Random vibration is a common state in many real structural problems concerning dynamic environment loads, as base excitation induced by rotating machinery or wind loads. In this work a full stochastic approach for optimal design of linear structures subject to random dynamic loads is presented. By adopting a covariance approach a reliability based optimum criterion is developed, where both objective function (OF) and constraints are defined in a stochastic way. This criterion can be applied both for stationary and for non stationary vibration conditions. Constraints impose a limit to failure probability, here associated with the first threshold crossing of a structural displacement, while the inertial acceleration variance or the elastic force variance are minimized in order to control vibration effects. Two applications are developed for simple structural vibration control problems to evaluate the efficiency of the proposed criterion. The first regards a vibration absorber modelled by a SDoF, while the second is a tuned mass damper represented by a TDoF. Both cases are subject to filtered white noise.

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