Band gaps and the electromechanical coupling coefficient of a surface acoustic wave in a two-dimensional piezoelectric phononic crystal

Abstract

In this paper we analyze the phononic band structure of bulk and surface waves in a two-dimensional periodic structure consisting of an array of piezoelectric cylinders in an isotropic background material. The explicit formulations of the bulk wave and the surface wave dispersion relations in such a structure are derived based on the plane wave expansion method. The band gaps and the electromechanical coupling coefficients for surface acoustic waves propagating in such a structure are calculated. The influences of material and geometrical anisotropy as well as the filling fraction on the electromechanical coupling coefficients are discussed, and some silent features are drawn. The results of this research may serve as an important reference for studying surface acoustic wave devices consisting of phononic structures.

Three-dimensional phononic band gap calculations using the FDTD method and a PC cluster system

“…In addition to the band gap analyses of bulk modes in 2D phononic structures, there is some literature on the investigation of band gaps of surface acoustic waves (SAW) [9]- [11]. More detailed studies of temperature effects of surface wave band gaps and electromechanical coupling coefficient in a piezoelectric phononic crystal are also reported [12], [13]. Instead of the PWE method, the multiple scattering theory (MST) has been applied to study the band gaps of bulk wave properties in three-dimensional (3D) periodic acoustic composites and the band structure of a phononic crystal consisting of complex and frequency-dependent Lamé coefficients [14]- [17].…”

Complete Band Gaps in Nano-Piezoelectric Phononic Crystals

“…where P is one of the c 11 ,c 12 ,c 66 ,c 44 ,e 15 ,ϵ 11 , ρ and g has the same expressions of g with m, n ∈ ℤ. We use g instead of g to highlight the difference between the Fourier series expansion of material properties and displacements.…”

“…Furthermore, we may expand c 11 ,c 12 ,c 66 ,c 44 ,e 15 ,ϵ 11 , ρ in Fourier series on the reciprocal space as: e z e z = -+ - …”

“…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]…”