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Iterated Improved Reduced System (IIRS) Method Combined with Sub-Structuring Scheme (II) - Nonclassically Damped Structural Systems -

부구조화 기법을 연동한 반복적인 동적 축소법 (II) - 비비례 감쇠 구조 시스템 -

  • 최동수 (서울대학교 기계항공공학부) ;
  • 김현기 (현대중공업 기술개발본부) ;
  • 조맹효 (서울대학교 기계항공공학부)
  • Published : 2007.02.01

Abstract

An iterated improved reduced system (IIRS) procedure combined with sub-structuring scheme for nonclassically damped structural systems is presented. For dynamic analysis of such systems, complex eigenproperties are required to incorporate properly the nonclassical damping effect. In complex structural systems, the equations of motion are written in the state space from. Thus, the number of degrees of freedom of the new equations of motion and the size of the associated eigenvalue problem required to obtain the complex eigenvalues and eigenvectors are doubled. Iterated IRS method is an efficient reduction technique because the eigenproperties obtained in each iteration step improve the condensation matrix in the next iteration step. However, although this reduction technique reduces the size of problem drastically, it is not efficient to apply this technique to a single domain finite element model with degrees of freedom over several thousands. Therefore, for a practical application of the reduction method, accompanying sub-structuring scheme is necessary. In the present study, iterated IRS method combined with sub-structuring scheme for nonclssically damped structures is developed. Numerical examples demonstrate the convergence and the efficiency of a newly developed scheme.

Keywords

Iterated IRS Method;Sub-Structuring Scheme;Nonclassically Damped Structural System

References

  1. Robert J. Guyan, 1965, 'Reduction of Stiffness and Mass Matrices,' AIAA Journal, Vol. 3, No. 2, p. 380 https://doi.org/10.2514/3.2874
  2. Bruce Irons., 1965, 'Structural Eigenvalue Problemselimination of Unwanted Variables,' AIAA Journal, Vol. 3, No. 5, pp. 961-962 https://doi.org/10.2514/3.3027
  3. Friswell M. I., Garvey S. D. and Penny J. E. T., 1995, 'Model Reduction Using Dynamic and Iterated IRS Techniques,' Journal of Sound and Vibration, Vol. 186, No. 2, pp. 311-323 https://doi.org/10.1006/jsvi.1995.0451
  4. Friswell M. I., Garvey S. D. and Penny J. E. T., 1998, 'The Convergence of the Iterated IRS Method,' Journal of Sound and Vibration, Vol. 211, No. 1, pp. 123-132 https://doi.org/10.1006/jsvi.1997.1368
  5. Qu Z. -Qu. and Fu Z. -F., 1998, 'New Structural Dynamic Condensation Method for Finite Element Models,' AIAA Journal, Vol. 36, No. 7, pp. 1320-1324 https://doi.org/10.2514/2.517
  6. Qu Zu-Qing and R. Panneer Selvam, 2002, 'Efficient Method for Dynamic Condensation of Nonclassically Damped Vibration Systems,' AIAA Journal, Vol. 40, No. 2, pp. 368-375 https://doi.org/10.2514/2.1655
  7. Qu Z. -Q., Jung Y. and Selvam R. P., 2003, 'Model Condensation for Non-Classically Damped Systems - Part Ⅰ: Static Condensation,' Mechanical Systems and Signal Processing, Vol. 17, No. 5, pp. 1003-1016 https://doi.org/10.1006/mssp.2002.1526
  8. Hyungi Kim and Maenghyo Cho, 2006, '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, Issues. 33-36, pp. 4244-4268 https://doi.org/10.1016/j.cma.2005.08.004
  9. Hyungi Kim and Maenghyo Cho, 2005, 'Dynamic Analysis of Reduced System Partitioned by Domain Decomposition,' 46th AiAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA 2005-2297
  10. Hyungi Kim and Maenghyo Cho, 2006, 'Improvement of Reduction Method Combined with Sub-domain Scheme in Large Scale Problem,' International Journal for Numerical Method in Engineering, (in press) https://doi.org/10.1002/nme.1868
  11. Hyungi Kim et al., 2006, 'Study on the Reduced System Based on the Sub-Domain Method,' Trans. of the KSME (A), Vol. 30, No. 9, pp. 1062-1069 https://doi.org/10.3795/KSME-A.2006.30.9.1062
  12. Hyungi Kim and Maenghyo Cho, 2006, 'Structural Design Optimization on the Reduced System Constructed from Large-Scaled Problem,' Trans. of the KSME (A), Vol. 30, No. 9, pp. 1070-1077 https://doi.org/10.3795/KSME-A.2006.30.9.1070
  13. Rivera M. A., Singh M. P. and Suarez L. E., 1999, 'Dynamic Condensation Approach for Nonclassically Damped Structures,' AIAA Journal, Vol. 37, No. 5, pp. 564-571 https://doi.org/10.2514/2.774
  14. Qu Z. -Q., Selvam R. P. and Jung Y., 2003, 'Model Condensation for Non-Classically Damped Systems - Part Ⅱ: Iterative Schemes for Dynamic Condensation,' Mechanical Systems and Signal Processing, Vol. 17, No. 5, pp. 1017-1032 https://doi.org/10.1006/mssp.2002.1527

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