Abstract
A nonlinear dynamic substructuring approach using Residual Flexibility method for geometrically nonlinear structures is investigated. In order to reduce the model order of a geometrically nonlinear structure, the closed form equations of motion for the substructures are classically required. However, in industrial applications these equations are often not available, because the model of interest is constructed in a commercial finite element software package. As a result, a non-intrusive reduction method is applied. To do so, the Rubin method which contains Residual Flexibility effect is used as a linear basis and the nonlinear terms with unknown coefficients – due to geometric nonlinearity – are added to them. These nonlinear stiffness coefficients of the reduced substructure are calculated using the Implicit Condensation and Expansion Method (ICE). Then, the nonlinear reduced substructures are assembled using Component Mode Synthesis (CMS). The performance of the free-interface method of Rubin as a linear basis for nonlinear substructuring is examined by implementing the proposed methods on an academic example developed in a commercial finite element software. The accuracy of the reduced order model is assessed by comparing the Nonlinear Normal Modes (NNMs) of the reduced order model with the ones of the original model before reduction.
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Craig, R.-R., Bampton, M.C.C.: Coupling of substructures for dynamics analyses. AIAA J. 6 (7), 1313 (1968). doi:10.2514/3.4741, ISSN:0001-1452
de Borst, R., Crisfield, M., Remmers, J., Verhoosel, C.: Non-Linear Finite Element Analysis of Solids and Structures, 2nd edn. (2012). doi:10.1002/9781118375938
Gordon, R.W., Hollkamp, J.J.: Reduced-order models for acoustic response prediction. Technical report. Air Force Research Laboratory AFRL-RB-WP-TR-2011-3040, pp. 1–224 (2011)
Guyan, R.J.: Reduction of stiffness and mass matrices. AIAA J. 3 (2), 380–380 (1965). doi:10.2514/3.2874
Hollkamp, J.J., Gordon, R.W.: Reduced-order models for nonlinear response prediction: implicit condensation and expansion. J. Sound Vib. 318 (4–5), 1139–1153 (2008). doi:10.1016/j.jsv.2008.04.035
Hurty, W.: Vibrations of structural systems by component mode synthesis. J. Eng. Mech. Div. 86 (4), 51–70 (1960). ISSN:0044-7951
Kerschen, G., Peeters, M., Golinval, J.-C., Vakakis, A.F.: Nonlinear normal modes, Part I: a useful framework for the structural dynamicist. Mech. Syst. Signal Process. 23 (1), 170–194 (2009)
Klerk, D.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). doi:10.2514/1.33274, ISSN:0001-1452
Kuether, R.J.: Nonlinear modal substructuring of geometrically nonlinear finite element models. Ph.D. thesis, Wisconsin-Madison, p. 181 (2014)
Kuether, R.J., Allen, M.S., Hollkamp, J.J.: Modal substructuring of geometrically nonlinear finite-element models. AIAA J. 54 (2), 1–12 (2015). doi:10.2514/1.J054036, ISSN:0001-1452
Kuether, R.J., Deaner, B.J., Hollkamp, J.J., Allen, M.S.: Evaluation of geometrically nonlinear reduced-order models with nonlinear normal modes. AIAA J. 53 (11), 3273–3285 (2015). doi:10.2514/1.J053838, ISSN:0001-1452
MacNeal, R.H.: A hybrid method of component mode synthesis. Comput. Struct. 1 (4), 581–601 (1971). doi:10.1016/0045-7949(71)90031-9
Mignolet, M.P., Przekop, A., Rizzi, S.A., Spottswood, S.M.: A review of indirect/non-intrusive reduced order modeling of nonlinear geometric structures. J. Sound Vib. 332 (10), 2437–2460 (2013). doi:10.1016/j.jsv.2012.10.017, ISSN:10958568
Nash, M.: Nonlinear structure dynamics by finite element modal synthesis. Ph.D. thesis, Imperial College London (1977)
Peeters, M., Viguié, R., Sérandour, G., Kerschen, G., Golinval, J.-C.: Nonlinear normal modes, Part II: toward a practical computation using numerical continuation techniques. Mech. Syst. Signal Process. 23 (1), 195–216 (2009)
Perez, R., Wang, X.Q., Mignolet, M.P.: Nonintrusive structural dynamic reduced order modeling for large deformations: enhancements for complex structures. J. Comput. Nonlinear Dyn. 9, 031008 (2014). doi:10.1115/1.4026155, ISSN:1555-1415
Rixen, D.J.: A dual Craig-Bampton method for dynamic substructuring. J. Comput. Appl. Math. 168 (1–2), 383–391 (2004). doi:10.1016/j.cam.2003.12.014
Rosenberg, R.M.: Normal modes of nonlinear dual-mode systems. J. Appl. Mech. 27 (2), 263–268 (1960)
Rubin, S.: Improved component-mode representation for structural dynamic analysis. AIAA J. 13 (8), 995–1006 (1975). doi:10.2514/3.60497, ISSN:0001-1452
van der Valk, P.L.C.: Model reduction and interface modeling in dynamic substructuring. Master’s thesis, Delft University of Technology, p. 177 (2010)
Wenneker, F., Tiso, P.: A substructuring method for geometrically nonlinear structures. In: Allen, M., Mayes, R., Rixen, D. (eds.) Dynamics of Coupled Structures, Volume 1: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, pp. 157–165. Springer International Publishing, Cham (2014). doi:10.1007/978-3-319-04501-6_14
Wu, L., Tiso, P.: Nonlinear model order reduction for flexible multibody dynamics: a modal derivatives approach. Multibody Syst. Dyn. 36 (4), 405–425 (2016). doi:10.1007/s11044-015-9476-5
Wu, L., Tiso, P., Keulen, F.V.: A modal derivatives enhanced Craig-Bampton method for geometrically nonlinear structural dynamics. In: Proceedings of ISMA 2016 – International Conference on Noise and Vibration Engineering, Leuven, pp. 3615–3524 (2016)
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Mahdiabadi, M.K., Buchmann, E., Xu, D., Bartl, A., Rixen, D.J. (2017). Dynamic Substructuring of Geometrically Nonlinear Finite Element Models Using Residual Flexibility Modes. In: Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 4. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-54930-9_19
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