Wave localization in randomly disordered periodic piezoelectric rods

Abstract

The wave propagation in periodic and disordered periodic piezoelectric rods is studied in this paper. The transfer matrix between two consecutive unit cells is obtained according to the continuity conditions. The electromechanical coupling of piezoelectric materials is considered. According to the theory of matrix eigenvalues, the frequency bands in periodic structures are studied. Moreover, by introducing disorder in both the dimensionless length and elastic constants of the piezoelectric ceramics, the wave localization in disordered periodic structures is also studied by using the matrix eigenvalue method and Lyapunov exponent method. It is found that tuned periodic structures have the frequency passbands and stopbands and localization phenomenon can occur in mistuned periodic structures. Furthermore, owing to the effect of piezoelectricity, the frequency regions for waves that cannot propagate through the structures are slightly increased with the increase of the piezoelectric constant.

Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

“…The proposed MTMM combines the Love rod theory [27,28], [29] (pp. 139-142), [30], the method of reverberation-ray matrix (MRRM) [5] and the transfer matrix method (TMM) [14][15][16][17][18][19]21,22,25] to analyze the dispersion curves by considering the Floquet-Bloch theorem [31,32] and to calculate the transmission spectra. The Love rod theory is adopted to model the longitudinal wave motions in the piezoelectric, elastic and electrode constituent rods of the unit cell.…”

“…Therefore, rod-type phononic crystals containing smart material components have been presented in order to control the longitudinal waves in an active mode. Their frequency bands can be adjusted by tuning the temperature [6,7], magnetic [8] or electric [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] field to suit the external excitations.…”

“…Among these smart periodic rods, the periodic piezoelectric rods [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] have particularly been paid more attention, because the piezoelectric materials are widely used and the electric field is comparatively easier to control. Thus far, two kinds of rod-type piezoelectric phononic crystals have been presented to actively control longitudinal-wave bands via electromechanical coupling.…”

“…Asiri et al [15] and Asiri [16,17] predicted the attenuation of longitudinal waves in periodic binary piezoelectric-elastic composite rods using the combination of spectral element method and TMM, and validated their analysis by experiment. Using the same TMM, Li et al [18] and Wang et al [19] analyzed the localization of frequency bands in randomly disordered periodic binary piezoelectric-elastic rods without and with initial stress, respectively. Recently, Degraeve et al [20] proposed to use periodic electrical boundary conditions realized by periodically embedded electrodes to tune Bragg bands in uniform homogeneous piezoelectric rods.…”

“…The influence of the elastic rod inserts on the band structures is not clear enough. (3) Two electrical control manners in general have been proposed, i.e., setting the external voltage through the feedback control gain [14][15][16][17] and tuning the external electric capacity [18][19][20][21][22][23][24][25][26], since the electric-open and electric-short conditions correspond to zero and infinity electric capacities, respectively. The connection and difference of the influences of the applied feedback control and of the applied electric capacity on the frequency bands are not known.…”