Thickness-shear vibration of AT-cut quartz plates carrying finite-size particles with rotational degree of freedom and rotatory inertia [Correspondence]

We study thickness-shear (TSh) vibration of a rotated Y-cut quartz crystal resonator (QCR) carrying finite-size circular particles that have a rotational degree of freedom and rotatory inertia. The particles are elastically attached to the QCR and are allowed to roll without sliding on the QCR surface. An analytical solution for particle-induced frequency shifts in the QCR is obtained. Examination of the frequency shifts shows that although they can be used to measure geometric/physical properties of the particles, the frequency shifts can have relatively complicated behaviors that cause deviations from the Sauerbrey equation and other anomalies in mass sensing. A frequency-dependent effective particle mass is introduced to classify and characterize different aspects of the particle-induced frequency shifts.