Acceleration-based effective damping ratio of tuned mass damper under seismic excitations

To investigate the effectiveness of a tuned mass damper (TMD) in controlling acceleration responses of a primary structure under seismic excitations, this paper proposes a practical method for the calculation of the acceleration-based effective damping ratio of TMD. Seismic ground motions were simulated by using the Kanai-Tajimi model, and the effect of site conditions on the TMD effective damping ratio was considered. The site filtering effect was expressed in a transfer function form, and the absolute acceleration dynamic amplification factor of a structure to bedrock was derived. In this study, the effectiveness of TMD was considered as the effective damping ratio added to each mode of the primary structure, and an analytical expression for the TMD effective damping ratio was therefore established. Results of the parametric analysis show that when the TMD mass ratio is less than 0.1, an increase in the TMD mass can enhance its effective damping ratio, as well as its acceleration response control performance. However, an increase in the structural damping ratio weakens the TMD control performance. Moreover, the TMD effective damping ratio significantly depends on site conditions, that is, the TMD may have a side effect in controlling acceleration responses in a certain frequency range. Numerical simulation of a 10-story shear frame structure exposed to soil- and rock-site earthquakes demonstrated that when it comes to the root mean square values of the structural absolute accelerations the error of the proposed method did not exceed 0.88%, indicating that it can precisely evaluate the effectiveness of the TMD.

Automated summary

This paper proposes a practical method for calculating the acceleration-based effective damping ratio of TMD. The effectiveness of TMD in controlling acceleration responses depends on the TMD mass ratio and the structural damping ratio. Moreover, the TMD effective damping ratio significantly depends on site conditions.