Maximizing phononic band gaps in piezocomposite materials by means of topology optimization.

Phononic crystals (PCs) can exhibit phononic band gaps within which sound and vibrations at certain frequencies do not propagate. In fact, PCs with large band gaps are of great interest for many applications, such as transducers, elastic/acoustic filters, noise control, and vibration shields. Previous work in the field concentrated on PCs made of elastic isotropic materials; however, band gaps can be enlarged by using non-isotropic materials, such as piezoelectric materials. Because the main property of PCs is the presence of band gaps, one possible way to design microstructures that have a desired band gap is through topology optimization. Thus in this work, the main objective is to maximize the width of absolute elastic wave band gaps in piezocomposite materials designed by means of topology optimization. For band gap calculation, the finite element analysis is implemented with Bloch-Floquet theory to solve the dynamic behavior of two-dimensional piezocomposite unit cells. Higher order frequency branches are investigated. The results demonstrate that tunable phononic band gaps in piezocomposite materials can be designed by means of the present methodology.