Temperature-compensated cuts for length-extensional and flexural vibrating modes in GaPO/sub 4/ beam resonators

Flexural modes are the basic vibrating mode of tuning forks used in quartz wrist watches; they also can be used as the basis for sensors. Very little work, if any, has been done for vibrating beam resonators in GaPO/sub 4/. In this paper, the possibility of temperature-compensated cuts in GaPO/sub 4/ is investigated for length-extensional and flexural vibrating modes. A theoretical investigation of rectangular cross-section GaPO/sub 4/ vibrating beam resonators is accomplished by analytical methods. Modeling temperature effect is achieved by the approximate but classical method in which the effective elastic constants, beam dimensions, and crystal mass density are varied as a function of temperature. Temperature-compensated cuts are given in GaPO/sub 4/ for length-extensional and flexural modes. Some temperature-compensated cuts of GaPO/sub 4/ exhibit inversion points at high temperatures.