Solution to Vibrations of Double-Beam Systems under General Boundary Conditions
Publication: Journal of Engineering Mechanics
Volume 147, Issue 10
Abstract
The problem of vibrations of double-beam systems is of technological interest and has been extensively studied in the literature. However, a general solution is yet to be developed for the general boundary conditions. In this paper, a general solution of the free and forced vibrations of double-beam systems under classical, nonclassical, and mixed boundary conditions is derived. The obtained mode-shape solutions are exact and explicit. The characteristic frequency equation of a double-beam system is of order-4 and order-8 for the classical boundary conditions and the nonclassical boundary conditions, respectively. The solution of forced vibrations is developed with the classical modal expansion technique. In addition to the theory, applications of the proposed method are illustrated by numerical examples. The obtained frequencies for special problems are compared with the literature, and the agreement between the proposed method and the literature is remarkably good. This shows that the proposed shape function method may be applied reliably to determine the transverse vibration mode shapes and natural frequencies of the double-beam system under the general boundary conditions. The solutions of free and forced vibrations of the double-beam systems presented in the paper could easily be programmed into a computer for vibration analyses.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The author would like to thank the two anonymous reviewers for their insightful suggestions and careful reading of the manuscript.
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Published In
Journal of Engineering Mechanics
Volume 147 • Issue 10 • October 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Nov 11, 2020
Accepted: Mar 8, 2021
Published online: Aug 4, 2021
Published in print: Oct 1, 2021
Discussion open until: Jan 4, 2022
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