Finite element computation of dispersion in piezoelectric waveguides

Abstract

Wave propagation characteristics can be computed analytically for simple geometries such as plates and cylinders but geometries that are more complex and waveguides comprising combinations of different materials require numerical analysis. Piezoelectric waveguide finite elements, which can model wave propagation in piezoelectric waveguides of arbitrary cross-section, were formulated and implemented. In these elements wave functions are used to describe the displacement variation along the waveguide with conventional finite element interpolation functions over the crosssection of the waveguide. The resulting two-dimensional element is very efficient for computing wave propagation in waveguides. The accuracy of the elements was verified by comparison with a three-dimensional finite element model with appropriate boundary conditions to represent a waveguide. An analytical expression was derived to compute the group velocities of waves in piezoelectric waveguides. Wavenumber and group velocity versus frequency curves were plotted for a piezoelectric waveguide with square cross-section. The elements were used to model 1-3 piezoelectric composite material. A unit cell, comprising one-quarter of the cross-section of the piezoelectric pillar and half the neighboring (non-piezoelectric) polymer was modeled with appropriate boundary conditions to represent the periodicity of the material. The results were verified with three-dimensional finite element modeling and the waveguide element model was found to be very accurate and efficient.