Skip to main content
Top

2023 | OriginalPaper | Chapter

8. Accuracy of Nonlinear Substructuring Technique in the Modal Domain

Authors : Jacopo Brunetti, Walter D’Ambrogio, Annalisa Fregolent, Francesco Latini

Published in: Dynamic Substructures, Volume 4

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The dynamic analysis of complex engineering systems can be performed by considering the assemblies as composed of subsystems and coupling them through substructuring techniques. A technique in the modal domain called Nonlinear Coupling Procedure (NLCP) has been recently defined to couple subsystems connected through nonlinear connections by using their Nonlinear Normal Modes (NNMs). It manages to capture the main dynamic features of the system, i.e., the backbone of each NNM, and it provides satisfactory results in terms of mode shape and resonance frequency as function of the excitation level of the assembled system, with a considerable reduction of the computational time. However the results may be inaccurate due to approximations either in the models of the subsystems or due to the considered coupling technique. Furthermore, nonlinear subsystems can be the cause of complex behaviors of the assembly and then their models need to be carefully characterized. Thus, it is necessary to evaluate the reliability of the method in terms of the accuracy of the solution. This is done by defining a reliability ratio based on energy concepts depending on the level of the excitation acting on the system. The effectiveness of the reliability ratio of nonlinear techniques is verified on the NLCP applied to a mechanical system with localized nonlinearities.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference de Klerk, D., Rixen, D.J., Voormeeren, S.N.: General framework for dynamic substructuring: history, review, and classification of techniques. AIAA J. 46(5), 1169–1181 (2008)CrossRef de Klerk, D., Rixen, D.J., Voormeeren, S.N.: General framework for dynamic substructuring: history, review, and classification of techniques. AIAA J. 46(5), 1169–1181 (2008)CrossRef
2.
go back to reference Brunetti, J., Culla, A., D’Ambrogio, W., Fregolent, A.: Experimental dynamic substructuring of the Ampair wind turbine test bed. In: Conference Proceedings of the Society for Experimental Mechanics Series, vol. 1, pp. 15–26. Springer New York LLC (2014) Brunetti, J., Culla, A., D’Ambrogio, W., Fregolent, A.: Experimental dynamic substructuring of the Ampair wind turbine test bed. In: Conference Proceedings of the Society for Experimental Mechanics Series, vol. 1, pp. 15–26. Springer New York LLC (2014)
3.
go back to reference Craig, R. Jr.: Coupling of substructures for dynamic analyses-an overview. In: 41st Structures, Structural Dynamics, and Materials Conference and Exhibit, p. 1573 (2000) Craig, R. Jr.: Coupling of substructures for dynamic analyses-an overview. In: 41st Structures, Structural Dynamics, and Materials Conference and Exhibit, p. 1573 (2000)
4.
go back to reference Rixen, D.J.: A dual Craig-Bampton method for dynamic substructuring. J. Comput. Appl. Math. 168(1–2), 383–391 (2004)MathSciNetCrossRef Rixen, D.J.: A dual Craig-Bampton method for dynamic substructuring. J. Comput. Appl. Math. 168(1–2), 383–391 (2004)MathSciNetCrossRef
5.
go back to reference Voormeeren, S.N., Rixen, D.J., A family of substructure decoupling techniques based on a dual assembly approach. Mech. Syst. Signal Process. 27, 379–396 (2012)CrossRef Voormeeren, S.N., Rixen, D.J., A family of substructure decoupling techniques based on a dual assembly approach. Mech. Syst. Signal Process. 27, 379–396 (2012)CrossRef
6.
go back to reference D’Ambrogio, W., Fregolent, A., Decoupling procedures in the general framework of frequency based substructuring. In Proceedings of 27th IMAC. Orlando (USA) (2009) D’Ambrogio, W., Fregolent, A., Decoupling procedures in the general framework of frequency based substructuring. In Proceedings of 27th IMAC. Orlando (USA) (2009)
7.
go back to reference Saeed, Z., Klaassen, S.W.B., Firrone, C.M., Berruti, T.M., Rixen, D.J.: Experimental joint identification using system equivalent model mixing in a bladed-disk. J. Vib. Acoust. 142(5), 1–29 (2020)CrossRef Saeed, Z., Klaassen, S.W.B., Firrone, C.M., Berruti, T.M., Rixen, D.J.: Experimental joint identification using system equivalent model mixing in a bladed-disk. J. Vib. Acoust. 142(5), 1–29 (2020)CrossRef
8.
go back to reference Saeed, Z., Firrone, C.M., Berruti, T.M.: Joint identification through hybrid models improved by correlations. J. Sound Vib. 494, 115889 (2021)CrossRef Saeed, Z., Firrone, C.M., Berruti, T.M.: Joint identification through hybrid models improved by correlations. J. Sound Vib. 494, 115889 (2021)CrossRef
9.
go back to reference Kalaycioğlu, T., Özgüven, H.N.: Harmonic response of large engineering structures with nonlinear modifications. In Proceedings of the 8th International Conference on Structural Dynamics, EURODYN, pp. 3623–3629 (2011) Kalaycioğlu, T., Özgüven, H.N.: Harmonic response of large engineering structures with nonlinear modifications. In Proceedings of the 8th International Conference on Structural Dynamics, EURODYN, pp. 3623–3629 (2011)
10.
go back to reference Kalaycıoğlu, T., Özgüven, H.N.: Nonlinear structural modification and nonlinear coupling. Mech. Syst. Signal Process. 46(2), 289–306 (2014)CrossRef Kalaycıoğlu, T., Özgüven, H.N.: Nonlinear structural modification and nonlinear coupling. Mech. Syst. Signal Process. 46(2), 289–306 (2014)CrossRef
11.
go back to reference Kalaycıoğlu, T., Özgüven, H.N., FRF decoupling of nonlinear systems. Mech. Syst. Signal Process. 102, 230–244 (2018)CrossRef Kalaycıoğlu, T., Özgüven, H.N., FRF decoupling of nonlinear systems. Mech. Syst. Signal Process. 102, 230–244 (2018)CrossRef
12.
go back to reference Vander Velde, W.E., Multiple-Input Describing Functions and Nonlinear System Design. McGraw-Hill, New York (1968)MATH Vander Velde, W.E., Multiple-Input Describing Functions and Nonlinear System Design. McGraw-Hill, New York (1968)MATH
13.
go back to reference Kuether, R.J., Allen, M.S., Hollkamp, J.J.: Modal substructuring of geometrically nonlinear finite-element models. AIAA J. 54(2), 691–702 (2015)CrossRef Kuether, R.J., Allen, M.S., Hollkamp, J.J.: Modal substructuring of geometrically nonlinear finite-element models. AIAA J. 54(2), 691–702 (2015)CrossRef
14.
go back to reference Hollkamp, J.J., Gordon, R.W., Spottswood, S.M.: Nonlinear modal models for sonic fatigue response prediction: a comparison of methods. Shock Vib. Digest 38(3), 232–233 (2006) Hollkamp, J.J., Gordon, R.W., Spottswood, S.M.: Nonlinear modal models for sonic fatigue response prediction: a comparison of methods. Shock Vib. Digest 38(3), 232–233 (2006)
15.
go back to reference Kuether, R.J., Allen, M.S., Nonlinear modal substructuring of systems with geometric nonlinearities. In 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, p. 1521 (2013) Kuether, R.J., Allen, M.S., Nonlinear modal substructuring of systems with geometric nonlinearities. In 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, p. 1521 (2013)
16.
go back to reference Latini, F., Brunetti, J., Kwarta, M., Allen, M.S., D’Ambrogio, W., Fregolent, A.: Experimental results of nonlinear structure coupled through nonlinear connecting elements. In Proceedings of ISMA 2020 - International Conference on Noise and Vibration Engineering and USD 2020 - International Conference on Uncertainty in Structural Dynamics (2020) Latini, F., Brunetti, J., Kwarta, M., Allen, M.S., D’Ambrogio, W., Fregolent, A.: Experimental results of nonlinear structure coupled through nonlinear connecting elements. In Proceedings of ISMA 2020 - International Conference on Noise and Vibration Engineering and USD 2020 - International Conference on Uncertainty in Structural Dynamics (2020)
17.
go back to reference Latini, F., Brunetti, J., D’Ambrogio, W., Allen, M.S., Fregolent, A.: Nonlinear substructuring in the modal domain: numerical validation and experimental verification in presence of localized nonlinearities. Nonlinear Dyn. 104(2), 1043–1067 (2021)CrossRef Latini, F., Brunetti, J., D’Ambrogio, W., Allen, M.S., Fregolent, A.: Nonlinear substructuring in the modal domain: numerical validation and experimental verification in presence of localized nonlinearities. Nonlinear Dyn. 104(2), 1043–1067 (2021)CrossRef
18.
go back to reference Latini, F., Brunetti, J., D’Ambrogio, W., Fregolent, A.: Substructures’ coupling with nonlinear connecting elements. Nonlinear Dyn. 99(2), 1643–1658 (2020)CrossRef Latini, F., Brunetti, J., D’Ambrogio, W., Fregolent, A.: Substructures’ coupling with nonlinear connecting elements. Nonlinear Dyn. 99(2), 1643–1658 (2020)CrossRef
19.
go back to reference Brunetti, J., D’Ambrogio, W., Fregolent, A., Latini, F.: Substructuring using NNMs of nonlinear connecting elements. In: Carcaterra, A., Paolone, A., Graziani, G. (eds.) Proceedings of XXIV AIMETA Conference 2019. AIMETA 2019. Lecture Notes in Mechanical Engineering. Springer (2020) Brunetti, J., D’Ambrogio, W., Fregolent, A., Latini, F.: Substructuring using NNMs of nonlinear connecting elements. In: Carcaterra, A., Paolone, A., Graziani, G. (eds.) Proceedings of XXIV AIMETA Conference 2019. AIMETA 2019. Lecture Notes in Mechanical Engineering. Springer (2020)
20.
go back to reference Brunetti, J., D’Ambrogio, W., Fregolent, A., Latini, F.: Dynamic substructuring using a combination of softening and hardening connecting elements. In Dynamic Substructures, vol. 4, pp. 23–33. Springer, Berlin (2022) Brunetti, J., D’Ambrogio, W., Fregolent, A., Latini, F.: Dynamic substructuring using a combination of softening and hardening connecting elements. In Dynamic Substructures, vol. 4, pp. 23–33. Springer, Berlin (2022)
21.
go back to reference 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), 170–194 (2009)CrossRef 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), 170–194 (2009)CrossRef
22.
go back to reference Peeters, M., Viguié, R., Sérandour, G., Kerschen, G., Golinval, J.: Nonlinear normal modes, part ii: toward a practical computation using numerical continuation techniques. Mech. Syst. Signal Process. 23(1), 195–216 (2009)CrossRef Peeters, M., Viguié, R., Sérandour, G., Kerschen, G., Golinval, J.: Nonlinear normal modes, part ii: toward a practical computation using numerical continuation techniques. Mech. Syst. Signal Process. 23(1), 195–216 (2009)CrossRef
23.
go back to reference Krack, M., Gross, J.: Harmonic Balance for Nonlinear Vibration Problems. Springer, Berlin (2019)CrossRef Krack, M., Gross, J.: Harmonic Balance for Nonlinear Vibration Problems. Springer, Berlin (2019)CrossRef
Metadata
Title
Accuracy of Nonlinear Substructuring Technique in the Modal Domain
Authors
Jacopo Brunetti
Walter D’Ambrogio
Annalisa Fregolent
Francesco Latini
Copyright Year
2023
DOI
https://doi.org/10.1007/978-3-031-04094-8_8