Impedance theory of wave propagation on infinite periodic structures

For linear acoustic and mechanical periodic structures from cells made of lumped and continuous elements introduced is the concept of the group impedance as a universal quantity through which all the basic wave characteristics of the structure (dispersion, energy, orthogonality, forced vibration) are expressed. Presented are the necessary expressions. Based on the unique properties of the group impedance, a new homogenization method is proposed useful for analysis and design of mechanical and acoustic metamaterials with prescribed wave properties.