TMD Damping for Structures with Uncertain Modal Parameters

The optimum tuning of the natural frequency and damping ratio of TMDs for structural modal parameters and various optimization criteria are well-known from the literature. However, when the eigenfrequency and modal mass of the target structural mode are uncertain due to estimation and measurement errors, significant life loads, temperature, and other time-varying effects, the existing TMD tuning rules are not necessarily optimal. An often-adopted method is to select the TMD damping ratio that is greater than optimal value to make the TMD less sensitive to variations of the target eigenfrequency and uncertainty in the modal mass. This heuristic approach is quantitatively investigated by the presented research. Computations are made for different TMD mass ratios, different uncertainties in target eigenfrequency and modal mass, different levels of increased TMD damping, and assuming harmonic excitation. The results demonstrate that there is no simple rule when increased TMD damping is advantageous. Therefore, beneficial TMD increase factors are given as functions of TMD mass ratio and deviations between actual and nominal modal structural properties. These data can be used by engineers for real TMD projects with uncertain modal parameters.