Optimal Parameters for Tuned Mass Dampers and Examination of Equal Modal Frequency and Damping Criteria

This work developed an idea and systematically explains ‘equal modal frequency and damping’ (EMFD) technique to derive the complete closed form solutions of tuned mass damper (TMD), to reduce dynamic response of structural system.

The optimum parameters for the damped system till date required numerical search technique or shootout technique, which is the trial-error method, of-course add complexity in selecting parameter obtained at optimality conditions. The study of optimum parameter based on EMFD shows the complete closed-form solution, independent to another optimum parameter.

The parameters solely depend on structural damping and mass ratio. The study reveals the multiple optimal solutions. This work investigates the various optimal parameters under harmonic excitation, also compare same with relevant researchers. To confirm its robustness under random excitation various real earthquake time history loads are applied to investigate behavior of different solutions. A demonstration of the shear building for harmonic and random excitation for various solutions provides valuable practical insights for the research endeavors.

Furthermore, the article presents a novel method for finding optimal parameters efficiently without requiring numerical calculations at any stages. The significance of multiple optimal solutions becomes evident when structural systems face random excitation.