Performance reliability based optimization criterion for elastic structures subject to random loads

A stochastic optimization which makes use of a reliability constraint, expressing a performance requirement, is proposed for linear elastic systems subject to random dynamic loads. The criterion selected for the optimum design is the minimization of a deterministic measure, whereas the constraint condition requires that system failure probability must be smaller than a given allowable level, where failure is associated to the first exceeding of system response from a safe domain. The proposed method is then developed for the optimum design of a Tuned Mass Damper, utilized for reducing undesirable vibrations originated in structures by random loads. Unlike conventional TMD designs based on minimizing the mean-square response, a reliability-based performance measure is then considered in the proposed design, which properly accounts for uncertainties in loads. A sensitivity analysis is carried out and results are shown in a useful manner for TMD design decision support