Numerical simulation of Lamb waves propagation in a functionally graded piezoelectric plate composed of GaAs-AlAs materials using Legendre polynomial approach

In this paper, the propagation of Lamb waves in the functionally graded piezoelectric plates discretized into sub-layers is studied. In this presentation, a Legendre polynomial method is proposed to solve the wave equation. This method has three specificities in comparison to traditional methods. It directly incorporates the boundary conditions into the constitutive equations and it allows a resolution by a non-iterative system to the eigenvalues ​​and eigenvectors. Furthermore, this method takes full account of converged results nature. The convergence of this method is discussed a thorough manner. Here, the converged results are obtained with very low truncation number M. In addition, the effect of the gradient coefficients on the Lamb phase velocities is illustrated. Consequently, the different results also reveal differences between the properties of Lamb waves propagation in the functionally graded piezoelectric plates and the corresponding properties in homogeneous plates. Furthermore, the effect of constituent volume fraction is also considered through gradient models. All the developments performed in this work were implemented in Matlab software.