Admittance of axially polarized lossy piezoceramic cylinders loaded with a viscoelastic liquid

Abstract

Analytical formulas for the electrical admittance of a viscoelastically loaded cylindrical piezoceramic resonator vibrating in a shear mode are established. In the analysis, mechanical losses in a piezoelectric ceramic and in a liquid were taken into account. The admittance was calculated based on the solutions of the equations of motion of the piezoelectric ceramics and viscoelastic liquid. These solutions fulfilled the appropriate boundary conditions on the cylindrical surfaces of the resonator. In this way, analytical formulas for admittance dependent on the material parameters of ceramics and viscoelastic liquid were established. Analyzing the obtained admittance diagrams, the changes in resonant frequencies Δfs and Δfm as a function of the liquid viscosity η were evaluated. From the numerical calculations of the authors it follows that the Kanazawa–Gordon formula, which is derived for planar resonators and relates the shift in resonant frequency to the viscosity of the Newtonian liquid, can also be valid for cylindrical resonators. The work shows that piezoelectric cylindrical resonator with a moderately low mechanical quality factor and high electromechanical coupling coefficient can be useful for measuring liquids of large viscosity. The results of this work can constitute the basis for the design and construction of viscosity sensors.