Phononic crystals? band gap manipulation via displacement modes

Phononic crystal band gaps (BGs), which are realized by Bragg scattering, have a central frequency and width related to the unit cell's size and the impedance mismatch between material phases. BG tuning has generally been performed by either trial and error or by computational tools such as topology optimization. In either case, understanding how to systematically change the design for a particular band structure is missing. This paper addresses this by closely studying the displacement modes within the wavebands that are responsible for the BG. We look at the variation in different displacement modes due to the changes in the geometry and correlate these changes to their corresponding band structures. We then use this insight to design the unit cell for a particular application, for instance, for generating partial BGs.