Layered cylindrical viscosity sensors

The electro-elastic behavior of a viscoelastically loaded layered cylindrical resonator comprising of two coupled hollow cylinders is presented. The inner cylinder is piezoelectric. The outer cylinder is a non-piezoelectric (passive) metallic cylinder. Analytical formulas for the elements of the impedance matrix Z of a cylindrical piezoelectric resonator vibrating in a shear mode are established. Moreover, analytical formulas for the electrical admittance of a compound layered cylindrical resonator loaded with a viscoelastic liquid are established. Admittance diagrams obtained using: (1) a continuum electromechanical model; and (2) the elements of the impedance matrix Z are exactly the same. The analysis presented in this paper can be utilized for the design and construction of cylindrical piezoelectric viscosity sensors, annular accelerometers, filters, transducers and multi-layer resonators.