Generation of time-independent torque by ultrasonic guided waves.

The excitation of acoustic waves by a unidirectional transducer, integrated in a piezoelectric cylindrical tube or disk, can lead to a time-independent torque. This phenomenon, demonstrated earlier in experiments and analyzed with coupling-of mode theory, is explained in detail, starting on the level of lattice dynamics of a piezoelectric crystal. Expressions are derived for the stationary torque in the form of integrals over the volume or surface of the piezoelectric, involving the electric potential and displacement field associated with the acoustic waves generated by the transducer.

Guided acoustic waves at the intersection of interfaces and surfaces.

In numerical calculations, guided acoustic waves, localized in two spatial dimensions, have been shown to exist and their properties have been investigated in three different geometries, (i) a half-space consisting of two elastic media with a planar interface inclined to the common surface, (ii) a wedge made of two elastic media with a planar interface, and (iii) the free edge of an elastic layer between two quarter-spaces or two wedge-shaped pieces of a material with elastic properties and density differing from those of the intermediate layer. For the special case of Poisson media forming systems (i) and (ii), the existence ranges of these 1D guided waves in parameter space have been determined and found to strongly depend on the inclination angle between surface and interface in case (i) and the wedge angle in case (ii). In a system of type (ii) made of two materials with strong acoustic mismatch and in systems of type (iii), leaky waves have been found with a high degree of spatial localization of the associated displacements, although the two materials constituting these structures are isotropic.

On the existence of guided acoustic waves at rectangular anisotropic edges.

The existence of acoustic waves with displacements localized at the tip of an isotropic elastic wedge was rigorously proven by Kamotskii, Zavorokhin and Nazarov. This proof, which is based on a variational approach, is extended to rectangular anisotropic wedges. For two high-symmetry configurations of rectangular edges in elastic media with tetragonal symmetry, a criterion is derived that allows identifying the boundary between the regions of existence for wedge modes of even and odd symmetry in regions of parameter space, where even- and odd-symmetry modes do not exist simultaneously.