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

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.