Effects of electrode inertia and stiffness on vibration of piezoelectric plate with dissipation

We here mainly investigate the mechanical effect of metal electrodes, such as mass effect and shear stiffness effect, and effects of viscosity and conductivity on the resonance frequency, capacitance ratio, and quality factor. We can finally find how those work to the electrical parameters with dissipation. And we have calculated the frequency for different piezoelectric materials with gold or silver electrodes with consideration of dissipation of piezoelectric plate. It can be found that the gold electrode has more remarkable effect than the silver electrode on the frequency for same viscous dissipation because gold is heavier than silver.