Closed-Form Derivation of Optimum Tuned Mass Damper Parameter Based on Modal Multiplicity Criteria

It is presently established that properly designed tuned mass dampers (TMD) systems can effectively control the vibrations induced due to the wind and/or the seismicity. The TMD is one of the most used passive control systems in high-rise structural systems in an era of recent developments. The optimum parameters for the damped system to date require a numerical search technique or shootout technique, which is the trial-error method, of-course add complexity in selecting parameters obtained at optimality conditions. The study of optimum parameters based on modal multiplicity criteria showcases the complete closed-form solution, independent to another optimum parameter. The parameters presented in this study solely depend on structural damping and mass ratio. The derived optimum parameters are compared with the existing parameters in this field. This study also investigates parametric uncertainty for structural configuration under the harmonic excitation. To confirm its robustness under random vibration, various earthquake time history loads are applied to study the effect of structural displacement and acceleration response. In the end, the energy concept is deployed to explain how effectively the optimum TMD parameters help to reduce the kinetic energy, damping energy, strain energy, and input energy.