Novel mathematical models based on regression analysis scheme for optimum tuning of TMD parameters

Tuned mass damper (TMD) has been widely used as an adopted strategy for vibration control of mechanical and structural systems. Tuning of TMD parameters plays an important role in its performance. In this paper, novel mathematical models based on regression analysis scheme are presented for optimum tuning of TMD parameters in a damped main system subjected to white noise base acceleration. For this purpose, a database of optimum frequency and damping ratio of TMD is created and then models based on regression analysis scheme are proposed for optimum tuning of TMD parameters. Considering the confidence index as a statistical measurement, the efficiency of the proposed mathematical models is compared with other explicit models in the literature. The results show that the proposed models are simple and, due to having the lowest estimated errors and the best agreement with optimum tuning from database, they are able to provide more accuracy than other explicit mathematical models for optimum tuning of TMD parameters. Also, the proposed models are more efficient and simple than the search-based optimization algorithms. Therefore, they can readily be used for engineering applications without the need of time-consuming calculations. Furthermore, it is found that the optimum TMD parameters are not influenced by the predominant frequency of filtered white-noise excitation. At the end, the efficiency of the proposed mathematical models is shown for a structure subjected to different earthquakes.