Robust design method of TMDs for a gable roof subjected to variation in the natural frequency and damping values

TMDs for spatial structures require a different design method than that for multi-story buildings because in spatial structures, multiple modes with close natural frequencies are excited, and their vibration shapes are complex. We have conducted the shaking table test to verify the vibration control effect of TMDs using a scaled-down model of a gable roof. In this experiment, we simulated damage to the column bases and compared responses by degree of damage. The results show that when seriously damaged, decrease of the natural frequency of the specimen causes TMDs to become ineffective and the responses are amplified because of the weight of the TMD devices. In addition, the vibration control effect seems to depend on the vibration characteristics of the TMD devices. Specifically, the friction of the guide roller can cause amplitude dependence of the damping values. In this paper, we propose a robust design method of TMDs with high robustness against variation in the natural frequency of the specimen and the damping values of the TMD devices. We study highly robust TMDs installation case against the natural frequency decrease, followed by search for cases which are robust against the damping values variation in those cases. Our analysis shows that the method of installing two TMDs, one tuned to the natural frequency of the controlled mode and the other to 30% smaller frequency, is effective for the natural frequency decrease. For the damping values variation, increasing the number of TMDs can lead to higher robustness. Thus, we conclude that the method of installing multiple TMDs with different frequencies is effective for both of those variations.