Nowadays, the acoustic waves propagating in isotropic cylindrical waveguides and in waveguides made of piezoelectric ceramics are well studied. It has previously been shown that some compression modes in piezoceramic cylinders have a high electromechanical coupling coefficient, which makes them attractive for creating various acoustoelectronic devices. However the piezoceramics for production of these wave guides must have longitudinal electric polarization that complicates production of long enough wave guides. Fabrication of cylindrical waveguides from piezoelectric crystals, such as lithium niobate, is more technologically. However, there are no directions with axial symmetry in this crystal, so the calculations became more complicated. In this paper we perform the theoretical study of acoustic waves propagating in a cylinder of lithium niobate whose crystallographic Z axis coincides with the axis of the cylinder. To solve this problem, we use the finite element method, which allowed us to determine the natural frequencies of the cylinder. Phase velocities of waves of different orders in the waveguide under study are calculated. Comparison with the results obtained by a semi-analytical method in which material of niobate of lithium assumed the transversely isotropic is carried out. The error to which leads absence of the accounting of anisotropy of material of a wave guide is estimated. The existence of piezoactive acoustic waves with mainly tangential polarization that would be impossible without anisotropy is predicted.
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