ones obtained from the identified nonlinear modal constants.
Conclusions
The RCT-HFS framework is successfully validated for the first time on a structure that exhibits continuously distributed geometrical nonlinearity. This study is a humble contribution towards making nonlinear experimental modal analysis a standard engineering practice.
Similar content being viewed by others
References
Noël JP, Kerschen G (2017) Nonlinear system identification in structural dynamics: 10 more years of progress. Mech Syst Signal Process 83:2–35
Rosenberg RM (1962) The normal modes of nonlinear n-degree-of-freedom systems. J Appl Mech 29:7–14
Rosenberg RM (1966) On nonlinear vibrations of systems with many degrees of freedom. Adv Appl Mech 9:155–242
Setio S, Setio HD, Jezequel L (1992) A method of nonlinear modal identification from frequency response tests. J Sound Vib 158(3):497–515
Gibert C (2003) Fitting measured frequency response using nonlinear modes. Mech Syst Signal Process 17(1):211–218
Szemplinska-Stupnicka W (1979) The modified single mode method in the investigations of the resonant vibrations of nonlinear systems. J Sound Vib 63(4):475–489
Peeters M, Kerschen G, Golinval JC (2011) Dynamic testing of nonlinear vibrating structures using nonlinear normal modes. J Sound Vib 330:486–509
Peeters M, Kerschen G, Golinval JC (2011) Modal testing of nonlinear vibrating structures based on nonlinear normal modes: experimental demonstration. Mech Syst Signal Process 25:1227–1247
Londono JM, Neild SA, Cooper JE (2015) Identification of backbone curves of nonlinear systems from resonance decay responses. J Sound Vib 348:224–238
Platten MF, Wright JR, Cooper JE, Dimitriadis G (2009) Identification of a nonlinear wing structure using an extended modal model. AIAA J Aircraft 46(5):1614–1626
Krack M (2021) Extension of the single nonlinear mode theory by linear attachments and application to exciter-structure interaction. J Sound Vib 505
Pacini BR, Kuether RJ, Roettgen DR (2022) Shaker-structure modeling and analysis for nonlinear force appropriation testing. Mech Syst Signal Process 162
Renson L, Gonzalez-Buelga A, Barton DAW, Neild SA (2016) Robust identification of backbone curves using control-based continuation. J Sound Vib 367:145–158
Sieber J, Krauskopf B (2008) Control based bifurcation analysis for experiments. Nonlinear Dyn 51:356–377
Peter S, Leine RI (2017) Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation. Mech Syst Signal Process 96:139–158
Denis V, Jossic M, Giraud-Audine C, Chomette B, Renault A, Thomas O (2018) Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form. Mech Syst Sig Process 106:430–452
Jezequel L, Lamarque C (1991) Analysis of non-linear dynamical systems by the normal form theory. J Sound Vib 149(3):429–459
Kwarta M, Allen MS (2022) Nonlinear Normal Mode backbone curve estimation with near-resonant steady state inputs. Mech Syst Signal Process 162
Anastasio D, Marchesiello S, Kerschen G, Noël JP (2019) Experimental identification of distributed nonlinearities in the modal domain. J Sound Vib 458:426–444
Wang X, Hill TL, Neild SA (2019) Frequency response expansion strategy for nonlinear structures. Mech Syst Signal Process 116:505–529
Marchesiello S, Garibaldi L (2008) A time domain approach for identifying nonlinear vibrating structures by subspace methods. Mech Syst Signal Process 22:81–101
Noël JP, Kerschen G (2013) Frequency-domain subspace identification for nonlinear mechanical systems. Mech Syst Signal Process 40:701–717
Karaağaçlı T, Özgüven HN (2021) Experimental modal analysis of nonlinear systems by using response-controlled stepped-sine testing. Mech Syst Signal Process 146
Karaağaçlı T, Özgüven HN (2020) Experimental identification of backbone curves of strongly nonlinear systems by using response-controlled stepped-sine testing (RCT). Vibration 3(3):266–280
Arslan Ö, Özgüven HN (2008) Modal identification of nonlinear structures and the use of modal model in structural dynamic analysis. Proceedings of the 26th International Modal Analysis Conference (IMAC) Orlando, FL, USA
Tanrıkulu Ö, Kuran B, Özgüven HN, Imregün M (1993) Forced harmonic response analysis of nonlinear structures using describing functions. AIAA J 31(7):1313–1320
Scheel M, Peter S, Leine RI, Krack M (2018) A phase resonance approach for modal testing of structures with nonlinear dissipation. J Sound Vib 435:56–73
Scheel M, Weigele T, Krack M (2020) Challenging an experimental nonlinear modal analysis method with a new strongly friction-damped structure. J Sound Vib 485
Karaağaçlı T, Özgüven HN (2021) Experimental modal analysis of geometrically nonlinear structures by using response-controlled stepped-sine testing. Proceedings of the 39th International Modal Analysis Conference (IMAC) Orlando, FL, USA
Abeloos G, Renson L, Collette C, Kerschen G (2021) Stepped and swept control based continuation using adaptive filtering. Nonlinear Dyn 104:3793-3808
Wang X, Zheng GT (2016) Equivalent dynamic stiffness mapping technique for identifying nonlinear structural elements from frequency response functions. Mech Syst Signal Process 68–69:394–415
Acknowledgements
The provision of TÜBİTAK-SAGE for modal testing and analysis capabilities is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Karaağaçlı, T., Özgüven, H.N. Experimental Quantification and Validation of Modal Properties of Geometrically Nonlinear Structures by Using Response-Controlled Stepped-Sine Testing. Exp Mech 62, 199–211 (2022). https://doi.org/10.1007/s11340-021-00784-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11340-021-00784-9