Structural Engineering and Mechanics

  • 제37권5호
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  • Pages.561-573
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  • 2011
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Investigation on efficiency and applicability of subspace iteration method with accelerated starting vectors for calculating natural modes of structures

  • Kim, B.W. (Marine Structure & Plant Research Department, KORDI/MOERI) ;
  • Jung, H.J. (Department of Civil and Environmental Engineering, KAIST) ;
  • Hong, S.Y. (Marine Structure & Plant Research Department, KORDI/MOERI)
  • 투고 : 2010.04.22
  • 심사 : 2010.11.17
  • 발행 : 2011.03.10
⟨ 이전 논문 다음 논문 ⟩

초록

For efficient calculation of natural modes of structures, a numerical scheme which accelerates convergence of the subspace iteration method by employing accelerated starting Lanczos vectors was proposed in 2005. This paper is an extension of the study. The previous study simply showed feasibility of the proposed method by analyzing structures with smaller degrees of freedom. While, the present study verifies efficiency of the proposed method more rigorously by comparing closeness of conventional and accelerated starting vectors to genuine eigenvectors. This study also analyzes an example structure with larger degrees of freedom and more complex constraints in order to investigate applicability of the proposed method.

키워드

참고문헌

  1. Akl, F.A., Dilger, W.H. and Irons, B.M. (1982), "Acceleration of subspace iteration", Int. J. Numer. Meth. Eng., 18, 583-589. https://doi.org/10.1002/nme.1620180408
  2. Bathe, K.J. and Ramaswamy, S. (1980), "An accelerated subspace iteration method", Comput. Meth. Appl. Mech. Eng., 23, 313-331. https://doi.org/10.1016/0045-7825(80)90012-2
  3. Bathe, K.J. and Wilson, E.L. (1972), "Large eigenvalue problems in dynamic analysis", J. Eng. Mech.-ASCE, 98, 1471-1485.
  4. Chen, P., Sun, S.L., Zhao, Q.C., Gong, Y.C., Chen, Y.Q. and Yuan, M.W. (2008), "Advances in solution of classical generalized eigenvalue problem", Interact. Multis. Mech., 1(2), 211-230. https://doi.org/10.12989/imm.2008.1.2.211
  5. Grosso, G., Martinelli, L. and Parravicini, G.P. (1993), "A new method for determining excited states of quantum systems", Il Nuovo Cimento D, 15, 269-277. https://doi.org/10.1007/BF02456910
  6. Kim, B.W., Cho, S.W., Kim, C.H. and Lee, I.W. (2005), "Determination of natural frequencies and mode shapes of structures using subspace iteration method with accelerated starting vectors", J. Struct. Eng.-ASCE, 131(7), 1146-1149. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:7(1146)
  7. Korea Ocean Research & Development Institute (2008), Development of Design Technology of Very Large Floating Structures, Research and Development Project Report of Ministry of Land, Transport and Maritime Affairs of Korea.
  8. Lam, Y.C. and Bertolini, A.F. (1994), "Acceleration of the subspace iteration method by selective repeated inverse iteration", Finite Elem. Anal. Des., 18, 309-317. https://doi.org/10.1016/0168-874X(94)90110-4
  9. Lanczos, C. (1950), "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators", J. Res. Natl. Bur. Stand., 45, 255-282. https://doi.org/10.6028/jres.045.026
  10. Pham, D.C., Wang, C.M. and Utsunomiya, T. (2008), "Hydroelastic analysis of pontoon-type circular VLFS with an attached submerged plate", Appl. Ocean Res., 30(4), 287-296. https://doi.org/10.1016/j.apor.2008.12.002
  11. Qian, Y.Y. and Dhatt, G. (1995), "An accelerated subspace method for generalized eigenproblems", Comput. Struct., 54, 1127-1134. https://doi.org/10.1016/0045-7949(94)00387-I
  12. Riggs, H.R., Suzuki, H., Ertekin, R.C., Kim, J.W. and Iijima, K. (2008), "Comparison of hydroelastic computer codes based on the ISSC VLFS benchmark", Ocean Eng., 35(7), 589-597. https://doi.org/10.1016/j.oceaneng.2008.01.012
  13. Sui, Y.F. and Zhong, W.X. (2006), "Eigenvalue problem of a large scale indefinite gyroscopic dynamic system", Appl. Math. Mech., 27(1), 15-22. https://doi.org/10.1007/s10483-006-0103-z
  14. Wang, X. and Zhou, J. (1999), "An accelerated subspace iteration method for generalized eigenproblems", Comput. Struct., 71, 293-301. https://doi.org/10.1016/S0045-7949(98)00153-9
  15. Wilson, E.L. and Itoh, T. (1983), "An eigensolution strategy for large systems", Comput. Struct., 16, 259-265. https://doi.org/10.1016/0045-7949(83)90166-9
  16. Zhao, Q.C., Chen, P., Peng, W.B., Gong, Y.C. and Yuan, M.W. (2007), "Accelerated subspace iteration with aggressive shift", Comput. Struct., 85(19/20), 1562-1578. https://doi.org/10.1016/j.compstruc.2006.11.033