Free-ultrasonic waves in multilayered piezoelectric plates: An improvement of the Legendre polynomial approach for multilayered structures with very dissimilar materials

In 1999, Legendre polynomial approach has been proposed to solve wave propagation in the multilayered piezoelectric plate. However, it can deal with the multilayered plate only when the material properties of two adjacent layers do not change significantly. In this paper, an improvement of the Legendre polynomial approach is promoted to solve wave propagation in multilayered piezoelectric plates whatever the dissimilarities of the layer material properties. Detailed formulations are given to highlight the differences from the conventional Legendre polynomial approach. The validity of the proposed improved approach is illustrated through a numerical comparison between the improved method’s results and the exact solution obtained from the reverberation-ray matrix method. It is shown that the conventional orthogonal polynomial approach cannot conceptually calculate accurately, neither the discontinuous distribution of the normal electric field nor the continuous distributions of the normal stress and normal electric displacement, even in multilayered plates with similar layer material properties while the proposed improved polynomial approach overcomes these major drawbacks. Finally, the influences of the stacking sequences and volume fractions on dispersion curves are illustrated. It is also found that the stress and electric displacement of high frequency waves always distribute on the layer with lower wave speed.