Thickness-shear vibrations of rotated Y-cut quartz plates with imperfectly bonded surface mass layers

A solution is obtained from the three-dimensional equations of linear piezoelectricity for the pure thickness-shear vibration of rotated Y-cut quartz or lang-asite plates with imperfectly bonded surface mass layers. The solution includes a few results in the literature as special cases. It is shown that the mass layers lower the resonant frequencies when they are relatively perfectly bonded to the crystal surface, and that loosely bonded mass layers may raise the frequencies. The results are useful in the analysis of frequency stability of quartz resonators and acoustic wave sensors.