Journal of Mechanical Science and Technology

, Volume 27, Issue 1, pp 113–124 | Cite as

Study on the system reduction under the condition of dynamic load

Article

Abstract

This study presents the methodology of the reduced system for dynamic analysis considering the selection criterion of the primary degrees of freedom based on the relation between natural frequency and external loading frequency. A well-constructed reduced system can provide the accurate representation of the dynamic behavior of a structure under arbitrary dynamic loads. If dynamic response based on a reduced system can be calculated accurately, the proposed method can save the computing time remarkably in problems which require repeated calculation such as optimization procedure or time integration. In addition, the proposed method shows the reliable dynamic response in multi-domain structure. Numerical examples demonstrate the reliability of the dynamic analysis obtained from a reduced system and responses of the reduced system are compared with those of a global system.

Keywords

Two-level condensation scheme (TLCS) Sequential elimination method (SEM) Ritz vector, Reduced system (RS) Reduce order model (ROM) 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. D. Henshell and J. H. Ong, Automatic masters from eigenvalues economization. J. Earthquake Equ. and Struct. Dyn., s3 (1975) 375–383.Google Scholar
  2. [2]
    V. N Shah and M. Raymund, Analytical selection of masters for the reduced eigenvalue problem. Int. J. Numer. Mech. Engng., 18(1) (1982) 89–98.CrossRefMATHGoogle Scholar
  3. [3]
    K. W. Matta, Selection of degrees of freedom for dynamic analysis. Journal of pressure vessel technology, 109(1) (1987) 65–69.CrossRefGoogle Scholar
  4. [4]
    R. L. Kidder, Reduction of structural frequency evaluations. AIAA Journal, 11(6) (1973) 892.CrossRefGoogle Scholar
  5. [5]
    K. O. Kim and Y. J. Choi, Energy method for selection of degrees of freedom in condensation. AIAA Journal, 38(7) (2000) 1253–1259.CrossRefGoogle Scholar
  6. [6]
    M. Cho and H. Kim, Element-based node selection method for reduction of eigenvalue problems. AIAA Journal, 42(8) (2004) 1677–1684.CrossRefGoogle Scholar
  7. [7]
    H. Kim and M. Cho, Two-level scheme for selection of primary degrees of freedom and semi-analytic sensitivity based on the reduced system, Comput. Methods Appl. Engrg., 195(33–36) (2006) 4244–4268.CrossRefMATHGoogle Scholar
  8. [8]
    J. O’Callahan, A procedure for an improved reduced system (IRS) model. Proceedings of the 7th international modal analysis conference, Union college, Schenectady. NY, (1989) 17–21.Google Scholar
  9. [9]
    R. J. Guyan, Reduction of stiffness and mass matrices. AIAA Journal, 3(2) (1965) 380.CrossRefGoogle Scholar
  10. [10]
    D. Zhang and S. W. Li, Succession-level approximate reduction (SAR) technique for structural dynamic model. Analysis conference (Nashville, TN), Union college press, Schenectady, NY (1995) 435–441.Google Scholar
  11. [11]
    H. Kim and M. Cho, Subdomain optimization of multidomain structure constructed by reduced system based on the primary degrees of freedom, Finite Elements Anal. Des. 43 (2007) 912–930.CrossRefGoogle Scholar
  12. [12]
    M. A. Aminpour, An assumed stress hybrid 4 node shell element with drilling degrees of freedom. Int. J. Numer. Mech. Eng. 33 (1992) 19–38.CrossRefMATHGoogle Scholar
  13. [13]
    T. J. R. Hughes and F. Brezzi On drilling degrees of freedom, Comput. Methods Appl. Engrg. 72 (1998) 105–121.MathSciNetCrossRefGoogle Scholar
  14. [14]
    H. Kim and M. Cho, Improvement of reduction method combined with Sub-domain scheme in large scale problem, Int. J. Numer. Mech. Eng. 70(2) (2007) 206–251.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Korea Aerospace Research InstituteDaejeonKorea
  2. 2.School of Mechanical and Aerospace EngineeringSeoul National Univ.SeoulKorea

Personalised recommendations