Thickness-extension vibration of magnetoelectric plate with electrodes

Based on the linearly magneto-electro-elastic theory, the equations of coupling vibration are obtained for the plate with two electrodes of unequal thickness. An exact solution is obtained for thickness-extension vibrations. The solution can be reduced to a few known results as special cases. Some numerical results are figured and presented by means of Matlab. Results show the effect of magnetoelectric on the thickness-extension vibrations frequency. The effects of unequal electrodes are also investigated, which needs to be considered in the design of very thin and high-frequency resonators.