Defect modes in imperfect periodic structures

Lack of periodicity in engineering structures can arise because of imperfections in the production process or a particular purpose to produce desirable physical effects. This contribution presents a series of numerical simulations that quantitatively characterize the influence of defects on the dispersion relation and associated eigenmodes of imperfect periodic structures. Local defects are introduced periodically on a scale larger than the size of the unit cell of the non-disturbed periodic structure. The observations reveal that these defects can give rise to non-propagating modes at frequencies situated within the bandgaps of the periodic structure. The eigenfrequency of such a defect mode varies monotonically with the amplitude of the defects, and its deformations are located in and around the disturbed cell. Furthermore, a bounded periodic medium with defects is studied by finite element analysis to demonstrate the existence of these defect modes in bounded imperfect periodic structures.