Calculation of propagation properties of Lamb waves in a functionally graded material (FGM) plate by power series technique

To investigate the propagation behavior of Lamb waves in a thermal stress relaxation type functionally graded material (FGM) plate with material parameters that vary continuously along the thickness, the power series technique, which has been proved to have good convergence and high precision, is employed for theoretical derivations. The influence of the gradient coefficients of FGM on the dispersion curves is illustrated. The numerical results also reveal differences between the properties of Lamb wave propagation in the FGM plate and the corresponding properties in a homogenous plate. In terms of results, we find that both the normal and anomalous dispersions exist in the first and the second modes of the Lamb wave that propagates in the FGM plate, while only the anomalous dispersion is in the first mode and only the normal dispersion is in the second mode for the homogenous plate. The wave structure is asymmetric due to the asymmetric properties of the material. The dominance of in-plane and out-plane displacements is different between the metal-rich and ceramic-rich surfaces. All these results give theoretical guidance not only for experimental measurement of material properties but also for nondestructive evaluation using an ultrasonic wave generation device.