An Explicit Solution of Modal-Damping Ratios for Higher Modes of a Cable with an External Damper
Publication: Journal of Engineering Mechanics
Volume 148, Issue 1
Abstract
Design of external dampers for stay cables requires repetitive evaluation of damping ratios for target modes of cables under various damper parameters and installation positions, and explicit formulas with high accuracy to estimate the modal-damping ratios for a cable-damper system are helpful in designing external dampers. This study deals with the evaluation of the modal damping of cables with an external viscous damper close to the anchorage. A considerably accurate and explicit formula for calculating the modal-damping ratios of the cable-damper system is derived by evaluating the imaginary and real part of the complex frequency equation. It is demonstrated that the formula is able to predict the modal-damping ratios of the cable-damper system both for lower and higher modes. Based on the proposed formula, the effects of the modal order and installation position on the modal-damping ratio of the cable-damper system are studied. A closed-form solution for the optimal damping coefficient is proposed and the maximum attainable modal damping is also obtained.
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Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The financial support from the National Key Research and Development Program of China (Grant 2019YFC1511101), the National Science Fund for Distinguished Young Scholars (Grant 52025082), the National Natural Science Foundation of China (Grant 51908210), and the Natural Science Foundation of Hunan Province (Grant 2020JJ5074) are greatly appreciated. The authors also gratefully acknowledge Sutong Bridge Co., Ltd., China, for the data support.
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Published In
Journal of Engineering Mechanics
Volume 148 • Issue 1 • January 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jan 28, 2021
Accepted: Sep 23, 2021
Published online: Nov 3, 2021
Published in print: Jan 1, 2022
Discussion open until: Apr 3, 2022
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