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

Abstract 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.