Asymptotic Analytical Solution on Lamb Waves in Functionally Graded Nano Copper Layered Wafer

In this study, the feasibility of using Lamb waves in functionally graded (FG) nano copper layered wafers nondestructive evaluation is evaluated. The elastic parameters and mass densities these vary with thickness due to variation grain size. power series technique used solve governing equations variable coefficients. To analyze multilayered structures, which material are continuous but underivable, a modified transfer matrix method proposed combined method. Results show that multiple modes exist FG wafers. Moreover, gradient property leads decrease phase velocity, absolute value velocity positively correlated coefficient. rate Mode 2 smaller than those other modes. findings indicate 4 recommended for evaluation. However, if number layers greater four, dispersion curves multilayer structures tend coincide equivalent uniform structures. results study provide theoretical guidance nanomaterial