Formulations for the optimal design of plane grids with maximum band gaps are presented. Periodic band-gap structures prevent waves in certain frequency ranges from propagating. Materials or structures with band gaps have many applications, including frequency filters, vibration protection devices and wave guides. Here, a simple model of a periodic plane grid structure is presented and then an optimization problem is formulated where the structure’s band gap above a particular frequency is maximized by the selective addition of non-structural masses. Numerical implementation issues are discussed and examples are presented.

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