Effect of an Array of Hemispherical Substance-Units Immersed in Liquid on the Thickness-Shear Vibrations of a Quartz Crystal Plate

The paper studied the effect of an array of hemispherical substance-units (HSUs) immersed in inviscid and incompressible liquid on resonance frequency of a quartz crystal resonator (QCR) under the thickness-shear mode (TSM) vibrations. A dynamic model of the compound QCR system, consisting of a QCR and HSUs, was established in advance. The frequency equation of the compound QCR system including the liquid-solid coupling was derived subsequently. Numerical results showed the frequency-shift characteristics of the compound system. The obtained results are useful in resonator design and applications.