Waves in periodic structures with imperfections

Abstract

Abstract The study of wave propagation in structures and discrete or continuous media has a significant history which follows from the examination of the dynamics of atomic and molecular lattices. Relatively recently, some of these ideas have been transferred and applied to the dynamic behavior of engineered structures. In particular, structures with periodic and almost periodic topologies and material properties have been extensively studied and important conclusions drawn regarding their energy-transmission properties. The attraction to wave propagation models is due to the efficient nature of the analytical tools available to study how energies of different frequency content are propagated or filtered by the structure. Such properties of a structure are profoundly affected by any imperfections or ‘near-periodicities’. It has been found that imperfections will have the effect of localizing energies about them, thus not allowing the development of normal modes of vibration as would be observed when assuming a perfect structure. It is envisioned that such understanding will permit the analyst to take advantage of localization effects to isolate locations experiencing loading. Additional applications possibly include the modeling of composite and layered structures and cracks. Also, one expects that structures with periodic boundary conditions will experience some sort of localization of energies in certain frequency ranges. Of particular interest there is the possibility that these ideas may apply to the concept of functionally graded materials and composites.