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Volumn 28, Issue 2, 1999, Pages 157-172

A computationally efficient algorithm for the solution of eigenproblems for large structures with non-proportional damping using Lanczos method

Author keywords

Eigenanalysis; Krylov sequence; Lanczos recursion; Non proportional damping system

Indexed keywords

DAMPING; DYNAMIC RESPONSE; EARTHQUAKE RESISTANCE; EIGENVALUES AND EIGENFUNCTIONS; PROBLEM SOLVING; VIBRATIONS (MECHANICAL);

EID: 0033081219     PISSN: 00988847     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1096-9845(199902)28:2<157::AID-EQE809>3.0.CO;2-2     Document Type: Article
Times cited : (13)

References (34)
  • 1
    • 0024910948 scopus 로고
    • Lanczos method for dynamic analysis of damped structural systems
    • B. Nour-Omid and M. E. Regelbrugge, 'Lanczos method for dynamic analysis of damped structural systems', Earthquake Engng. Struct. Dyn. 18, 1091-1104 (1989).
    • (1989) Earthquake Engng. Struct. Dyn. , vol.18 , pp. 1091-1104
    • Nour-Omid, B.1    Regelbrugge, M.E.2
  • 4
    • 85024576291 scopus 로고
    • Classical normal modes in damped linear dynamic systems
    • T. K. Caughey and M. E. J. O'Kelly, 'Classical normal modes in damped linear dynamic systems', J. Appl. Mech. ASME 32, 583-588 (1965).
    • (1965) J. Appl. Mech. ASME , vol.32 , pp. 583-588
    • Caughey, T.K.1    O'Kelly, M.E.J.2
  • 5
    • 0000356673 scopus 로고
    • An algorithm for generalized matrix eigenvalue problems
    • C. B. Moler and G. W. Stewart, 'An algorithm for generalized matrix eigenvalue problems', SIAM J. Numer. Anal. 10, 241-256 (1973).
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 241-256
    • Moler, C.B.1    Stewart, G.W.2
  • 6
    • 0016116199 scopus 로고
    • LZ algorithm to solve the generalized eigenvalue problem
    • L. Kaufman, 'LZ algorithm to solve the generalized eigenvalue problem', SIAM J. Numer. Anal. 11, 997-1024 (1974).
    • (1974) SIAM J. Numer. Anal. , vol.11 , pp. 997-1024
    • Kaufman, L.1
  • 7
    • 0020783068 scopus 로고
    • A global Jacobi method for a symmetric indefinite problem Sχ = λTχ
    • L. Veselic, 'A global Jacobi method for a symmetric indefinite problem Sχ = λTχ', Comput. Meth. Appl. Mech. Engng. 38, 128-143 (1983).
    • (1983) Comput. Meth. Appl. Mech. Engng. , vol.38 , pp. 128-143
    • Veselic, L.1
  • 8
    • 0027341093 scopus 로고
    • Partial eigensolution of damped structural systems by Arnold's method
    • H. C. Chen, 'Partial eigensolution of damped structural systems by Arnold's method', Earthquake Engng. Struct. Dyn. 22, 63-74 (1993).
    • (1993) Earthquake Engng. Struct. Dyn. , vol.22 , pp. 63-74
    • Chen, H.C.1
  • 9
    • 0016329553 scopus 로고
    • Eigenproblem solution of damped structural systems
    • K. K. Gupta, 'Eigenproblem solution of damped structural systems', Int. J. Numer. Meth. Engng. 8, 877-911 (1974).
    • (1974) Int. J. Numer. Meth. Engng. , vol.8 , pp. 877-911
    • Gupta, K.K.1
  • 10
    • 0019527050 scopus 로고
    • Development of a unified numerical procedure for free vibration analysis of structures
    • K. K. Gupta, 'Development of a unified numerical procedure for free vibration analysis of structures', Int. J. Numer. Meth. Engng. 17, 187-198 (1981).
    • (1981) Int. J. Numer. Meth. Engng. , vol.17 , pp. 187-198
    • Gupta, K.K.1
  • 11
    • 0017301185 scopus 로고
    • Standard forms of the eigenvalue problems associated with gyroscopic systems
    • K. Huseyin, 'Standard forms of the eigenvalue problems associated with gyroscopic systems', J. Sound Vib. 45(1), 23-37 (1976).
    • (1976) J. Sound Vib. , vol.45 , Issue.1 , pp. 23-37
    • Huseyin, K.1
  • 12
    • 0016942467 scopus 로고
    • Alternative formulations for discrete gyroscopic eigenvalue problems
    • R. H. Plaut, 'Alternative formulations for discrete gyroscopic eigenvalue problems', A.I.A.A. J. 14, 431-435 (1976).
    • (1976) A.I.A.A. J. , vol.14 , pp. 431-435
    • Plaut, R.H.1
  • 13
    • 0019923439 scopus 로고
    • Solution of linear gyroscopic systems
    • F. Janssens, 'Solution of Linear Gyroscopic Systems', J. Guidance Control Dyn. 5(1), 92-94 (1982).
    • (1982) J. Guidance Control Dyn. , vol.5 , Issue.1 , pp. 92-94
    • Janssens, F.1
  • 14
    • 0020477350 scopus 로고
    • On the free vibration analysis of spinning structures by using discrete or distributed mass moments
    • W. H. Wittrick and F. W. Williams, 'On the free vibration analysis of spinning structures by using discrete or distributed mass moments', J. Sound Vib. 82(1), 1-15 (1982).
    • (1982) J. Sound Vib. , vol.82 , Issue.1 , pp. 1-15
    • Wittrick, W.H.1    Williams, F.W.2
  • 15
    • 0021623692 scopus 로고
    • Computation of eigenpairs of Aχ = λBχ for vibrations for spinning deformable bodies
    • S. Utku and L. M. Clemente, 'Computation of eigenpairs of Aχ = λBχ for vibrations for spinning deformable bodies', Comput. Struct. 19, 843-847 (1984).
    • (1984) Comput. Struct. , vol.19 , pp. 843-847
    • Utku, S.1    Clemente, L.M.2
  • 16
    • 0022891747 scopus 로고
    • Formulation of numerical procedures for dynamic analysis of spinning structures
    • K. K. Gupta, 'Formulation of numerical procedures for dynamic analysis of spinning structures', Int. J. Numer. Methods Engng. 23, 2347-2357 (1986).
    • (1986) Int. J. Numer. Methods Engng. , vol.23 , pp. 2347-2357
    • Gupta, K.K.1
  • 17
    • 0024621991 scopus 로고
    • A subspace iteration method for the eigensolution of large undamped gyroscopic systems
    • J. F. D. Rodrigues and T. E. C. Gumer, 'A subspace iteration method for the eigensolution of large undamped gyroscopic systems', Int. J. Numer. Meth. Engng. 28, 511-522 (1989).
    • (1989) Int. J. Numer. Meth. Engng. , vol.28 , pp. 511-522
    • Rodrigues, J.F.D.1    Gumer, T.E.C.2
  • 18
    • 0024944150 scopus 로고
    • Eigenproblems from finite element analysis of fluid-structure interactions
    • L. Olson and T. Vandini, 'Eigenproblems from finite element analysis of fluid-structure interactions', Comput. Struct. 33(3), 679-687 (1989).
    • (1989) Comput. Struct. , vol.33 , Issue.3 , pp. 679-687
    • Olson, L.1    Vandini, T.2
  • 19
    • 0000527277 scopus 로고
    • Subspace iteration method for complex symmetric eigenproblems
    • A. Y. T. Leung, 'Subspace iteration method for complex symmetric eigenproblems', J. Sound Vib. 184(4), 627-637 (1995).
    • (1995) J. Sound Vib. , vol.184 , Issue.4 , pp. 627-637
    • Leung, A.Y.T.1
  • 20
    • 0000094594 scopus 로고
    • An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
    • C. Lanczos, 'An iteration method for the solution of the eigenvalue problem of linear differential and integral operators', J. Res. Natl. Bur. Stand. 45, 255-282 (1950).
    • (1950) J. Res. Natl. Bur. Stand. , vol.45 , pp. 255-282
    • Lanczos, C.1
  • 22
    • 72449139170 scopus 로고
    • Computational variants of the Lanczos method for the eigenproblem
    • C. C. Paige, 'Computational variants of the Lanczos method for the eigenproblem', J. Inst. Math. Appl. 10, 373-381 (1972).
    • (1972) J. Inst. Math. Appl. , vol.10 , pp. 373-381
    • Paige, C.C.1
  • 23
    • 53849148874 scopus 로고
    • Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix
    • C. C. Paige, 'Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix', J. Inst. Math. Appl. 18, 341-349 (1976).
    • (1976) J. Inst. Math. Appl. , vol.18 , pp. 341-349
    • Paige, C.C.1
  • 24
    • 84968487118 scopus 로고
    • The Lanczos algorithm with selective orthogonalization
    • B. N. Parlett and D. S. Scott, 'The Lanczos algorithm with selective orthogonalization', Math. Comput. 33, 217-238 (1979).
    • (1979) Math. Comput. , vol.33 , pp. 217-238
    • Parlett, B.N.1    Scott, D.S.2
  • 25
    • 84968519566 scopus 로고
    • The Lanczos algorithm with partial reorthogonalization
    • H. D. Simon, 'The Lanczos algorithm with partial reorthogonalization', Math. Comput. 42, 115-142 (1984).
    • (1984) Math. Comput. , vol.42 , pp. 115-142
    • Simon, H.D.1
  • 26
    • 0017531916 scopus 로고
    • Efficient solution of quadratic eigenproblems arising in dynamic analysis of structures
    • M. Borri and P. Mantegazza, 'Efficient solution of quadratic eigenproblems arising in dynamic analysis of structures', Comput. Meth. Appl. Mech. Engng. 12, 19-31 (1977).
    • (1977) Comput. Meth. Appl. Mech. Engng. , vol.12 , pp. 19-31
    • Borri, M.1    Mantegazza, P.2
  • 27
    • 0022783562 scopus 로고
    • A solution of the eigenproblem for undamped gyroscopic systems with the Lanczos algorithm
    • O. A. Bauchau, 'A solution of the eigenproblem for undamped gyroscopic systems with the Lanczos algorithm', Int. J. Numer. Meth. Engng. 23, 1705-1713 (1980).
    • (1980) Int. J. Numer. Meth. Engng. , vol.23 , pp. 1705-1713
    • Bauchau, O.A.1
  • 28
    • 0024103778 scopus 로고
    • Structural dynamics analysis using an unsymmetric block Lanczos algorithm
    • H. M. Kim and R. R. Craig Jr, 'Structural dynamics analysis using an unsymmetric block Lanczos algorithm', Int. J. Numer. Meth. Engng. 26, 2305-2318 (1988).
    • (1988) Int. J. Numer. Meth. Engng. , vol.26 , pp. 2305-2318
    • Kim, H.M.1    Craig R.R., Jr.2
  • 29
    • 0024016146 scopus 로고
    • Development of a block Lanczos algorithm for free vibration analysis of spinning structures
    • K. K. Gupta and C. L. Lawson, 'Development of a block Lanczos algorithm for free vibration analysis of spinning structures', Int. J. Numer. Meth. Engng. 26, 1029-1037 (1988).
    • (1988) Int. J. Numer. Meth. Engng. , vol.26 , pp. 1029-1037
    • Gupta, K.K.1    Lawson, C.L.2
  • 30
    • 0026883715 scopus 로고
    • On development of a finite dynamic element and solution of associated eigenproblem by a block Lanczos procedure
    • K. K. Gupta, C. L. Lawson and A. R. Ahmadi, 'On development of a finite dynamic element and solution of associated eigenproblem by a block Lanczos procedure', Int. J. Numer. Meth. Engng. 33, 1611-1623 (1992).
    • (1992) Int. J. Numer. Meth. Engng. , vol.33 , pp. 1611-1623
    • Gupta, K.K.1    Lawson, C.L.2    Ahmadi, A.R.3
  • 31
    • 0001265480 scopus 로고
    • Solution of eigenproblems for damped structural systems by Lanczos algorithm
    • H. C. Chen and R. L. Taylor, 'Solution of eigenproblems for damped structural systems by Lanczos algorithm', Comput. Struct. 30(1/2), 151-161 (1988).
    • (1988) Comput. Struct. , vol.30 , Issue.1-2 , pp. 151-161
    • Chen, H.C.1    Taylor, R.L.2
  • 32
    • 0027594911 scopus 로고
    • Lanczos algorithm for the quadratic eigenvalue problem in engineering applications
    • C. Rajakumar, 'Lanczos algorithm for the quadratic eigenvalue problem in engineering applications', Int. J. Numer. Meth. Engng. 105, 1-22 (1993).
    • (1993) Int. J. Numer. Meth. Engng. , vol.105 , pp. 1-22
    • Rajakumar, C.1
  • 33
    • 0019055271 scopus 로고
    • An accelerated subspace iteration method
    • K. J. Bathe and S. Ramaswamy, 'An accelerated subspace iteration method', Comput. Struct. 23, 313-331 (1980).
    • (1980) Comput. Struct. , vol.23 , pp. 313-331
    • Bathe, K.J.1    Ramaswamy, S.2
  • 34
    • 0021819031 scopus 로고
    • A subspace Lanczos method for the generalized symmetric eigenproblem
    • H. Matthies, 'A subspace Lanczos method for the generalized symmetric eigenproblem', Comput. Methods Appl. Mech. Engng. 21, 319-325 (1985).
    • (1985) Comput. Methods Appl. Mech. Engng. , vol.21 , pp. 319-325
    • Matthies, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.