Elastic Band Gaps in Two-dimensional Phononic Crystals Based on Multiple-scattering Theory

Two dimensional solid phononic crystals such as plates,shells can be widely applied to the control of vibration and noise as a kind of structural materials.It is very significant to study the band gaps in two dimensional phononic crystals to apply them in the vibration and noise control for structures and as a filter for acoustical signal.The multiple-scattering theory is integrated with wave equations to study the elastic wave band gaps in two-dimensional phononic crystals.The carbon/proxy system is used as numerical example.The results show that a full band gap is presented when carbon cylinder with high propagation velocity is arranged periodically in proxy with low propagation velocity.