A new theory for electroded piezoelectric plates and its finite element application for the forced vibrations analysis of quartz crystal resonators

For crystal resonators, it is always desirable to calculate the electric properties accurately for application purposes. As an extension of the Mindlin plate theory based finite element analysis of crystal resonators, a new theory for the electroded plates is derived and the piezoelectrically forced vibrations are formulated and implemented in this paper in a manner similar to our previous work. The effect of the electrodes and the electric boundary conditions are taken into considerations through the modification of the higher-order plate equations by changing the expansion function of the electric potential for this particular problem. Through the conventional discretization of the new plate theory, the linear equations for the piezoelectric plate under thickness excitation are constructed and solved with efficient numerical computation techniques such as the sparse matrix handling. Numerical examples showing good predictions of the resonance frequency and capacitance ratio of electroded crystal plates of AT-cut quartz are presented with experimental data.