Characterization of functionally graded elastic materials using a thickness-shear mode quartz resonator

We propose the use of a quartz crystal plate thickness-shear (TSh) mode resonator to measure material property variations in a functionally graded material (FGM). A theoretical analysis is performed on TSh vibrations of an AT-cut quartz plate carrying a layer of an FGM whose density and stiffness vary along its thickness. The effect of the material property gradient on the resonant frequencies of the two-layer plate as a compound resonator is examined. It is shown that this effect may be used to measure the material property gradient of the FGM.