Modeling guided wave propagation in functionally graded plates by state-vector formalism and the Legendre polynomial method

A numerical method is presented for the investigation of the propagation characteristic of guided waves in functionally gradient material (FGM) plates. Based on the State-vector formalism and Legendre polynomial method, the typical non-stratified computing of dispersion curves of FGMs is realized, by introducing the univariate nonlinear regression to optimize the arbitrary gradient distribution of material component. Comparing with the conventional Matrix method, the proposed method avoids the exhausting root-locating algorithm of solving the transcendental equation by a single-variable scanning process. This method turns it into an algebraic eigenvalue problem, which mainly depends on the orthogonal completeness and strong recursive property of Legendre polynomial series. It provides a fast and flexible approach to extracting the dispersion curves, displacement distribution and stress profile, simultaneously. Results from chrome-ceramic FGM plate are compared with those from the previous articles to confirm the feasibility and accuracy of the proposed method. Then, this approach is further applied to iron based alumina FGM. The dispersion curves with different gradient function are calculated to illustrate the influence of the gradient variation. Moreover, the influence of the cut-off order of Legendre orthogonal polynomials on the convergence of dispersion curves is also revealed through numerical examples. Utilizing the mapping relationship between the gradient distribution and the propagation characteristics, it gives theoretical support for nondestructive evaluation and quantitative estimation of the structural characteristics of FGM plates.