Multiobjective Optimization Criteria for Linear Structures Subject to Random Vibrations

A structural optimization criterion for linear mechanical systems subject to random vibrations is presented for supporting engineer’s design. It is based on a multiobjective approach whose Objective Function (OF) vector is done by stochastic reliability performance and structural cost indices. The first ones are structural reliabilities, and are evaluated for one or more failure types; they are related to designer’s required performances defined in the pre-design phase. The second OF vector indices concerned cost or similar deterministic measures. The reliability based performance criteria here proposed is properly able to take into account the design required performances and so it is an efficient support for structural engineering decision making. The proposed criteria is different from other used conventional optimum design for random vibrating structure, that are based on minimizing displacement or on acceleration variance of main structure responses, but are not able to consider explicitly the required performances against structural failure.

As example of proposed criteria, the multiobjective optimum design of a Tuned Mass Damper (TMD) has been developed, for a typical seismic design problem; it deals with control of structural vibrations induced on a multi-storey building structure excited by non stationary base acceleration random process. A numerical application of this specific problem has been done with reference to a three storey building, and a sensitivity analysis is carried out. Its results are shown in a useful manner for TMD design decision support.