The analog of the Kanazawa-Gordon formula for cylindrical resonators

In this paper, a formula relating the shift in the resonant frequency of a shear piezoceramic cylindrical resonator to the viscosity of a Newtonian liquid that loads the resonator surface was established. This formula is analogous to the classical Kanazawa-Gordon formula that describes the change in the resonant frequency of a shear planar resonator loaded with a Newtonian liquid. To this end, the author applied the perturbation method to analyze the behavior of the piezoceramic cylindrical resonators vibrating in a shear mode and loaded with a viscous liquid. The shift in resonant frequency obtained using the perturbation method (mechanical model) was compared to an exact value of the shift in resonant frequency obtained from the complete electromechanical model (admittance diagrams) that describes shear vibrations of a piezoceramic cylindrical resonator loaded with a viscous liquid. Good conformity between the two types of results obtained can prove the correctness of the analytical formulas established in this paper. The results of this work can be applied for the design and construction of viscosity sensors.