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

Abstract

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