Multiobjective Optimization Criteria for Linear Structures Subject to Random Vibrations

Giuseppe Carlo Marano*
Technical University of Bari, Department of Environmental Engineering and Sustainable Development, viale del Turismo, 10 - 74100 Taranto (Italy - EU).

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© 2008 Giuseppe Carlo Marano.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Technical University of Bari, Department of Environmental Engineering and Sustainable Development, viale del Turismo, 10 - 74100 Taranto (Italy - EU); E-mail:


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.

Keywords: Structural optimization, Multiobjective optimization, Random vibration, Tuned mass damper.