Robust equilibrium optimization of structural dynamic characteristics considering different working conditions

In the design of complex products such as turbo-generators and compressors, it is very important to optimize the dynamic characteristics of the key components by moving their natural frequencies away from the excitation ones as well as their multiples to avoid resonances and resultant malfunctions. At the same time, the uncertainties such as the fluctuations of material properties inherent in the manufacture of key components will inevitably cause the variation of their structural dynamic characteristics and thus need to be fully considered in the optimization process. Considering that the robustness requirement of structures with uncertain material properties (specifically, uncertain elastic modulus and density) usually varies under different working conditions, the robust equilibrium optimization of structural dynamic characteristics considering different working conditions is investigated in this paper for the first time. Firstly, the robust optimization model for the dynamic characteristics of uncertain structures is constructed with the uncertainties described as interval variables. Subsequently, a novel robust equilibrium optimization algorithm is proposed to solve the constructed robust optimization model. Specifically, a new concept of overlap coefficient between interval boundary angles (OCBA) is proposed with the introduction of an overlap sensitivity factor, based on which the constraint robustness considering the requirements of different working conditions can be flexibly assessed. Then, the robust equilibrium strategy for all structural performance indices are proposed for the direct ranking of various design vectors, based on which the robust equilibrium optimization algorithm is developed. The validity and effectiveness of the proposed robust equilibrium optimization approach are demonstrated by realistic engineering examples including the cone ring fixture of a large turbo-generator and the compressor shell of a refrigerator.