The anti-plane vibration of quartz plate with an additional partial non-uniform mass layer

The anti-plane vibration of a quartz plate having an additional partial non-uniform mass layer on its upper surface is solved by ignoring the effect of small c₅₆ in comparison with other elastic constants. Based on the Fourier sine and cosine series solution, the convergence and verification are examined. The frequency spectrum, as well as the energy trapping, are discussed. Compared with the homogeneous mass layer, the non-homogeneous layer with greater inertia leads to more modes trapped under the same condition. All the results obtained give theoretical guidance for physical phenomena explanations of layer properties in quartz crystal microbalance.