Computation of dispersion relations of functionally graded rectangular bars

The propagation characteristics of elastic wave in the functional graded rectangular bars are studied by the two dimensional Rayleigh-Ritz method. Legendre orthogonal polynomials are used as trial functions. The material properties are assumed to be graded along the width direction. This dispersion equation is obtained from the 3D variational formulation governing elastodynamics. The convergence and accuracy are demonstrated by comparisons with the available solution of the scaled boundary finite element method. Finally, we give some phase and group curves of various rectangle waveguides and analyze influences of the width to length ratio and volume fraction indexes on dispersive behavior for wave propagation.