Investigation of wave propagation in piezoelectric helical waveguides with the spectral finite element method

The dispersion behaviors of wave propagation in waveguides of piezoelectric helical structures are investigated. By using the tensor analysis in the helical curve coordinate, the general strain − displacement relationship of piezoelectric helix is firstly considered. This paper's formulation is based on the spectral finite element which just requires the discretization of the cross-section with high-order spectral elements. The eigenvalue matrix of the dispersion relationship between wavenumbers and frequencies is obtained. Numerical examples on PZT5A and Ba2NaNb5O15 helical waveguides of a wide range of lay angles are presented. The effects of the piezoelectric on the dispersive properties and the variation tendency of dispersion curves on helix angles are shown. The mechanism of mode separation in piezoelectric helical waveguides is further analyzed through studying waves structures of the flexural modes.