Damping ratio measurements of multi-degree-of-freedom systems

MD MAHBUB ALAM; Feiran  Chen; Hongjun  Zhu; Chunning  Ji; Mostafa  Zeinoddini; Vahid  Tamimi; Tinghai  Cheng

doi:10.59400/sv3752

Damping ratio measurements of multi-degree-of-freedom systems

MD MAHBUB ALAM
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
Feiran Chen
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
Hongjun Zhu
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China
Chunning Ji
State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation, Tianjin University, Tianjin 300350, China
Mostafa Zeinoddini
Faculty of Civil Engineering, K.N. Toosi University of Technology, Tehran 19697-64499, Iran
Vahid Tamimi
School of Civil Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran
Tinghai Cheng
Beijing Institute of Nanoenergy and Nanosystems, Chinese Academy of Sciences, Beijing 101400, China

Article ID: 3752

DOI: https://doi.org/10.59400/sv3752

Keywords: modal damping ratio; MDOF systems; filter-based method; HQGM; modal coupling

Abstract

Accurate estimation of modal damping ratios is essential for predicting and controlling the dynamic response of multi-degree-of-freedom (MDOF) structures, particularly in bridge and structural vibration studies. Despite the availability of various methods for estimating damping ratios in MDOF systems, most approaches rely on modal decoupling, which often involves considerable complexity and effort. This work introduces two approaches that eliminate the need for modal decoupling: a filter-based method and an improved Half-Quadratic Gain Method (HQGM). The filter-based approach extracts decay characteristics directly from displacement signals using frequency-domain filtering and logarithmic envelope analysis, achieving damping ratio estimates within 3% error for both free and forced vibrations and for systems with low or high damping. The HQGM, originally formulated for single-degree-of-freedom systems, is extended here to MDOF systems and further enhanced by a correction formula that suppresses coupling-induced secondary peaks in frequency response functions. Comparative analysis demonstrates that while the original HQGM performs well in weakly coupled systems, the improved HQGM yields superior accuracy under strong coupling conditions. Both methods provide a robust framework for identifying damping characteristics across a wide range of dynamic systems. The proposed techniques offer practical advantages for structural engineering applications, where damping properties are difficult to measure directly.

Published

2026-02-05

How to Cite

ALAM, M. M., Chen, F., Zhu, H., Ji, C., Zeinoddini, M., Tamimi, V., & Cheng, T. (2026). Damping ratio measurements of multi-degree-of-freedom systems. Sound & Vibration, 60(1), 1-31. https://doi.org/10.59400/sv3752

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Vol. 60 No. 1 (2026)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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