Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

Abstract

Phononic crystals can be used to control elastic waves due to their frequency bands. This paper analyzes the passive and active control as well as the dispersion properties of longitudinal waves in rod-type piezoelectric phononic crystals over large frequency ranges. Based on the Love rod theory for modeling the longitudinal wave motions in the constituent rods and the method of reverberation-ray matrix (MRRM) for deriving the member transfer matrices of the constituent rods, a modified transfer matrix method (MTMM) is proposed for the analysis of dispersion curves by combining with the Floquet-Bloch principle and for the calculation of transmission spectra. Numerical examples are provided to validate the proposed MTMM for analyzing the band structures in both low and high frequency ranges. The passive control of longitudinal-wave band structures is studied by discussing the influences of the electrode's thickness, the Poisson's effect and the elastic rod inserts in the unit cell. The influences of electrical boundaries (including electric-open, applied electric capacity, electric-short and applied feedback control conditions) on the band structures are investigated to illustrate the active control scheme. From the calculated comprehensive frequency spectra over a large frequency range, the dispersion properties of the characteristic longitudinal waves in rod-type piezoelectric phononic crystals are summarized.

Band Structures Analysis of Elastic Waves Propagating along Thickness Direction in Periodically Laminated Piezoelectric Composites

“…Ref. [58] for periodic piezoelectric rods with various electrical boundaries. For example: the bandgaps are bounded by frequencies corresponding to 0 and  phases; The passbands and stopbands appear alternately; The frequency-wavelength curves approach to infinite wavelength at bounding frequencies, so do the frequency-phase velocity curves except the two spectra starting from 0 frequency.…”

“…[57] for periodic elastic rods and in Ref. [58] for periodic piezoelectric rods with various electrical boundaries. The eigenvalue amplitude |µ| spectra also appear in reciprocal pairs, which is a supplement feature.…”

Band Tunability of Coupled Elastic Waves along Thickness in Laminated Anisotropic Piezoelectric Phononic Crystals

“…By contrast, "LiNbO Table 1. Note that the parameters for "LiNbO 3 A " are exactly excerpted from Auld [82], while those for "LiNbO 3 B " and "LiNbO The material parameters of Glass and Brass have also been provided in our previous studies [55,85]. For the convenience of drawing the dispersion curves, the dimensionless frequency ωH/(πv), the dimensionless wavenumber qH/π, the dimensionless wavelength λ/H, and the dimensionless phase…”

Complete Band Gaps in Nano-Piezoelectric Phononic Crystals

“…In some cases, rectangular lattice can produce broader gaps. In this context, we extend the studies about piezoelectric PCs [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] considering the influence of different inclusion geometries -circular, hollow circular, square and rotated square with 45º angle of rotation with respect to the x and y axes, and different lattices -square, rectangular, triangular, honeycomb and Kagomé on the band structure. Furthermore, researches have used PCs on the scale µm 10,17,64,65 and mm, resulting in band gaps ranging from GHz and kHz to MHz, respectively.…”

“…PCs have many applications, such as vibration isolation technology [18][19][20][21][22] , acoustic barriers/filters [23][24][25] , noise suppression devices [26][27] , surface acoustic devices 28 , architectural design 29 , sound shields 30 , acoustic diodes 31 , elastic metamaterials [21][22]25,27,32 and thermal metamaterials [33][34][35][36][37][38][39] . There are also smart PCs that have been studied, such as piezoelectric [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] , piezomagnetic [55][56][57][58] and magnetoelectroelastic 14,[59][60][61]…”