Understanding Limitations of Nonlinear Damping Ratio Identification Methods from Force Appropriation Tests.

Energy dissipation (i.e., damping) is a critical quantity to identify in order to understand the dynamic performance of a mechanical design as the dissipation directly influences response amplification near resonance. In linear systems, dissipation is often modeled with constant viscous damping for each mode and can be extracted directly from modal tests in the form of damping ratio. For nonlinear systems there have been many proposed techniques for characterizing damping from experimental measurements, however researchers have yet to reach a consensus on a unified approach. This work investigates three damping identification methods and evaluates each of their limitations. The context for the identification is the nonlinear force appropriation testing technique. The study conducts virtual experiments utilizing multi-harmonic balance solutions where phase resonance is enforced on single-degree-of-freedom models with different nonlinearities – both conservative and non-conservative. In this way, the calculated damping ratios are compared directly to corresponding analytical approximations from the models to enable a critical assessment of their accuracy and of any limitations of each damping identification technique. Additionally, the effect of higher harmonics (both in phase resonance and uncontrolled) on the damping ratio estimates is explored by including an electro-mechanical model of a shaker. In addition to identifying limitations for each damping identification technique considered, this work shows that the trend in the damping ratio does not necessarily reflect the true nature of the nonlinear damping restoring force. Moreover, the damping ratio trend identified from nonlinear force appropriation experiments is sensitive to higher harmonics in the excitation force regardless of whether they are maintained in phase resonance or uncontrolled.