Research Papers

Numerical Assessment of Reduced Order Modeling Techniques for Dynamic Analysis of Jointed Structures With Contact Nonlinearities

[+] Author and Article Information
Jie Yuan

Department of Mechanical Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: jie.yuan@Imperial.ac.uk

Fadi El-Haddad

Department of Mechanical Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: f.el-haddad@imperial.ac.uk

Loic Salles

Department of Mechanical Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: l.salles@imperial.ac.uk

Chian Wong

Rolls-Royce plc,
P.O. Box 31,
Derby DE24 8BJ, UK
e-mail: Chian.Wong@Rolls-Royce.com

1Corresponding author.

Manuscript received June 28, 2018; final manuscript received July 20, 2018; published online November 1, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(3), 031027 (Nov 01, 2018) (12 pages) Paper No: GTP-18-1396; doi: 10.1115/1.4041147 History: Received June 28, 2018; Revised July 20, 2018

This work presents an assessment of classical and state of the art reduced order modeling (ROM) techniques to enhance the computational efficiency for dynamic analysis of jointed structures with local contact nonlinearities. These ROM methods include classical free interface method (Rubin method, MacNeal method), fixed interface method Craig-Bampton (CB), Dual Craig-Bampton (DCB) method and also recently developed joint interface mode (JIM) and trial vector derivative (TVD) approaches. A finite element (FE) jointed beam model is considered as the test case taking into account two different setups: one with a linearized spring joint and the other with a nonlinear macroslip contact friction joint. Using these ROM techniques, the accuracy of dynamic behaviors and their computational expense are compared separately. We also studied the effect of excitation levels, joint region size, and number of modes on the performance of these ROM methods.

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Brake, M. R. W. , Groß, J. , Lacayo, R. M. , Salles, L. , Schwingshackl, C. W. , Reuß, P. , and Armand, J. , 2018, “ Reduced Order Modeling of Nonlinear Structures With Frictional Interfaces,” The Mechanics of Jointed Structures: Recent Research and Open Challenges for Developing Predictive Models for Structural Dynamics, M.R.W., Brake , ed., Springer International Publishing, Cham, pp. 427–450.
Ibrahim, R. A. , and Pettit, C. L. , 2005, “ Uncertainties and Dynamic Problems of Bolted Joints and Other Fasteners,” J. Sound Vib., 279(3–5), pp. 857–936. [CrossRef]
Goyder, H. , Lancereau, D. , Ind, P. , and Brown, D. , 2016, Friction and Damping Associated With Bolted Joints: Results and Signal Processing, ISMA, Leuven, Belgium.
Krack, M. , and Panning-von Scheidt, L. , 2018, Nonlinear Modal Analysis and Modal Reduction of Jointed Structures, the Mechanics of Jointed Structures, Springer, Cham, pp. 525–538.
Beards, C. F. , 1979, “ Damping in Structural Joints, Shock and Vibration Information Center,” The Shock and Vibration Digest, 11(9), pp. 35–41.
Petrov, E. P. , and Ewins, D. J. , 2006, “ Effects of Damping and Varying Contact Area at Blade-Disk Joints in Forced Response Analysis of Bladed Disk Assemblies,” ASME J. Turbomach., 128(2), pp. 403–410. [CrossRef]
Petrov, E. P. , 2011, “ A High-Accuracy Model Reduction for Analysis of Nonlinear Vibrations in Structures With Contact Interfaces,” ASME J. Eng. Gas Turbines Power, 133(10), p. 102503. [CrossRef]
Krack, M. , Salles, L. , and Thouverez, F. , 2017, “ Vibration Prediction of Bladed Disks Coupled by Friction Joints,” Arch. Comput. Methods Eng., 24(3), pp. 589–636. [CrossRef]
Yuan, J. , Scarpa, F. , Allegri, G. , Titurus, B. , Patsias, S. , and Rajasekaran, R. , 2017, “ Efficient Computational Techniques for Mistuning Analysis of Bladed Discs: A Review,” Mechanical Systems and Signal Processing, 87(Part A), pp. 71–90.
Huang, S. , 2008, “ Dynamic Analysis of Assembled Structures With Nonlinearity, Department of Mechanical Engineering,” Ph. D. thesis, Imperial College London, UK.
Zucca, S. , and Epureanu, B. I. , 2014, “ Bi-Linear Reduced-Order Models of Structures With Friction Intermittent Contacts,” Nonlinear Dyn., 77(3), pp. 1055–1067. [CrossRef]
Pichler, F. , Witteveen, W. , and Fischer, P. , 2017, “ Reduced-Order Modeling of Preloaded Bolted Structures in Multibody Systems by the Use of Trial Vector Derivatives,” ASME J. Comput. Nonlinear Dyn., 12(5), p. 051032. [CrossRef]
Armand, J. , Pesaresi, L. , Salles, L. , and Schwingshackl, C. W. , 2017, “ A Multiscale Approach for Nonlinear Dynamic Response Predictions With Fretting Wear,” ASME J. Eng. Gas Turbines Power, 139(2), p. 022505. [CrossRef]
Gasch, R. , and Knothe, K. X. , 1989, Strukturdynamik: Bd. 2. Kontinua Und Ihre Diskretisierung, Springer-Verlag, Heidelberg, Germany.
Becker, J. , and Gaul, L. , 2008, “ CMS Methods for Efficient Damping Prediction for Structures With Friction,” IMAC-XXVI, Orlando, FL, Feb. 4–7. https://pdfs.semanticscholar.org/5b00/3a35f60c707da88a80423db8daaf4aebfbd8.pdf
Witteveen, W. , and Irschik, H. , 2009, “ Efficient Mode-Based Computational Approach for Jointed Structures: Joint Interface Modes,” AIAA J., 47(1), p. 252. [CrossRef]
Witteveen, W. , and Pichler, F. , 2014, “ Efficient Model Order Reduction for the Dynamics of Nonlinear Multilayer Sheet Structures With Trial Vector Derivatives,” Shock Vib., 2014, p. 913136.
Segalman, D. J. , 2007, “ Model Reduction of Systems With Localized Nonlinearities,” ASME J. Comput. Nonlinear Dyn., 2(3), pp. 249–266. [CrossRef]
Jain, S. , 2015, “ Model Order Reduction for Non-Linear Structural Dynamics,” Master's thesis, Delft University of Technology, Delft, The Netherlands. https://repository.tudelft.nl/islandora/object/uuid%3Acb1d7058-2cfa-439a-bb2f-22a6b0e5bb2a
Pesaresi, L. , Salles, L. , Jones, A. , Green, J. S. , and Schwingshackl, C. W. , 2017, “ Modelling the Nonlinear Behaviour of an Underplatform Damper Test Rig for Turbine Applications,” Mech. Syst. Signal Process., 85, pp. 662–679. [CrossRef]
Gruber, F. M. , and Rixen, D. J. , 2016, “ Evaluation of Substructure Reduction Techniques With Fixed and Free Interfaces,” Strojniški Vestnik-J. Mech. Eng., 62(7–8), pp. 452–462. [CrossRef]
Bograd, S. , Reuss, P. , Schmidt, A. , Gaul, L. , and Mayer, M. , 2011, “ Modeling the Dynamics of Mechanical Joints,” Mech. Syst. Signal Process., 25(8), pp. 2801–2826. [CrossRef]
Petrov, E. P. , and Ewins, D. J. , 2002, “ Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Discs,” ASME Paper No. GT2002-30325.
Salles, L. , Blanc, L. , Thouverez, F. , Gouskov, A. M. , and Jean, P. , 2009, “ Dynamic Analysis of a Bladed Disk With Friction and Fretting-Wear in Blade Attachments,” ASME Paper No. GT2009-60151.
Cameron, T. M. , and Griffin, J. H. , 1989, “ An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems,” ASME J. Appl. Mech., 56(1), pp. 149–154. [CrossRef]
Seydel, R. , 2009, Practical Bifurcation and Stability Analysis, Springer Science & Business Media, Berlin, Germany.
Nacivet, S. , Pierre, C. , Thouverez, F. , and Jezequel, L. , 2003, “ A Dynamic Lagrangian Frequency–Time Method for the Vibration of Dry-Friction-Damped Systems,” J. Sound Vib., 265(1), pp. 201–219. [CrossRef]
Sarrouy, E. , and Sinou, J.-J. , 2011, “ Non-Linear Periodic and Quasi-Periodic Vibrations in Mechanical Systems-on the Use of the Harmonic Balance Methods,” Advances in Vibration Analysis Research, InTech, London.
Pastor, M. , Binda, M. , and Harčarik, T. , 2012, “ Modal Assurance Criterion,” Procedia Eng., 48, pp. 543–548. [CrossRef]


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Fig. 1

An illustration of a nonlinear jointed structure with contact local nonlinearities

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Fig. 2

An illustration of the FE modeling of a jointed beam with springs

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Fig. 3

An illustration of Newton-Raphson solver with AFT scheme

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Fig. 4

Natural frequencies and mode shapes of linear jointed beam system

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Fig. 5

Natural frequency relative errors of the jointed beams with increasing number of interface nodes at 6, 18, 30, and 42. Note: RR stands for reduction ratio (of the number of DOFs).

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Fig. 6

Modal assurance criterion errors of jointed structures with increasing number of jointed nodes

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Fig. 7

Natural frequency relative errors of the jointed beams between the ROMs with the same size

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Fig. 8

The NFs and modes of a linearized joint beam with contact friction stiffness

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Fig. 9

Forced frequency response close to the NFs of the first tangential modes under different excitation levels

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Fig. 10

Forced frequency response close to the resonance frequency of the second normal mode pair with different levels of excitation force

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Fig. 11

Forced frequency response close to the second normal mode pair with the increasing number of interface nodes

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Fig. 12

An example of the forced frequency response using different types of ROMs (CB, Rubin, MacNeal, DCB, JIM, TVD, and free interface modes)

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Fig. 13

Relative FRF errors of various ROM methods with different excitation levels in the region of out-of-phase mode

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Fig. 14

Relative FRF errors of various ROM methods with the different size of the contact interface in the region of out-of-phase mode

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Fig. 15

Relative FRF errors of various ROM methods with the increasing mode number in the region of out-of-phase mode



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