Thickness twist anharmonic modes in lithium tantalate and lithium niobate plate resonators

The thickness twist vibrations of LiTa0₃ and LiNbO₃ plate resonators are investigated for a partially electroded, infinite-plate model. A crystal orientation is chosen for which the fundamental thickness vibrations are dominated by a single shear mode. The strong electromechanical coupling associated with these materials requires that the full piezoelectric equations of motion be used. Resonance frequencies are calculated as a function of plate dimensions, electrode dimensions and electrode mass loading. The adjustment of resonator geometry for selective trapping of vibrational energy under the electrodes is discussed. Design criteria for LiTa0₃ and LiNb0₃ resonators are developed for application in crystal filters. From calculations of relative activities of the various resonant modes, the efficiency of energy trapping in the suppression of unwanted modes is assessed.