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The results of theoretical numerical-analytical investigation of some kinematic characteristics of the nonlinear second harmonics for monochromatic axisymmetric normal elastic torsional waves along the axial direction in transversely isotropic cylinder of circular cross section with a rigid fixed of lateral surface. Frequency-parametric analysis of amplitude and shape of wave motion into the second harmonic for normal waves of the investigated type was conducted for the cylinder made from a gadolinium using the proposed method. The regularities inherent in wave processes of this type are described.

In the present paper the problem of elastic waves propagation in piezoceramic cylindrical waveguides of noncircular cross section is studied for the cylinders of circular and hollow cross section with sector cut of arbitrary angular measure. Boundary surfaces of sector cut are covered by non-extensible membranes and cylindrical surfaces can have arbitrary boundary conditions. The equations of motion of the piezoelectric cylinder are analytically integrated and dispersion equations that exactly satisfy the boundary conditions are obtained. A selected set of numerical results including dispersion spectrums, distributions of cutoff frequencies and phase velocities for cylinders with various cross section geometry and boundary conditions is presented, and main effects of their transformation are discussed. Results are in good agreement with the results obtained by other researches for the special case of circular and hollow cylinders. The model can be used to control the dispersion spectrums and wave characteristics by changing the geometry and mechanical properties of the waveguides.

The work is devoted to theoretical research of normal elastic and electroelastic waves in anisotropic cylindrical waveguides class C6v hexagonal systems of not typical geometry cross-section from piezoactive and nonpiezoactive materials. Waveguides of the circular sections with sector cuts of any sizes and waveguides of the concentric ring sections with sector cuts are considered. Possibilities of using section geometry for changing structure and properties of spectrum of traveling and edge stationary normal waves are investigated. The approach is based on exact analytical integration of the wave dynamics equations for linear elastic and electroelastic medium of hexagonal system with the generalized wave potentials introduction and reducing the considered problem to a spectrum boundary problem in the section of a waveguide. The potentials expressed through special cylindrical functions of different types with fractional indexes are used for satisfaction the edge conditions on boundary parts of section.