Base On Mindlin Plate Theory Vibration Mode Identification, Coupling Assessment And Measurements In AT-cut Quartz Crystal Plate

Spurious modes are one of the most familiar problems of AT-cut quartz crystal resonators.There are many theories focused on calculating the frequency spectra, mode shapes, temperaturebehavior characteristics of thickness shear mode and spurious mode intending to avoid the modecoupling problems. But most of the research before was based on quartz crystal plate with relativelarge length, width and thickness. Today, the dimensions of quartz plates have decreasedenormously due to continuous miniaturization. Whether the calculation of previous theory stillhave great agreement with new AT-cut quartz crystal plate product is the problem we have to solve.This paper considered quartz crystal plate and partial plated quartz crystal plate, using first-orderplate theory and finite element method based on first-order plate theory respectively, to calculatethe characteristic of thickness shear mode, face shear mode, flexure mode and inharmonic overtone.To verify the theory for miniaturization quartz crystal product, we chose small size resonators to doexperiments. The result shows, even the size of quartz crystal plate is much smaller than before，the experiment data still can match the calculation result very well.The most direct way to study the vibration mode of quartz crystal plate is measuring thedisplacement of the plate directly. In this paper we using laser radiation instrument to detect thevibration shapes. It can clearly tell the displacements in each axle which help to distinguish thevibration modes easier. By this instrument thickness shear mode and Inharmonic overtone have bemeasured. The result matches theory quite well. This laser radiation instrument can help engineersto resolve the coupling problem by distinguishing the mode first and then finding the way to solvecoupling problem.