The power series technique and detection of zero-group velocity Lamb waves in a functionally graded material plate

Abstract

This paper presents a technique for measuring the variation of the material properties along the thickness in a functionally graded material (FGM) plate. To investigate the propagation behavior of Lamb waves in a thermal stress relaxation type 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 method exploits the resonance at the minimum frequency of the S1 - zero group velocity (ZGV) mode. At this minimum frequency (f0), the group velocity vanishes, whereas the phase velocity remains finite. The numerical results also reveal differences between the ZGV frequency in the FGM plate and the corresponding frequency in a homogenous plate. In terms of results, we find that the in-plane and out-plane displacements are different between Al-rich and Si-rich surfaces. The plots of the involved stresses within the plate are added to check the performed calculations. Besides, the study covers the sensitivity of S1-ZGV resonance frequency to the FGM character and any slight variation of the plate thickness. 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.