Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)This paper presents a concurrent topology optimization methodology for minimizing the frequency responses of multiscale systems composed of macro and micro phases. Although there is existing research on the topology optimization of structures and optimization of the materials for frequency responses, topology optimization approaches considering both scales simultaneously are relatively limited. The methodology proposed here aims to apply the bi-directional evolutionary structural optimization (BESO) method to find the optimum layout on both macro and micro scales of the structure, with the objective of minimizing the frequency response in the macro structure. For this coupled system, it is assumed that the macro structure is composed of a periodic material whose effective properties are obtained using the homogenization theory. The designs of the macro and micro structures are conducted simultaneously. The homogenized elasticity matrix used in the finite element analysis of the macro structure is obtained from considering the layout of the micro structure. A series of numerical examples are presented to validate the optimization procedure and to demonstrate the effectiveness and the efficiency of the proposed method. (C) 2015 Elsevier B.V. All rights reserved.301 116136FAPESP (Sao Paulo Research Foundation) [2011/09730-6, 2013/08293-7, 2013/20022-9]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)