Research Article
Dec 1979
Forced Vibration of Beams by Eigenmatrix Method
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VIEW THE REPLYAuthors: Bennosuke Tanimoto, Kiyoshi Ishikawa, and Shotaro NatsumeAuthor Affiliations
Publication: Journal of the Structural Division
Volume 105, Issue 12
Abstract
The eigenmatrix method and the operational displacement one are presented for the forced vibration problem of beams and frames. The differential equation for flexure is due to the classical Bernoulli-Euler's theory, and it can be extended to the excellent Timoshenko's one. The stress-strain relationship can also be extended from Hooke's law to the visco-elastic Voigt's law. Avoiding the prevailing lumped mass or finite element philosophy, the structures are treated as continuum solid body as they appear. The method consists of the three traditional branches in structural analysis: (1) Eigenvalue problem, (2)boundary-value problems, and (3)initial-value problem. The eigenmatrix method is in a sense the algebraic transfer matrix one, in which case the load term can be separated, and it is suited for one-dimensional structures. The operational displacement method is fitted for frames, in which case the complete stiffness matrix is tridiagonal.
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Published In
Journal of the Structural Division
Volume 105 • Issue 12 • December 1979
Pages: 2725 - 2749
Copyright
© 1979 American Society of Civil Engineers.
History
Published in print: Dec 1979
Published online: Feb 1, 2021
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Affiliations
Bennosuke Tanimoto
Prof. of Civ. Engrg., Kanazawa Inst. of Tech., Nonoichi, Kanazawa, Japan; and Head of the Inst. for Developments at Operational Method (IDOM), Tobishima Construction Co., Inc., Kudan, Tokyo, Japan
Kiyoshi Ishikawa
Asst., Dept. of Civ. Engrg., Shinshu Univ., Nagano, Japan
Shotaro Natsume
Assoc. Prof., Dept. of Civ. Engrg., Shinshu Univ., Nagano, Japan
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