Abstract
This work proposes a new reduced order modelling method to improve the computational efficiency for the dynamic simulation of a jointed structures with localized contact friction non-linearities. We reformulate the traditional equation of motion for a joint structure by linearising the non-linear system on the contact interface and augmenting the linearised system by introducing an internal non-linear penalty variable. The internal variable is used to compensate the possible non-linear effects from the contact interface. Three types of reduced basis are selected for the Galerkin projection, namely, the vibration modes (VMs) of the linearised system, static modes (SMs) and also the trial vector derivatives (TVDs) vectors. Using these reduced basis, it would allow the size of the internal variable to change correspondingly with the number of active non-linear DOFs. The size of the new reduced order model therefore can be automatically updated depending on the contact condition during the simulations. This would reduce significantly the model size when most of the contact nodes are in a stuck condition, which is actually often the case when a jointed structure vibrates. A case study using a 2D joint beam model is carried out to demonstrate the concept of the proposed method. The initial results from this case study is then compared to the state of the art reduced order modeling.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bograd, S., Reuss, P., Schmidt, A., Gaul, L., Mayer, M.: Modeling the dynamics of mechanical joints. Mech. Syst. Signal Process. 25(8), 2801–2826 (2011)
Craig, R., Bampton, M.: Coupling of substructures for dynamic analyses. AIAA J. 6(7), 1313–1319 (1968)
Gruber, F.M., Rixen, D.J.: Evaluation of substructure reduction techniques with fixed and free interfaces. Strojniški vestnik-J. Mech. Eng. 62(7–8), 452–462 (2016)
Krack, M., Salles, L., Thouverez, F.: Vibration prediction of bladed disks coupled by friction joints. Arch. Comput. Meth. Eng. 24(3), 589–636 (2017)
Pesaresi, L., Salles, L., Jones, A., Green, J., Schwingshackl, C.: Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications. Mech. Syst. Signal Process. 85, 662–679 (2017)
Petrov, E.: A high-accuracy model reduction for analysis of nonlinear vibrations in structures with contact interfaces. J. Eng. Gas Turbines Power 133(10), 102503 (2011)
Pinnau, R.: Model reduction via proper orthogonal decomposition. In: Model Order Reduction: Theory, Research Aspects and Applications, pp. 95–109. Springer (2008)
Rubin, S.: Improved component-mode representation for structural dynamic analysis. AIAA J. 13(8), 995–1006 (1975)
Sarrouy, E., Sinou, J.-J.: Non-linear periodic and quasi-periodic vibrations in mechanical systems-on the use of the harmonic balance methods. In: Advances in Vibration Analysis Research, InTech (2011)
Witteveen, W., Irschik, H.: Efficient mode based computational approach for jointed structures: joint interface modes. AIAA J. 47(1), 252–263 (2009)
Witteveen, W., Pichler, F.: Efficient model order reduction for the dynamics of nonlinear multilayer sheet structures with trial vector derivatives. Shock Vibr. 2014 (2014)
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. J. Eng. Gas Turbines Power 141(3), 031027 (2019)
Yuan, J., Scarpa, F., Allegri, G., Titurus, B., Patsias, S., Rajasekaran, R.: Efficient computational techniques for mistuning analysis of bladed discs: a review. Mech. Syst. Signal Process. 87, 71–90 (2017)
Acknowledgements
The authors would like to acknowledge the support of Rolls-Royce plc for this research through the Vibration University Technology Centre (UTC) at the Imperial College London, UK. Special acknowledgement goes also to GEMiniDS WP3—Innovate UK Project 113088, which is jointly supported by Innovate UK and Rolls-Royce plc.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Yuan, J., Salles, L., Wong, C., Patsias, S. (2020). A Novel Penalty-Based Reduced Order Modelling Method for Dynamic Analysis of Joint Structures. In: Fehr, J., Haasdonk, B. (eds) IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018. IUTAM Bookseries, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-030-21013-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-21013-7_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-21012-0
Online ISBN: 978-3-030-21013-7
eBook Packages: EngineeringEngineering (R0)