TMDs for Vibration Control of Systems with Uncertain Properties

The use of tuned mass dampers (TMDs) to reduce the vibrations of single‐degree‐of‐freedom systems with uncertain properties subjected to white‐noise random excitation is considered. The uncertainties of the system are modeled as random variables and are assumed to be time‐independent. The statistics of the system response are found by using a second‐order Taylor expansion or numerical integration methods. Using these methods and an optimization software the optimum design parameters of the TMD are computed. Validation calculations show that Taylor expansion can predict the system response for low and moderate levels of uncertainty in the system properties. It is found that parameter uncertainties may have a significant effect on the TMD efficiency. Finally, it is recommended that the “probabilistic tuning” approach described in this paper be used whenever there is a significant uncertainty in the system properties.