Natural Frequencies of a Very Large–Sag Extensible Cable
Publication: Journal of Engineering Mechanics
Volume 144, Issue 2
Abstract
This technical note presents a model formulation that can be used for analyzing the in-plane free vibration behaviors of a very large–sag extensible cable supported at the same and different levels. The formulation model developed in this study is based on a variational approach, which involves the virtual strain energy because of axial stretching, the virtual work done by cable self-weight, and by the inertia forces. The coupled equations of motion in the Cartesian coordinates are obtained by taking into account the difference of Euler’s equations between equilibrium and displaced states. The Galerkin finite element method is used to obtain the mass and stiffness matrices and then the eigenvalue problem is solved. The numerical analysis results are given to demonstrate the dynamic free vibration on natural frequencies and mode shapes of various characteristics of cables from very small–sag to very large–sag cable configurations, the special case of a very large–sag cable was investigated and compared with the natural frequencies and mode shapes of the simple hanging chain.
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Acknowledgments
The authors would like to acknowledge the Institutional Research Capability Development Grant from Thailand Research Fund (TRF) and King Mongkut’s University of Technology Thonburi (KMUTT).
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Published In
Journal of Engineering Mechanics
Volume 144 • Issue 2 • February 2018
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jan 26, 2017
Accepted: Aug 8, 2017
Published online: Dec 8, 2017
Published in print: Feb 1, 2018
Discussion open until: May 8, 2018
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