Theoretical and experimental investigation on beam resonators of Gallium Orthophosphate GaPO4

We report progress in theoretical and experimental investigations on vibrating beam resonators made with gallium orthophosphate (GaPO4) crystals. Three kinds of vibrating modes are investigated: length extensional, flexural and torsional. Analytical models to simulate vibrating beam resonators with a rectangular cross-section have been developed and validated by comparison with quartz data on extensional, flexural and torsional GaPO₄ resonators. Temperature-compensated cuts have been found theoretically for all three kinds of beam resonators in GaPO₄. Experimental devices have been fabricated by ultrasound machining on Z-cut plates. Experimental results on vibrating mode identification and comparison with finite element analysis are presented.