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

The paper is concerned with the interfacial acoustic waves localized at the internal boundary of two different perfectly bonded semi-infinite one-dimensional phononic crystals represented by periodically layered or functionally graded elastic structures. The unit cell is assumed symmetric relative to its midplane, whereas the constituent materials may be of arbitrary anisotropy. The issue of the maximum possible number of interfacial waves per full stop band of a phononic bicrystal is investigated. It is proved that, given a fixed tangential wavenumber, the lowest stop band admits at most one interfacial wave, while an upper stop band admits up to three interfacial waves. The results obtained for the case of generally anisotropic bicrystals are specialized for the case of a symmetric sagittal plane.

Non-leaky surface acoustic waves in the passbands of one-dimensional phononic crystals

The paper theoretically investigates the occurrence of non-leaky surface acoustic waves (SAWs) in the passbands of the Floquet-Bloch spectra of half-infinite one-dimensional phononic crystals. The phononic crystal is represented by a periodic structure of perfectly bonded anisotropic elastic layers. The traction-free boundary plane truncates the phononic crystal at the edge of a period. For the general case of unrestricted anisotropy of the constitutive layers, it is shown that if the passband allows only two partial bulk modes, then the non-leaky SAW must simultaneously satisfy three real equations imposed on problem parameters such as the SAW frequency and tangential wavenumber, the angle of its propagation direction along the given boundary plane, and the characteristics of the medium. If there are four bulk modes in the passband, then the non-leaky SAW must satisfy at least five real equations. In the case where the layers possess a common plane of crystallographic symmetry which is either parallel to the layer interfaces or perpendicular to the direction of propagation, the number of real equations conditioning the occurrence of non-leaky SAWs in the passbands with two and with four bulk modes reduces to two and three, respectively. If the sagittal plane is a plane of symmetry, then the sagittally polarized non-leaky passband SAW must satisfy three real equations; however, if this sagittal symmetry plane coexists with another plane of symmetry which is either parallel to the layer interfaces or perpendicular to the direction of propagation, then the existence of non-leaky passband SAW requires the fulfillment of two conditions only. In particular, this is always the case when the constitutive layers are elastically isotropic. The general conclusions are illustrated by numerical examples.

Shear surface waves in phononic crystals

The existence of shear horizontal (SH) surface waves in two-dimensional periodic phononic crystals with an asymmetric depth-dependent profile is theoretically reported. Examples of dispersion spectra with bandgaps for subsonic and supersonic SH surface waves are demonstrated. The link between the effective (quasistatic) speeds of the SH bulk and surface waves is established. Calculation and analysis is based on the integral form of a projector on the subspace of evanescent modes which means no need for their explicit finding. This method can be extended to the vector waves and the three-dimensional case.