Abstract
This paper describes a methodology for developing reduced-order dynamic models of structural systems that are composed of an assembly of nonlinear component structures. The approach is a nonlinear extension of the fixed-interface component mode synthesis (CMS) technique developed for linear structures by Hurty and modified by Craig and Bampton. Specifically, the case of nonlinear substructures is handled by using fixed-interface nonlinear normal modes (NNMs). These normal modes are constructed for the various substructures using an invariant manifold approach, and are then coupled through the traditional linear constraint modes (i.e., the static deformation shapes produced by unit interface displacements). A class of systems is used to demonstrate the concept and show the effectiveness of the proposed procedure. Simulation results show that the reduced-order model (ROM) obtained from the proposed procedure outperforms the ROM obtained from the classical fixed-interface linear CMS approach as applied to a nonlinear structure. The proposed method is readily applicable to large-scale nonlinear structural systems that are based on finite-element models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hurty, W. C., ‘Vibration of structural systems by component mode synthesis’, Proceedings of the American Society of Civil Engineers 85(4), 1960, 51–69.
Hurty, W. C., ‘Dynamic analysis of structural systems using component modes’, AIAA Journal 3(4), 1965, 678–685.
Craig, R. R. and Bampton, M. C. C., ‘Coupling of substructures for dynamic analyses’, AIAA Journal 6(7), 1968, 1313–1319.
Craig, R. R., ‘Substructure methods in vibration’, Journal of Mechanical Design 117, 1995, 207–213.
Wang, W. and Kirkhope, J., ‘Component mode synthesis for damped rotor systems with hybrid interfaces’, Journal of Sound and Vibration 177(3), 1994, 393–410.
Chang, C. J., ‘A General Procedure for Substructure Coupling in Dynamic Analysis’, Ph.D. Thesis, The University of Texas, Austin, TX, 1977.
Craig, R. R. and Chang, C. J., ‘Free-interface methods of substructure coupling for dynamic analysis’, AIAA Journal 14(11), 1976, 1633–1635.
Craig, R. R. and Chang, C. J., ‘On the use of attachment modes in substructure coupling for dynamic analysis’, in AIAA/ASME 18th Structures, Structural Dynamics, and Materials Conference, San Diego, CA, 1977, No. 77-405, pp. 89–99.
Rubin, S., ‘Improved component-mode representation for structural dynamic analysis’, AIAA Journal 13(8), 1975, 995–1006.
MacNeal, R. H., ‘A hybrid method of component mode synthesis’, Computers & Structures 1(4), 1971 581–601.
Seshu, P., ‘Review substructuring and component mode synthesis’, Shock and Vibration 4(3), 1997, 199–210.
Bamford, R., Wada, B. K., Garba, J. A., and Chisholm, J., ‘Dynamic analysis of large structural systems’, in Synthesis of Vibrating Systems, ASME Booklet, 1971.
Farhat, C. and Geradin, M., ‘On a component mode synthesis method and its application to incompatible substructures’, Computers & Structures 51(5), 1994, 459–473.
Goldenberg, S. and Shapiro, M., A study of modal coupling procedures for the space shuttle, Technical report, Grumman Aerospace Corp., NASA Contractor Report 112252, 1972.
Spanos, J. T. and Tsuha, W. S., ‘Selection of component modes for flexible multibody simulation’, Journal of Guidance, Control, and Dynamics 14(2), 1991, 278–286.
Noor, A. K., ‘Recent advances and applications of reduction methods’, Applied Mechanics Reviews 47(5), 1994, 125–146.
Shaw, S. W. and Pierre, C., ‘Normal modes for non-linear vibratory systems’, Journal of Sound and Vibration 164(1), 1993, 85–124.
Shaw, S. W. and Pierre, C., ‘Normal modes of vibration for non-linear continuous systems’, Journal of Sound and Vibration 169(3), 1994, 319–347.
Shaw, S. W., Pierre, C., and Pesheck, E., ‘Modal analysis-based reduced-order models for nonlinear structures-an invariant manifold approach’, The Shock and Vibration Digest 31(1), 1999, 3–16.
Pesheck, E., Pierre, C., and Shaw, S. W., ‘Model reduction of a nonlinear rotating beam through nonlinear normal modes’, Journal of Vibration and Acoustics 124, 2002, 229–236.
Pesheck, E., Pierre, C., and Shaw, S. W., ‘A new Galerkin-based approach for accurate nonlinear normal modes through invariant manifolds’, Journal of Sound and Vibration 249(5), 2002, 971–993.
Pesheck, E., Pierre, C., and Shaw, S. W., ‘Accurate reduced order models for a simple rotor blade model using nonlinear normal modes’, Mathematical and Computer Modelling 33, 2001, 1085–1097.
Apiwattanalunggarn, P., Shaw, S. W., Pierre, C., and Jiang, D., ‘Finite-element-based nonlinear modal reduction of a rotating beam with large-amplitude motion’, Journal of Vibration and Control 9(3–4), 2003, 235–263.
Jiang, D., Pierre, C., and Shaw, S. W., ‘The construction of nonlinear normal modes for systems with internal resonance’, International Journal of Nonlinear Mechanics 40, 2005, 729–746.
Boyd, J. P., Chebyshev and Fourier Spectral Methods, Dover Publications, New York, 2001.
Villadsen, J. V. and Stewart, W. E., ‘Solution of boundary-value problems of orthogonal collocation’, Chemical Engineering Science 22, 1967, 1483–1501.
Meirovitch, L., Analytical Methods in Vibrations, Macmillan, New York, 1967.
Apiwattanalunggarn, P., ‘Model Reduction of Nonlinear Structural Systems Using Nonlinear Normal Modes and Component Mode Synthesis’, PhD thesis, Michigan State University, East Lansing, MI, 2003.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Apiwattanalunggarn, P., Shaw, S.W. & Pierre, C. Component Mode Synthesis Using Nonlinear Normal Modes. Nonlinear Dyn 41, 17–46 (2005). https://doi.org/10.1007/s11071-005-2791-2
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11071-005-2791-2