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In the optimal design of a composite structure under dynamic loading through a topology optimization procedure, considering cellular or multi-material for the design domain may affect the mechanical behaviors of the structures. For instance, cellular material inclusion may enlarge some structures flexibility and energy absorption capability. Different types of dynamic loading, i.e., modal, harmonic, and, transient loadings, are considered. For each type of loading, the relevant physical response function derived previously for single material in the proposed topology optimization method is rewritten in a new statement comprising cellular or multi-material properties. The proposed topology optimization method is devolved based on the single material to be employed for multi-material topology optimization using the newly residue physical response function scheme. Numerical examples are presented to validate the …