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Analytical selection of masters for the reduced eigenvalue problem
Author(s) -
Shah V. N.,
Raymund M.
Publication year - 1982
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.1620180108
Subject(s) - eigenvalues and eigenvectors , divide and conquer eigenvalue algorithm , degrees of freedom (physics and chemistry) , mathematics , reduction (mathematics) , selection (genetic algorithm) , algorithm , process (computing) , inverse iteration , mathematical optimization , computer science , geometry , artificial intelligence , physics , quantum mechanics , operating system
Masters are defined as the degrees‐of‐freedom that are retained in the reduced eigenvalue problem. Various qualitative guidelines to select masters are published in the literature, but it is difficult to apply them to complex structures. In this paper a computational algorithm to select masters for complex structures is presented. This algorithm is based on a guideline 14 which assures that the associated Guyan reduction process is valid. This algorithm eliminates one degree‐of‐freedom at a time satisfying the guideline, and preserves lower frequencies in the reduced eigenvalue problem. The algorithm presented in this paper is used to select masters for four different structural models. The natural frequencies of the associated reduced eigenvalue problems are calculated and compared with those calculated from the full eigenvalue problems.