Accurate Modelling of Wave Propagation in Functionally Graded Solids Using Wave Packet Enriched Finite Elements

A wave packet enriched finite element (FE) formulation is presented for solving two-dimensional wave propagation problems in functionally graded media. The standard Lagrangian interpolation functions of the displacement field variables are extrinsically enriched with element-domain sinusoidal wave packet functions and the derived FE equations are solved using the Newmark- \(\beta \) direct time integration. The effective properties of the functionally graded material (FGM) are computed using the volume-fraction-based Voigt’s rule of mixture (ROM) model. A variety of wave propagation problems including high-frequency Lamb wave propagation in FGM plates and impact waves in axially functionally graded bars are solved using the present formulation and the results are validated with available solutions. The efficacy of the present solution in comparison with the conventional FE is evaluated for all the studied problems. The effect of the inhomogeneity parameter on the transient wave behaviour is also presented for all the problems.