Finite element investigation of the effectiveness of the tubular piezoelectric vibratory gyroscope depending on the type of polarization and boundary conditions

In the present paper, a dynamic behavior of piezoelectric vibratory gyroscope in the form of a hollow piezoelectric cylinder with two pairs of electrodes placed crosswise on the outer side surface has been analyzed. In the case of one fixed end, two variants of the piezoceramic material polarization have been considered, namely, full radial polarization and partial radial polarization only under the electrodes on the outer side surface. For a completely polarized material (in addition to the case of a cantilevered end) two other variants of the fixations simulating the conditions of hinged opening were also considered. The behavior of the harmonic oscillation of gyroscope has been studied in the framework of linear theory of piezoelectricity (electroelasticity) which takes into account mechanical damping and rotational effects in the relative coordinate system. All of the investigated variants admit the availability of electrically active bending oscillation modes in two perpendicular planes which can be controlled by given electric potentials on the two pairs of electrodes. In such configurations when the gyroscope operates near to the corresponding resonance frequencies the primary flexural vibrations are generated in one plane and the secondary flexural motions are created due to the axial gyroscope rotation in the perpendicular plane. These secondary oscillations can be a measure to determine the value of the rotation frequency. The finite element method, ANSYS finite element package and specially designed computer programs written in the macro language APDL ANSYS were used for numerical calculations. The results of computational experiments have shown that the variant with one fixed end and with a full radial polarization of the piezoceramic material gives the largest maximum of the output potential in the presence of gyroscope rotation. It has been found that the variant of the gyroscope with the fixations simulating the conditions of hinged opening is also quite promising for application.