A model-based generalization of the bandwidth method for damping estimation

The classical half-power bandwidth is one of several approaches that can be used to estimate the modal damping ratio of a dynamic system from its frequency response function (FRF). Although relatively simple to implement, this method is accurate when applied to the displacement and velocity FRFs of lightly damped, harmonically forced viscous systems for which the vibration modes are far enough apart. In this work, we introduce a modified definition of the bandwidth along with a generalized approach that we use to develop exact expressions for the damping parameter of viscously and hysteretically damped single-degree-of-freedom systems under different inputs over a range of permissible amplitude ratios. When considering a direct force input, we find that the same closed-form expression can be used to determine the damping parameter from the displacement and acceleration FRFs. We also utilize this technique to establish exact damping parameter expressions for harmonic base excitation cases for the first time in the literature. Application of the modified bandwidth method to experimentally obtained FRFs from single- and two-degree-of-freedom systems reveals that this approach is far superior to its classical alternative at high damping ratios and generally comparable at lower ones in the higher-confidence data regions.