Evaluation of the Lever-type Multiple Tuned Mass Dampers for Mitigating Harmonically Forced Vibration

The lever-type multiple tuned mass dampers (LT-MTMD), consisting of several lever-type tuned mass dampers (LT-TMDs) with a uniform distribution of natural frequencies, are proposed for the vibration control of long-span bridges. Using the analytical expressions for the dynamic magnification factors (DMF) of the LT-MTMD structure system, an evaluation, with inclusion of the LT-MTMD stroke, is conducted on the performance of the LT-MTMD with identical stiffness and damping coefficients but unequal masses for mitigating harmonically forced vibrations. The LT-MTMD is found to possess the near-zero optimum average damping ratio regimen when the total number of dampers exceeds a certain value. In comparison, the LT-MTMD without the near-zero optimum average damping ratio and the traditional hanging-type multiple tuned mass dampers (HT-MTMD) without the near-zero optimum average damping ratio can achieve approximately the same optimum frequency spacing (an indicator for robustness), effectiveness, and stroke. Compared with the HT-MTMD, the LT-MTMD needs lesser optimum average damping ratio but significantly higher optimum tuning frequency ratio. Its main advantage is that the static stretching of the spring may be adjusted to meet the practical requirements through the support movement, while maintaining the same robustness, effectiveness, and stroke. Consequently, the LT-MTMD is a better choice for suppressing the vibration of long-span bridges as the static stretching of the spring required is not large.