×

A Lanczos-based technique for exact vibration analysis of skeletal structures. (English) Zbl 0775.73152


MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Kolouse, Ing. Archiv. 12 pp 363– (1941)
[2] Dynamics in Engineering Structures, Halsted Press, New York, 1973.
[3] William, J. Struct. Eng. 109 pp 169– (1983)
[4] William, Int. J. Mech. Sci. 12 pp 781– (1970)
[5] Wittric, Quart. J. Mech. and Appl. Math 24 pp 263– (1971)
[6] Swannel, Comput. methods appl. mech. eng. 16 pp 291– (1978)
[7] ’Automatic computation of the natural frequencies of structural frames using an exact matrix technique’, in Theory and Practice in Finite Element Structural Analysis, University of Tokyo Press, Japan, 1973 pp. 289-303.
[8] Richard, J. Sound Vib. 55 pp 363– (1977)
[9] Hallaue, J. Sound Vib. 85 pp 105– (1982)
[10] Anderson, J. Spacecraft 24 pp 353– (1987)
[11] Anderso, AIAA J. 24 pp 163– (1986)
[12] Gupt, Int. j. numer. methods eng. 33 pp 1611– (1992)
[13] Theory of Matrix Structural Analysis, McGraw-Hill, New York, 1968.
[14] Melos, J. Eng. Mech. 115 pp 543– (1989)
[15] Smit, Comp. Struct. 36 pp 531– (1990)
[16] Smit, Int. j. numer. methods eng. 29 pp 1219– (1990)
[17] Smith, J. Eng. Mech. 117 pp 1198– (1990)
[18] Sorense, SIAM J. Matrix Anal. Appl. 13 pp 357– (1990)
[19] and , Algorithms for Large Symmetric Eigenvalue Computations, I Theory, Birkhauser, Boston, 1985.
[20] Parlet, Math. Comput. 33 pp 217– (1979)
[21] The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, N.J., 1980. · Zbl 0431.65017
[22] Gupt, Int. j. numer. methods eng. 26 pp 1029– (1988)
[23] Bauchau, Int. j. numer. methods eng. 23 pp 1705– (1986)
[24] and , Matrix Computations, Johns Hopkins University Press, Baltimore, 1989.
[25] and , ’The implementation of a block shifted and inverted Lanczos algorithm for eigenvalue problems in structural engineering’, ETA-TR-39, Boeing Computer Services, Seattle, WA, 1986.
[26] Jai, Comput methods appl. mech. eng. 40 pp 277– (1983)
[27] Ruh, SIAM J. Numer. Anal. 10 pp 674– (1973)
[28] Yang, Comp. Struct. 29 pp 353– (1988)
[29] Greenber, SIAM J. Math. Anal. 20 pp 182– (1989)
[30] Johnsto, Int. j. numer. methods eng. 15 pp 911– (1980)
[31] William, Int. j. numer. methods eng. 26 pp 1825– (1988)
[32] Simpso, Quart. J. Mech. Appl. Math. XXI pp 1– (1967)
[33] ’The Kron methodology and practical algorithms for eigenvalue, sensitivity and response analyses of large scale structural systems’, Aeronautical J., 417-433 (1980).
[34] and , ’Performance comparison of the mixed, h-and p-formulations of the finite element method for vibration analysis’, submitted to Computers and Structures.
[35] Simpso, J. Sound Vib. 97 pp 153– (1978)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.