Wave propagation in axially polarized piezoelectric hollow cylinders of sector cross section

Abstract

In this paper, the problem of electroelastic waves propagating in piezoelectric hollow cylinders of sector cross section is studied for the case when the boundary surfaces of sector cut are covered by non-extensible membranes. The three-dimensional linear equations of motion for the piezoelectric cylinder are analytically integrated and different boundary conditions on the cylindrical surfaces yield frequency equations, which relate the frequencies of elastic waves to their wavenumbers. Numerical results for waveguides with various boundary conditions are presented to illustrate the approach. Analysis of the dispersion spectra is carried out, and cutoff frequencies are obtained and characterized; mode asymptotic behavior and amplitude distributions of wave characteristics are analyzed. The main effects of their transformation by variation of the angular measure and the ratio of inner and outer radii are discussed. The results obtained are in good agreement with the results for the special case of a hollow semicircular cylinder.