In this study, the influence on wave propagation of periodic structures having defects is investigated. Defects are used in periodic structures to study the unique characteristics of wave propagation in a periodic system. A structural rod model is developed to study the problems of one-dimensional periodic structures with defects. A finite element model and a transfer matrix method are developed to study these problems to predict the performance of the system; moreover, a shape memory alloy (SMA) is used to control the characteristics of the system. The behaviors of the periodic structure are evaluated at different length ratios and material properties of the defects. The effects of the SMA when applied at various temperatures are also discussed. The location and width of stop bands can be changed with different configurations of the additional defects.