Optimal design of rotational inertial double tuned mass dampers under random excitation

The rotational inertial double tuned mass damper (RIDTMD) is a type of passive mass damper which includes a physical mass as well as a rotational mass. This rotational mass is produced by an inerter which is capable of providing large effective mass utilizing very little physical mass. By selecting the proper design parameters, the RIDTMD show promise at more effective response reduction of underlying primary systems in comparison to conventional tuned mass dampers (TMDs). However, when the primary system is subjected to random loads, the previously considered optimum design values for harmonic excitation are not effective. This motivates an investigation to determine the exact analytical optimum solution for selecting the stiffness and damping design values of RIDTMD when the primary structure is subjected to random force and base excitation. In this paper, an exact optimization solution procedure is presented with the goal of finding the optimum design values of the RIDTMD when mitigating the response of a structure subjected to random force and base excitation. Utilizing the obtained optimum design values, the effectiveness of the RIDTMD is also studied in comparison to conventional TMDs. The results of this study show that the RIDTMD with optimized stiffness and damping values outperforms the optimized conventional TMD; however, the degree of its increased effectiveness in reducing the main mass response is reliant upon the selection of appropriate pairs of secondary and rotational mass.