Skip to main content
SpringerLink
Log in

Efficient frequency response and its direct sensitivity analyses for large-size finite element models using Krylov subspace-based model order reduction

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

In this paper, we examine an efficient calculation of the approximate frequency response (FR) for large-size finite element (FE) models using the Krylov subspace-based model order reduction (MOR) and its direct design sensitivity analysis with respect to design variables for sizing. Information about both the FR and its design sensitivity is necessary for typical gradient-based optimization iterations; therefore, the problem of high computational cost may occur when FRs of a large-size FE models are involved in the optimization problem. In the method suggested in this paper, reduced order models, generated from the original full-order FE models through the Arnoldi process, are used to calculate both the FR and FR sensitivity. This maximizes the speed of numerical computation of the FR and its design sensitivity. Assuming that the Krylov basis vectors remain constant with respect to the perturbation of a design variable, the FR sensitivity analysis is performed in a more efficient manner. As numerical examples, a car body with 535,992 degrees of freedom (DOF) and a 6 × 6 micro-resonator array with 368,424 DOF are adopted to demonstrate the numerical accuracy and efficiency of the suggested approach. Using the reduced-order models, we found that the FR and FR sensitivity are in a good agreement with those using the fullorder FE model. The reduction in computation time is also found to be significant because of the use of Krylov subspace-based reduced models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Z. Q. Qu, Hybrid expansion method for frequency responses and their sensitivities, part I: undamped systems, Journal of Sound and Vibration, 231(1) (2000) 175–193.

    Article  Google Scholar 

  2. Z. Q. Qu and R. P. Selvam, Hybrid expansion method for frequency responses and their sensitivities, part II: viscously damped systems, Journal of Sound and Vibration, 238(3) (2000) 369–388.

    Article  Google Scholar 

  3. Z. Q. Qu, Accurate methods for frequency responses and their sensitivities of proportionally damped systems, Computers and Structures, 79 (2001) 87–96.

    Article  Google Scholar 

  4. Z. Q. Qu, Adaptive mode superposition and acceleration technique with application to frequency response function and its sensitivity, Mechanical Systems and Signal Processing, 21(1) (2007) 40–57.

    Article  Google Scholar 

  5. T. Ting, Design sensitivity analysis of structural frequency response, AIAA Journal, 31(10) (1993) 1965–1967.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. S. Han, Direct design sensitivity analysis of frequency response function using Krylov subspace based model order reduction, Journal of the Computational Structural Engineering Institute of Korea, 23(2) (2010) 153–163.

    Google Scholar 

  7. J. K. Bennighof and M. F. Kaplan, Frequency sweep analysis using multi-level substructuring, global modes and iteration, Proceedings of 39th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference (1998).

  8. D. Choi, H. Kim and M. Cho, Improvement of substructuring reduction technique for large eigenproblems using an efficient dynamic condensation method, Journal of Mechanical Science and Technology, 22(2) (2008) 255–268.

    Article  Google Scholar 

  9. C. W. Kim and J. K. Bennighof, Fast frequency response analysis of large-scale structures with non-proportional damping, International Journal for Numerical Methods in Engineering, 69(5) (2006) 978–992.

    Article  Google Scholar 

  10. W. Gao, X. S. Li, C. Yang and Z. Bai, An implementation and evaluation of the AMLS method for sparse eigenvalue problems, ACM Transactions on Mathematical Software, 34(4) (2008) 20:1–28.

    Article  MathSciNet  Google Scholar 

  11. H. Kim and M. Cho, Subdomain optimization of multidomain structure constructed by reduced system based on the primary degrees of freedom, Finite Elements in Analysis and Design, 43 (2007) 912–930.

    Article  Google Scholar 

  12. H. Kim, M. Cho, H. Kim and H. G. Choi, Efficient construction of a reduced system in multi-domain system with free subdomains, Finite Elements in Analysis and Design, 47 (2011) 1025–1035.

    Article  Google Scholar 

  13. J. H. Ko, D. Byun and J. S. Han, An efficient numerical solution for frequency response function of micromechanical resonator arrays, Journal of Mechanical Science and Technology, 23(10) (2009) 2694–2702.

    Article  Google Scholar 

  14. J. S. Han, E. B. Rudnyi and J. G. Korvink, Efficient optimization of transient dynamic problems in MEMS devices using model order reduction, Journal of Micromechanics and Microengineering, 15(4) (2005) 822–832.

    Article  Google Scholar 

  15. K. K. Choi and J. H. Lee, Sizing design sensitivity analysis of dynamic frequency response of vibrating structures, Journal of Mechanical Design, 114(1) (1992) 166–173.

    Article  Google Scholar 

  16. H. Kim and M. Cho, Two-level scheme for selection of primary degrees of freedom and semi-analytic sensitivity based on the reduced system, Computer Methods in Applied Mechanics and Engineering, 195(33–36) (2006) 4244–4268.

    Article  MATH  Google Scholar 

  17. R. W. Freund, Krylov-subspace methods for reduced-order modeling in circuit simulation, J. Comput. Appl. Math., (123) (2000) 395–421.

  18. Z. Bai, Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems, Applied Numerical Mathematics, (43) (2002) 9–44.

    Google Scholar 

  19. E. Rudnyi and J. Korvink, Model order reduction for large scale engineering models developed in ANSYS, Lecture Notes in Computer Science, 3732 (2006) 349–356.

    Article  Google Scholar 

  20. J. S. Han, Efficient vibration simulation using model order reduction, Transactions of the KSME A, 30(3) (2006) 310–317.

    Google Scholar 

  21. R. Eid, B. Salimbahrami, B. Lohmann, E. Rudnyi and J. Korvink, Parametric order reduction of proportionally damped second-order systems, Sensors and Materials, 19(3) (2007) 149–164.

    Google Scholar 

  22. J. Choi, M. Cho and J. Rhim, Efficient prediction of the quality factors of micromechanical resonators, Journal of Sound and Vibration, 329(1) (2009) 84–95.

    Article  Google Scholar 

  23. W. H. Greene and R. T. Haftka, Computational aspects of sensitivity calculations in transient structural analysis, Computers & Structures, 32(2) (1989) 433–443.

    Article  Google Scholar 

  24. ANSYS, Inc., ANSYS Paramesh Training Manual, Release 3.0, Canonsburg (2004).

  25. ANSYS, Inc., Theory Reference for ANSYS and ANSYS Workbench, ANSYS Release 11.0, Canonsburg (2007).

  26. A. Kropp and D. Heiserer, Efficient broadband vibroacoustic analysis of passenger car bodies using an FE-based component mode synthesis approach, Journal of Computational Acoustics, 11(2) (2003) 139–157.

    Article  Google Scholar 

  27. J. S. Han and J. H. Ko, Frequency response analysis of array-type MEMS resonators by model order reduction using Krylov subspace method, Transactions of the KSME A, 33(9) (2009) 878–885.

    Google Scholar 

  28. Y. Xie, S. S. Li, Y. W. Lin, Z. Ren and C. T. C. Nguyen, UHF micromechanical extensional wing-glass mode ring resonators, Technical digest, 2003 IEEE International electron devices meeting, Washington DC (2003).

  29. M. Shalaby, M. Abdelmoneum and K. Saitou, Design of spring coupling for high Q, high frequency MEMS filter, Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, Chicago, Illinois, USA (2006).

  30. The MathWorks, Inc. MATLAB Getting Started Guide (2011).

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Design Engineering, Andong National University, Andong, 760-749, Korea

    Jeong Sam Han

Authors
  1. Jeong Sam Han
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeong Sam Han.

Additional information

Recommended by Associate Editor Maenghyo Cho

Jeong Sam Han received his B.S. degree in Mechanical Engineering from Kyungpook National University, Korea, in 1995. He then went on to receive his M.S. and Ph.D. degrees from KAIST, Korea, in 1997 and 2003, respectively. Dr. Han is currently a professor at the Department of Mechanical Design Engineering at Andong National University in Andong, Korea. Prof. Han’s research interests cover the areas of model order reduction, structural optimization, and MEMS simulation, etc.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Han, J.S. Efficient frequency response and its direct sensitivity analyses for large-size finite element models using Krylov subspace-based model order reduction. J Mech Sci Technol 26, 1115–1126 (2012). https://doi.org/10.1007/s12206-012-0227-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-012-0227-8

Keywords

Search

Navigation