The properties of thickness-twist (TT) wave modes in a rotated Y-cut quartz plate with a functionally graded material top layer

• TT-wave propagation relations in an FGM-crystal plate are obtained analytically.
• Existence condition of pure FS-wave mode is given in an FGM-crystal plate.
• Ratio of density to stiffness is the most important factor in determining cutoff frequency.
• A theoretical approach for measuring FGM properties is proposed.

We propose the use of thickness-twist (TT) wave modes of an AT-cut quartz crystal plate resonator for measurement of material parameters, such as stiffness, density and material gradient, of a functionally graded material (FGM) layer on its surface, whose material property varies exponentially in thickness direction. A theoretical analysis of dispersion relations for TT waves is presented using Mindlin’s plate theory, with displacement mode shapes plotted, and the existence of face-shear (FS) wave modes discussed. Through numerical examples, the effects of material parameters (stiffness, density and material gradient) on dispersion curves, cutoff frequencies and mode shapes are thoroughly examined, which can act as a theoretical reference for measurements of unknown properties of FGM layer.