A Computationally Efficient Method for Optimum Tuning of Single-Sided Pounding Tuned Mass Dampers for Structural Vibration Control

Pounding tuned mass dampers (PTMD), which relies on impact to dissipate vibration energy, have shown remarkable performance in suppressing structural vibrations with its modest design. However, the optimum design of PTMDs is computationally expensive due to non-smooth contact-impact behavior. This study provides a computationally efficient approach to determine the optimal parameters of single-sided PTMDs used in vibration control of structural systems. An optimization strategy is used to minimize the maximum response of the controlled structure. As is well-known, the calculation of the dynamic response of a structure could be cumbersome when conventional time-stepping techniques are used in each iteration of the optimization routine. Hence, an exact analytical solution of the steady-state vibration is used to calculate the response for different excitation frequencies, which substantially decreases the computational burden. The adopted method is computationally very inexpensive with respect to the conventional time-stepping techniques used to solve the nonlinear equations of motion to obtain response quantities. The exact solution only requires the solution of the system of five nonlinear equations in order to evaluate the steady-state response per each excitation frequency of harmonic force. A four-storey shear building is used to evaluate the optimally-tuned PTMD by the proposed procedure. In addition, simplified design equations for the coefficient of restitution and frequency ratio are provided using curve and surface fitting for preliminary design. It was shown that the effect of damping ratio of the primary structure on the optimal coefficient of restitution value is not considerable, while it has significant influence on the optimal frequency ratio. It was also realized that the objective function used in optimum parameter design has only one local optimum, which is suitable for the application of gradient-based optimization methods.