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A phononic crystal (PnC) is an artificially engineered periodic structure that exhibits extraordinary phenomena, such as a phononic band gap. The phononic band gap refers to a certain range of frequencies within which mechanical waves cannot propagate through the PnC. The main purpose of this paper is to propose a topology optimization formulation for phononic band gap maximization that simultaneously takes into account a target driving frequency. In the proposed topology optimization formulation, a relative band gap is considered as an objective function to be maximized. In addition, an equality constraint is imposed on the central frequency of the band gap. The topology optimization problem is solved using the globally convergent method of moving asymptotes, which is a gradient-based optimization algorithm. Numerical examples are computed to demonstrate the effectiveness of the proposed topology optimization formulation.

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