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Application of the simultaneous iteration method to undamped vibration problems
Author(s) -
Jennings Alan,
Orr D. R. L.
Publication year - 1971
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620030105
Subject(s) - eigenvalues and eigenvectors , vibration , degrees of freedom (physics and chemistry) , mathematics , modal matrix , transformation (genetics) , mathematical analysis , matrix (chemical analysis) , stiffness , stiffness matrix , mass matrix , diagonalizable matrix , symmetric matrix , physics , structural engineering , acoustics , engineering , biochemistry , chemistry , materials science , quantum mechanics , neutrino , nuclear physics , composite material , gene
The simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems. This method is of significance when a few of the dominant eigenvalues and eigenvectors are required from a large matrix, and hence is particularly suitable for vibration problems involving a large number of degrees of freedom. It is shown that advantage may be taken of both the symmetry and the band form of the mass and stiffness matrices, thus making it feasible to process on a computer larger order vibration problems than can be processed using transformation methods. A method of allowing for body freedom is given and some numerical tests are discussed.