Analytical optimization and performance evaluation of non-traditional tuned mass damper for stochastic base excited structures considering dual solutions

Compared with traditional tuned mass damper (TMD), non-traditional tuned mass damper (NTMD) has higher damping efficiency in some conditions. Nevertheless, the analytical optimization problem of NTMD has not been well solved; especially, multiple optimal solutions are not discussed. In this study, the closed-form optimal expressions of the NTMD using tuning stiffness are derived based on H ₂ norm optimization. And the vibration mitigation performance of the NTMD is evaluated considering dual-solutions situation subjected to typical ground motion and impulse excitation. Different from solving the unique optimal frequency ratio, there exist two sets of optimal stiffness and damping ratio derived using tuned spring elements for given mass ratio, and the effective mass ratio is also limited as 1/3. The vibration mitigation or isolation performance and robustness of H ₂ optimized NTMD with higher stiffness ratio are far superior to NTMD with lower stiffness ratio. NTMD using larger optimal tuning stiffness ratio also can be seen as an optimized form of Maxwell model using additional mass. Hence, using a large stiffness, namely, a large frequency ratio to design NTMD is recommended, which is different from traditional TMD. The case of NTMD with large stiffness can be adopted when the demands of practical engineering are not met using the optimal parameters of small stiffness. And a compromise scheme can also be provided, which are the combination with a larger mass ratio but is less than the maximum limit value 1/3 and a not very large stiffness ratio but is exceeded 0.5 according to demands of practical engineering.