ABSTRACT
CH A P T E R 16 Wave Propagation in Periodic Waveguides
Periodic structures can be defined as heterogeneous domains with a characteristic recursive pattern obtained through the translation in space of a repetitive element called the elementary unit cell or repetitive volume element (RVE). These structures are constructed fundamentally from a number of identical structural components normally referred to as periodic elements, which are joined together in all possible directions to form the whole structure. The atomic lattices of pure crystals are an example of a periodic structure, and constitute perfect periodic structures. However, their mathematical description is based on discrete stiffnesses and masses interconnected by forces derived from inter-atomic potentials. Using continuum assumptions, which we normally use to derive waveguide theories, the mass and elasticity of structural members are continuous, and constitute periodic structures when arranged in regular arrays. A typical periodic structure is shown in Figure 16.1(a). Unit cells feature different levels of structural complexity, according to the shape and composition of the medium. The more complex the pattern of the medium, the higher the complexity and/or the size of the representative unit cell. Several considerations about the behavior of a periodic assembly can be made through a simple unit cell analysis, and are therefore independent of the size of the domain or the number of unit cells it contains.
