Localization of flexural waves in a disordered periodic piezoelectric beam

Localization of bending waves in a disordered periodic piezoelectric beam is studied in this paper. The equation of the wave motion for a piezoelectric beam is derived on the assumption of an Euler–Bernoulli beam, and the harmonic solution is presented. The transfer matrix between two consecutive unit cells in the structures is obtained by using the continuity conditions. The expression of the localization factor is given by Wolf's algorithm. Numerical examples are presented and the effects of several disordered parameters on the localization factor are analyzed. The results show that piezoelectricity has obvious effects on the passbands and stopbands of the periodic piezoelectric beam. The behavior of wave propagation and localization in disordered periodic piezoelectric beams can be altered by tuning different structural parameters.