Browse > Article
http://dx.doi.org/10.5139/IJASS.2008.9.1.085

Efficient Dynamic Response Analysis Using Substructuring Reduction Method for Discrete Linear System with Proportional and Nonproportional Damping  

Choi, Dong-Soo (School of Mechanical and Aerospace Engineering Seoul National University)
Cho, Maeng-Hyo (School of Mechanical and Aerospace Engineering Seoul National University)
Kim, Hyun-Gi (Korea Aerospace Research Institute)
Publication Information
International Journal of Aeronautical and Space Sciences / v.9, no.1, 2008 , pp. 85-99 More about this Journal
Abstract
The dynamic response analysis for large structures using finite element method requires a large amount of computational resources. This paper presents an efficient vibration analysis procedure by combining node-based substructuring reduction method with a response analysis scheme for structures with undamped, proportional or nonproportional damping. The iterative form of substructuring reduction scheme is derived to reduce the full eigenproblem and to calculate the dynamic responses. In calculating the time response, direct integration scheme is used because it can be applied directly to the reduced model. Especially for the non proportional damping matrix, the transformation matrices defined in the displacement space are used to reduce the system. The efficiency and the effectiveness of the present method are demonstrated through the numerical examples.
Keywords
Substructuring reduction method; Nonproportional damping; Newmark's scheme;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Zu-Qing Qu and Wenjun Chang, 2000, 'Dynamic condensation method for viscously damped vibration systems in engineering', Engineering Structures, Vol. 22, No. 11, pp. 1426-1432   DOI   ScienceOn
2 Bathe KJ., 1996, 'Finite Element Procedure', Prentice Hall, pp. 887-888
3 Robert J. Guyan, 1965, 'Reduction of stiffness and mass matrices,' AIAA Journal, Vol. 3, No. 2, pp. 380   DOI
4 Bruce Irons, 1965, 'Structural eigenvalue problems : elimination of unwanted variables', AIAA Journal, Vol. 3, No. 5, pp. 961-962
5 Zu-Qing Qu and Panneer Selvam, 2005, 'Model Order Reduction of Viscously Damped Vibration Systems Using Accelerated Iterative Dynamic Condensation', Journal of Applied Mechanics, Vol. 72, No. 5, pp. 761-771   DOI   ScienceOn
6 Hyungi Kim and Maenghyo Cho, 2005, 'Two-level scheme for selection of degrees of freedom and semi-analytic sensitivity based on the reduced system', Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 33-36, pp. 4244-4268
7 J.C.O'Cahhahan, 1989, 'A new procedure for an improved reduced system (IRS) model', Proceedings of the 7th International Modal Analysis Conference, pp. 17-21
8 Gordis and Joshua H., 1992, 'An analysis of the improved reduced system (IRS) model reduction procedure', Proceedings of the 10th International Modal Analysis Conference, Vol. 1 (A94-12476 02-39), pp. 471-479
9 M.I.Friswell, S.D.Garvey and J.E.T.Penny, 1995, 'Model reduction using dynamic and iterated IRS techniques', Journal of Sound and Vibration, Vol. 186, No. 2, pp. 311-323   DOI   ScienceOn
10 M.I.Friswell, S.D.Garvey and J.E.T.Penny, 1995, 'The convergence of the iterated IRS method', Journal of Sound and Vibration, Vol. 211, No. 1, pp. 123-132   DOI   ScienceOn
11 K.A. Foss, 1958, 'Co-ordinates which uncoupled the equations of motion of damped linear dynamic system', Journal of Applied Mechanics, Vol. 25, pp. 361-364
12 Kolja Elssel and Heinrich Voss, 2006, 'An a priori bound for automated multilevel substructuring', SIAM J. Matrix anal. Appl., Vol. 28, No. 2, pp. 386-397   DOI   ScienceOn
13 Hyungi Kim and Maenghyo Cho, 2007, 'Improvement of reduction method combined with sub-domain scheme in large-scale problem', Int. J. of Num. Meth. Eng., Vol. 70, No. 2, pp. 206-251   DOI   ScienceOn
14 Dongsoo Choi and Maenghyo Cho, 2007, 'Iterative Method for Dynamic Condensation Combined with Substructuring Scheme', 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 23-26 April
15 Craig, R. R., Jr., 1968, 'Coupling of substructures for dynamic analyses', AIAA Journal, Vol. 6, No. 7, pp. 1313-1319   DOI
16 N.Bouhaddi and R.Fillod, 1992, 'Substructuring using a linearized dynamic condensation method', Computer & Structures, Vol. 45, No. 4, pp. 679-683   DOI   ScienceOn
17 Maenghyo and Hyungi Kim, 2004, 'Element-based node selection method for reduction of eigenvalue problems', AIAA Journal, Vol. 42, No. 8, pp. 1677-1684   DOI   ScienceOn
18 N.Bouhaddi and R.Fillod, 1996, 'Substructuring by a two-level dynamic condensation method', Computer & Structures, Vol. 60, No. 3, pp. 403-409   DOI   ScienceOn
19 Jeffrey K. Bennighof and R. B. Lehoucq., 2004, 'An automated multilevel substructuring method for eigenspace computation in linear elastodynamics', SIAM J. Sci. Comput. Vol. 25, No. 6, pp. 2084-2106   DOI   ScienceOn
20 Daniel J. Rixen, 2004, 'A dual Craig-Bampton method for dynamic substructuring', J. Compt. Appl. Math., Vol. 168, No. 1-2, pp. 383-391   DOI   ScienceOn