Robust optimization for tmd with uncertain bounded system parameters and stochastic excitation

In this work a robust optimum design for mechanical parameters of linear Tuned Mass Damper devices is proposed. In this field, standard approaches are based on the implicit assumption that all system parameters are deterministically known quantities. When this hypothesis is removed, a robust optimum design criterion for Tuned Mass Damper should be developed, where robustness is obtained by finding solutions which are less sensitive to variation of system parameters, originated by the uncertainty. In this study the load condition for the analysed system is represented by a stationary stochastic process which models the base acceleration, and here modelled by the Kanai- Tajimi stochastic process. The main system, which is equipped by a single Tuned Mass Damper, is described by a system with a single degree of freedom: system mass and stiffness are assumed to be affected by uncertainty, and then are represented by random-bounded variables. The ratio between the protected and unprotected main system covariance displacement is assumed as Objective Function, and then its mean and standard deviation are evaluated. Robust optimum design is formulated as a multi-objective optimization problem, in which both the first and the second statistical moments are minimized simultaneously, with different weights. In this way, optimal Pareto fronts are obtained: after that a sensitivity analysis is carried out in order to assess the variation of robust solution with respect to some parameters, and moreover in order to evaluate the differences with respect to conventional deterministic solution.