Vibration of a thickness-twist mode piezoelectric resonator with asymmetric, nonuniform electrodes

We studied the effect of electrodes with varying thicknesses on thickness-twist modes in a piezoelectric plate resonator of crystals of 6 mm symmetry. The focus is on the effects of asymmetric electrodes, which do not seem to have been examined before. A theoretical analysis is performed using the theory of linear piezoelectricity. A trigonometric series solution is obtained that is relatively rare from the equations of piezoelectricity. Numerical calculations are made based on the series solution. Results show that asymmetric, nonuniform electrodes have a strong effect on vibration mode shapes. This effect offers the possibility of using nonuniform electrodes in design to achieve various goals. The quantitative results in this paper are useful for the purpose.