Polygonal elements with high precision are used in finite element modeling along with a multiresolution scheme for topology optimization to achieve high resolution design with a coarse finite element mesh. A polygonal multiresolution scheme is proposed to perform a topology optimization of multi-material structures for dynamic stiffness. This combined modelling strategy of polygonal finite element with higher resolution density and design discretization is extended to optimal multi-material structural design problem, which is based on the concept that a polygonal element for dynamic analysis is split into fine design variable elements for optimization and overlapped density variable elements for representation of material distribution. To minimize the mean dynamic compliance subjected to the volume fraction constraints of each candidate material, a topology optimization model of multi-material structure is established. The HHT-α
method is adopted to solve the structural dynamic problem. Following the sensitivity analysis of objective function and constraints by the adjoint variable method, the ZPR design variable update scheme is employed to solve highly nonlinear and non-convex optimization problem with multiple regional volume constraints. Several benchmark numerical examples are presented to analyze the feasibility of the proposed algorithm, and the influence of the duration time of dynamic load on the optimized results is analyzed.