Keywords: optimization, system reliability, target reliabilities, frequency, safety factors.

The optimal design of structures with frequency constraints is extremely useful in order to minimize vibration and noise, maximizing safety. For example, in most low-frequency vibration problems, the structural response to dynamic excitation is primarily a function of its fundamental frequencies and mode shapes. Therefore, finding the optimal design of the selected frequencies can significantly improve the performance of the structure. The structural optimization is frequently applied for effective cost reduction of engineering systems under frequency constraints.

The reliability-based design optimization (RBDO) methodology is a contemporary approach to designing economical and safe structures. The RBDO methodology allows us to reach effectively balanced cost-safety configurations, by controlling the structural uncertainties during the design process, which cannot be achieved by deterministic optimization. A practical formulation of the RBDO methodology consists of minimizing the expected cost under reliability constraints. Generally, when the structural dynamic behaviour is considered, the reliability constraint is formulated on the basis of the fundamental frequency. In this way, the RBDO problem becomes a component formulation based on a single limit state. However, as structural failure is rarely confined to only the first eigen-mode, the system reliability approach becomes necessary to deal with realistic situation which several eigen-frequencies are involved. In other words, the RBDO of vibrating structures based on the first frequency does not lead to an optimal and reliable design of the whole structure. To some extent, the system reliability approach may be considered through several limit states described by the significant eigen-frequencies.

In this paper, a new methodology of reliability-based design optimization of vibrating structures is proposed. An efficient RBDO procedure is developed in order to find the best compromise between satisfying the target system reliability and optimizing the structural cost. The proposed approach is based on the concept of the decoupled approach, where the RBDO problem is converted to several cycles of deterministic design optimization followed by the calibration of the partial safety factors. The originality of the present work lies in taking account of several eigen-frequencies rather than the single fundamental frequency, where the partial safety factors are optimally calibrated on the basis of the overall system performance. The numerical application shows the interest and the good-standing of the proposed method.

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