Common vehicles, such as automobiles, airplanes, ships and other equipment, are needed to bear complicated vibration excitation in practice. These motivations are often random and irregular, and will bring specific components of these devices a lot of vibration problems. In this paper, Bi-directional Evolutionary Structural Optimization(BESO) under the constraint of random dynamic response is investigated. First of all, the stochastic vibration of the structure is briefly described, and the mean square dynamic response formula of the structure is obtained. Secondly, the optimal mathematical model under the constraint of random dynamic response is established, the sensitivity formula of the mean square dynamic response is deduced, and the BESO method iteration process is given. Finally, compared with the initial design, the optimized topology is proved to be effective and correct. A numerical example of the two-dimensional beam structure under harmonic loads is given. The results show that the proposed method can solve the structural topology optimization problem under the constraint of random dynamic response and broaden the application range of BESO method.
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