Existence of surface acoustic waves in one-dimensional piezoelectric phononic crystals of general anisotropy

Abstract

The paper is concerned with the surface acoustic waves propagating in half-infinite one-dimensional piezoelectric phononic crystals of general anisotropy. The phononic crystal is formed of periodically repeated perfectly bonded layers, and its exterior boundary is one of the layer boundaries. The surface waves occurring in the so-called full stop bands are considered. It appears that the number of surface waves existing within a full stop band for a given layered structure is interrelated with their number in the same stop band for the phononic crystal different from the given one only due to the reversed ordering of layers within a period. A series of statements is proved on the maximum possible number of surface waves per full stop band for both these structures in total, i.e., embracing surface-wave occurrences in either one or the other structure. The analysis is performed for the electrically closed, electrically open, and electrically free types of boundary conditions on the mechanically free crystal surface, in which cases it admits a correspondingly different number of surface waves. A subsidiary instance of mechanically clamped surface is addressed as well. It is observed that the piezoelectric coupling can create new surface waves which disappear when piezoelectric coefficients turn to zero. Besides the general case of arbitrary anisotropy, we also consider two specific situations where the crystallographic symmetry allows the existence of sagittally polarized piezoactive surface waves and of shear horizontally polarized piezoactive surface waves. Numerical examples of surface-wave branches under various boundary conditions are provided.

Interfacial acoustic waves in one-dimensional anisotropic phononic bicrystals with a symmetric unit cell

“…The combination of anisotropy and (periodic) spatial inhomogeneity essentially prevents explicit solutions to the boundary problem (which is already complicated enough in the case of homogeneous crystals) being reached, so SAW properties used to be investigated mainly by numerical means. However, it appears that the analytical approach underlying the Lothe-Barnett-Chadwick theory of SAWs in crystals can be developed and applied to the problem of the existence and number of SAWs in the spectra of 1D elastic and piezoelectric phononic crystals [24][25][26].…”

Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

“…The problem of SAW existence in halfinfinite 1D phononic crystals of general anisotropy composed of purely elastic and piezoelectric layers was considered in Refs. [46,47], respectively. It is clear that explicit solutions for the wave characteristics in terms of the material parameters are certainly out of reach; however, developing the methods of anisotropic piezoacoustics of homogeneous media established in Refs.…”

“…On the methodological side, we note that the theory of [48,49] exploits the properties of the eigenvectors of the so-called Stroh matrix, whereas Refs. [46,47] use the properties of the eigenvectors of the transfer matrix derived from the Stroh matrices of the constituent layers.…”

“…Thus this case has to be considered independently, i.e., the sought predictions on SAW existence cannot be extracted as a corollary the derivations of Ref. [47] developed for the case of an asymmetric unit cell. Note that a number of SAWs per a stop band established in the asymmetric case embraces their occurrence in the given structure and in its "reversed" modification [47].…”

“…[47] developed for the case of an asymmetric unit cell. Note that a number of SAWs per a stop band established in the asymmetric case embraces their occurrence in the given structure and in its "reversed" modification [47]. Both arrangements are identical to each other in the symmetric case, hence the maximum possible number of SAWs must cannot be greater than a half of the above aggregate number in the asymmetric case.…”