A correction of the half-power bandwidth method for estimating damping

The half-power bandwidth method is commonly used to evaluate the system damping by using frequency response curves and assuming a small damping ratio. Preceding derivations obtain the third-order corrections to the classical formula but still show large errors when the damping ratio is high, especially for the acceleration case. In this note, new approximate formulas for damping ratio in terms of the half-power bandwidth are established using displacement and acceleration frequency response functions, respectively. The proposed formulas, third-order correction and classical approximations are compared by using relative errors of calculated damping ratios for both displacement and acceleration cases. The new formulas for damping ratio are brief and show excellent accuracy for small as well as high damping ratios.