Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32451
An Approach for Transient Response Calculation of large Nonproportionally Damped Structures using Component Mode Synthesis

Authors: Alexander A. Muravyov


A minimal complexity version of component mode synthesis is presented that requires simplified computer programming, but still provides adequate accuracy for modeling lower eigenproperties of large structures and their transient responses. The novelty is that a structural separation into components is done along a plane/surface that exhibits rigid-like behavior, thus only normal modes of each component is sufficient to use, without computing any constraint, attachment, or residual-attachment modes. The approach requires only such input information as a few (lower) natural frequencies and corresponding undamped normal modes of each component. A novel technique is shown for formulation of equations of motion, where a double transformation to generalized coordinates is employed and formulation of nonproportional damping matrix in generalized coordinates is shown.

Keywords: component mode synthesis, finite element models, transient response, nonproportional damping

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1730


[1] Hurty W.C. Dynamic analysis of structural systems using component modes, AIAA Journal, 1965; 3 (4): 678--685.
[2] Craig R.R. and Bampton M.C., Coupling of Substructures for Dynamic Analysis, AIAA Journal, 1968; 6 (7): 1313ÔÇö1319.
[3] Craig R.R. and Ni Z. Component mode synthesis for model order reduction of nonclassically damped systems, Journal of Guidance, Control and Dynamics, 1989; 12 (4): 577--584.
[4] Muravyov A.A., Hutton S.G. Component mode synthesis for nonclassically damped structures, AIAA Journal, 1996; 34 (8): 664-- 1670.
[5] Goldman R.L., Vibration Analysis by Dynamic Partitioning, AIAA Journal, 1969; 7(6): 1152ÔÇö1154.
[6] Hintz R.M., Analytical Methods in Component Modal Synthesis, AIAA Journal, 1975; 13(8): 1007ÔÇö1016.
[7] Dowell E.H., Free Vibrations of an Arbitrary Structure in Terms of Component Modes, Journal of Applied Mechanics, 1972; Vol. 39: 727ÔÇö 732.
[8] Hasselman T.K., Kaplan A., Dynamic Analysis of Large Systems by Complex Mode Synthesis, Journal of Dynamic Systems, Measurement, and Control, 1974; Vol. 96, Series G: 327ÔÇö333.
[9] B. Yin, W. Wang, Y. Jin, "The application of component mode synthesis for the dynamic analysis of complex structures using ADINA", Computers and Structures, 64, 931-938, 1997.
[10] Hou S., Review of Modal Synthesis by Dynamic Partitioning, The Shock and Vibration Bulletin, 1969; No. 40, pt. 4; 25ÔÇö39.
[11] MacNeal R.H., A Hybrid Method of Component Mode Synthesis, Journal of Computers and Structures, 1971; 1(4): 581ÔÇö601.
[12] Rubin S., Improved Component-Mode Representation for Structural Dynamic Analysis, AIAA Journal, 1975; 13(8): 995ÔÇö1006.
[13] M.P. Singh, L.E. Suarez, "Dynamic condensation with synthesis of substructure Eigenproperties", Joumal of Sound and Vibration, 159, 139- 155, 1992.
[14] J.H. Kang, Y.Y. Kim, "Field-consistent higher-order free-interface component mode synthesis", International Journal for Numerical Methods in Engineering, 50, 595-610, 2001.
[15] B. Biondi, G. Muscolino, "Component-mode synthesis methods variants in the dynamics of coupled structures", Meccanica, 35, 17-38, 2000.
[16] J.B. Qiu, Z.G. Ying, F.W. Williams, "Exact modal synthesis techniques using residual constraint modes", International Journal for Numerical Methods in Engineering, 40, 2475-2492, 1997.
[17] A. de Kraker, D.H. van Campen, "Rubin's CMS reduction method for general state-space models", Computers and Structures, 58, 597-060, 1996.
[18] C. Farhat, M.Geradin, "On a component mode synthesis method and its application to incompatible substructures", Computers and Structures, 51, 459-473, 1994.
[19] Muravyov A.A. Forced vibration responses of a viscoelastic structure, Journal of Sound and Vibration, 1998; 218 (5): 892--907.
[20] Nicol T. (editor) UBC Matrix book (A guide to solving matrix problems), Computing Centre, University of British Columbia, 1982; Vancouver, B.C., Canada..