Abstract: A concurrent topology optimization method for dynamic designs associating materials and structures with periodical microstructures of different sizes was presented and related numerical experiments were carried out. In the method, the optimization object was to maximize the structure fundamental frequency, rational approximation of material properties (RAMP) was adopted to ensure clear topologies in both macro and micro scales, and design variables for macro structure and microstructures were defined separately and integrated into one system by using the super-element technique. Based on the numerical experiments, the effects of representative volume element (RVE) sizes and materials ratios of both the macro-scale and the micro-scale on structural topology were investigated, and the results indicate that the proposed method is effective and can be used as an innovative dynamic design one for lightweight structures.