Periodic binary elastic/acoustic composites can give rise to genuine band gaps in the band structure. The term genuine refers to the complete gaps, which persist independently of the polarization of the wave and of its direction of propagation. Within these complete gaps sound and vibrations are forbidden, the "acoustic crystals" stand still, and the total silence reigns. Thus a vibrator (or defect) introduced into a periodic elastic composite would be unable to generate sound or vibrations within the gap. The existence of complete gaps in the band structure is closely associated with the (classical) Anderson localization of sound and vibrations. The search for phononic band-gap materials is of comparable interest to the pursuit of photonic band-gap materials. Thus the phononic crystals are to acoustics as photonic crystals are to optics. In comparison to the photonic crystals, there are additional parameters (the mass densities and two velocities - longitudinal and transverse) involved in the phononic crystals, which make the physics richer and leaves us with more options in the quest of creating full stop bands in the system. As regards the applications, the phononic crystals are envisioned to find ways in the acoustic waveguides, improvements in designing the transducers, elastic/acoustic filters, noise control, ultrasonics, and medical imaging, to name a few. Since the interesting phenomena emerging from the phononic crystals are all consequences of the existence of the gap(s), a major part of the research efforts has focused on the search for phononic band-gap crystals. As such, we report and emphasize on the spectral gaps in the band structure for cleverly synthesized N-dimensional (N = 1, 2, 3) phononic crystals. PACS numbers:
Shape optimization of phononic band gap structures using the homogenization approach
