Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

Sun, Yekai; Yuan, Jie; Vizzaccaro, Alessandra; Salles, Loïc

doi:10.1007/s11071-021-06567-0

Article (Scientific journals)

Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

Sun, Yekai; Yuan, Jie; Vizzaccaro, Alessandra et al.

2021 • In Nonlinear Dynamics, 104 (4), p. 3077 - 3107

Peer reviewed

Permalink
https://hdl.handle.net/2268/334057

DOI
10.1007/s11071-021-06567-0

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

yekai-NLdyn2021b.pdf

Publisher postprint (5.02 MB)

Download

All documents in ORBi are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Nonlinear damping; Damped nonlinear normal modes; Nonlinear vibration; Nonlinear modal analysis

Abstract :

[en] The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-periodic dNNMs using classic methods for periodic problems, two concepts have been developed in the last two decades: complex nonlinear mode (CNM) and extended periodic motion concept (EPMC). A critical assessment of these two concepts applied to different types of non-conservative nonlinearities and industrial full-scale structures has not been thoroughly investigated yet. Furthermore, there exist two emerging techniques which aim at predicting the resonant solutions of a nonlinear forced response using the dNNMs: extended energy balance method (E-EBM) and nonlinear modal synthesis (NMS). A detailed assessment between these two techniques has been rarely attempted in the literature. Therefore, in this work, a comprehensive comparison between CNM and EPMC is provided through two illustrative systems and one engineering application. The EPMC with an alternative damping assumption is also derived and compared with the original EPMC and CNM. The advantages and limitations of the CNM and EPMC are critically discussed. In addition, the resonant solutions are predicted based on the dNNMs using both E-EBM and NMS. The accuracies of the predicted resonances are also discussed in detail.

Disciplines :

Mechanical engineering

Author, co-author :

Sun, Yekai

Yuan, Jie

Vizzaccaro, Alessandra

Salles, Loïc ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Vibration of Turbomachines ; Imperial College London > Mechanical Engineering > Vibration University Technology Center

Language :

English

Title :

Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities

Publication date :

2021

Journal title :

Nonlinear Dynamics

ISSN :

0924-090X

eISSN :

1573-269X

Volume :

104

Issue :

Pages :

3077 - 3107

Peer reviewed :

Peer reviewed

Available on ORBi :

since 06 July 2025

Statistics

Number of views

20 (0 by ULiège)

Number of downloads

18 (0 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Allgower, E.L., Georg, K.: Introduction to numerical continuation methods. Class. Appl. Math. 45, xxvi-388 (2003)
Ascher, U., Christiansen, J., Russell, R.D.: A collocation solver for mixed order systems of boundary value problems. In: Mathematics of Computation, pp. 659–679 (1979)
Cameron, T.M., Griffin, J.H.: An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems. J. Appl. Mech. 56(1), 149–154 (1989) DOI: 10.1115/1.3176036
Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proc. R. Soc. A Math. Phys. Eng. Sci. 476(2234), 20190494 (2020)
Craig Jr., R.R., Bampton, M.C.C.: Coupling of substructures for dynamic analyses. AIAA J. 6(7), 1313–1319 (1968) DOI: 10.2514/3.4741
Heinze, T., Panning-von Scheidt, L., Wallaschek, J.: Global detection of detached periodic solution branches of friction-damped mechanical systems. Nonlinear Dyn. 99(3), 1841–1870 (2020) DOI: 10.1007/s11071-019-05425-4
Hill, T., Cammarano, A., Neild, S., Wagg, D.: Interpreting the forced responses of a two-degree-of-freedom nonlinear oscillator using backbone curves. J. Sound Vib. 349, 276–288 (2015) DOI: 10.1016/j.jsv.2015.03.030
Jahn, M., Tatzko, S., von Scheidt, L.P., Wallaschek, J.: Comparison of different harmonic balance based methodologies for computation of nonlinear modes of non-conservative mechanical systems. Mech. Syst. Signal Process. 127, 159–171 (2019) DOI: 10.1016/j.ymssp.2019.03.005
Jezequel, L., Lamarque, C.: Analysis of non-linear dynamical systems by the normal form theory. J. Sound Vib. 149(3), 429–459 (1991) DOI: 10.1016/0022-460X(91)90446-Q
Kerschen, G., Peeters, M., Golinval, J., Vakakis, A.: Nonlinear normal modes, part I: a useful framework for the structural dynamicist. Mech. Syst. Signal Process. 23(1), 170–194 (2009), special Issue: Non-linear Structural Dynamics
Krack, M.: Nonlinear modal analysis of nonconservative systems: extension of the periodic motion concept. Comput. Struct. 154, 59–71 (2015) DOI: 10.1016/j.compstruc.2015.03.008
Krack, M., Gross, J.: Harmonic Balance for Nonlinear Vibration Problems. Springer, Berlin (2019) DOI: 10.1007/978-3-030-14023-6
Krack, M., Salles, L., Thouverez, F.: Vibration prediction of bladed disks coupled by friction joints. Arch. Comput. Methods Eng. 24, 589–636 (2016) DOI: 10.1007/s11831-016-9183-2
Krack, M., Panning-von Scheidt, L., Wallaschek, J.: A method for nonlinear modal analysis and synthesis: application to harmonically forced and self-excited mechanical systems. J. Sound Vib. 332(25), 6798–6814 (2013) DOI: 10.1016/j.jsv.2013.08.009
Laxalde, D., Thouverez, F., Sinou, J.J., Lombard, J.P.: Qualitative analysis of forced response of blisks with friction ring dampers. Eur. J. Mec. A Solids 26(4), 676–687 (2007) DOI: 10.1016/j.euromechsol.2006.10.002
Laxalde, D., Gibert, C., Thouverez, F.: Experimental and numerical investigations of friction rings damping of blisks. ASME. Paper No.GT2008–50862 (2008)
Laxalde, D., Salles, L., Blanc, L., Thouverez, F.: Non-linear modal analysis for bladed disks with friction contact interfaces. ASME. Paper No. GT2008-50860 (2008)
Laxalde, D., Thouverez, F.: Complex non-linear modal analysis for mechanical systems: application to turbomachinery bladings with friction interfaces. J. Sound Vib. 322(4), 1009–1025 (2009) DOI: 10.1016/j.jsv.2008.11.044
Laxalde, D., Thouverez, F., Lombard, J.P.: Forced response analysis of integrally bladed disks with friction ring dampers. J. Vib. Acoust. 132(1), 011013 (2010) DOI: 10.1115/1.4000763
Lupini, A., Mitra, M., Epureanu, B.I.: Application of tuned vibration absorber concept to blisk ring dampers: a nonlinear study. J. Eng. Gas Turbines Power 141(10), 101016 (2019) DOI: 10.1115/1.4044684
Peletan, L., Baguet, S., Torkhani, M., Jacquet-Richardet, G.: A comparison of stability computational methods for periodic solution of nonlinear problems with application to rotordynamics. Nonlinear Dyn. 72(3), 671–682 (2013) DOI: 10.1007/s11071-012-0744-0
Pesheck, E., Pierre, C., Shaw, S.: A new Galerkin-based approach for accurate non-linear normal modes through invariant manifolds. J. Sound Vib. 249(5), 971–993 (2002) DOI: 10.1006/jsvi.2001.3914
Rosenberg, R.M.: Normal modes of nonlinear dual-mode systems. J. Appl. Mech. 27(2), 263–268 (1960) DOI: 10.1115/1.3643948
Salles, L., Blanc, L., Thouverez, F., Gouskov, A.M., Jean, P.: Dynamic analysis of a bladed disk with friction and fretting-wear in blade attachments. GT2009-60151 (2009)
Salles, L., Blanc, L., Thouverez, F., Gouskov, A.M., Jean, P.: Dual time stepping algorithms with the high order harmonic balance method for contact interfaces with fretting-wear. J. Eng. Gas Turbines Power 134(3): 032503 (2012)
Sarrouy, E.: Phase driven modal synthesis for forced response evaluation. In: 7th International Conference on Nonlinear Vibrations, Localization and Energy Transfer. Marseille, France (2019)
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, 56–73 (2018) DOI: 10.1016/j.jsv.2018.07.010
Shaw, S.W., Pierre, C.: Non-linear normal modes and invariant manifolds. J. Sound Vib. 150(1), 170–173 (1991) DOI: 10.1016/0022-460X(91)90412-D
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 Dyn. 103(4), 3315–3333 (2021) DOI: 10.1007/s11071-020-05793-2
Sun, Y., Yuan, J., Denimal, E., Salles, L.: Nonlinear modal analysis of frictional ring damper for compressor blisk. J. Eng. Gas Turbines Power 143(3), 031008 (2021) DOI: 10.1115/1.4049761
Sun, Y., Yuan, J., Denimal, E., Salles, L.: A study of the contact interface for compressor blisks with ring dampers using nonlinear modal analysis. In: IOP Conference Series: Materials Science and Engineering, vol. 1081, p. 012041 (2021)
Sun, Y., Yuan, J., Pesaresi, L., Denimal, E., Salles, L.: Parametric study and uncertainty quantification of the nonlinear modal properties of frictional dampers. J. Vib. Acoust. 142(5), 051102 (2020) DOI: 10.1115/1.4046953
Sun, Y., Yuan, J., Pesaresi, L., Salles, L.: Nonlinear vibrational analysis for integrally bladed disk using frictional ring damper. J. Phys. Conf. Ser. 1106, 012026 (2018) DOI: 10.1088/1742-6596/1106/1/012026
Szemplińska-Stupnicka, W.: The modified single mode method in the investigations of the resonant vibrations of non-linear systems. J. Sound Vib. 63(4), 475–489 (1979) DOI: 10.1016/0022-460X(79)90823-X
Wang, X., Hill, T.L., Neild, S.A., Shaw, A.D., Khodaparast, H.H., Friswell, M.I.: Model updating strategy for structures with localised nonlinearities using frequency response measurements. Mech. Syst. Signal Process. 100, 940–961 (2018) DOI: 10.1016/j.ymssp.2017.08.004
Wang, X., Zheng, G.T.: Equivalent dynamic stiffness mapping technique for identifying nonlinear structural elements from frequency response functions. Mech. Syst. Signal Process. 68, 394–415 (2016) DOI: 10.1016/j.ymssp.2015.07.011
Wu, Y., Li, L., Fan, Y., Zucca, S., Gastaldi, C., Ma, H.: Design of dry friction and piezoelectric hybrid ring dampers for integrally bladed disks based on complex nonlinear modes. Comput. Struct. 233, 106237 (2020) DOI: 10.1016/j.compstruc.2020.106237
Yang, B., Chu, M., Menq, C.: Stick-slip-separation analysis and non-linear stiffness and damping characterization of friction contacts having variable normal load. J. Sound Vib. 210(4), 461–481 (1998) DOI: 10.1006/jsvi.1997.1305
Yuan, J., El-Haddad, F., Salles, L., Wong, C.: Numerical assessment of reduced order modeling techniques for dynamic analysis of jointed structures with contact nonlinearities. ASME. Paper No. GT2018-75303 (2019)