Thickness-shear Frequencies of an Infinite Quartz Plate with Material Property Variation Along the Thickness

摘要

Properties of the quartz crystal blank of a resonator is assumed homogeneous,uniform, and perfect in design, manufacturing, and applications. As endproducts, quartz crystal resonators are frequently exposed to gases and liquidswhich can cause surface damage and internal degradation of blanks underincreasingly hostile conditions. The combination of service conditions andmanufacturing process including chemical etching and polishing can inevitablymodify the surface of quartz crystal blanks with changes of materialproperties, raising the question of what will happen to vibrations of quartzcrystal resonators of thickness-shear type if such modifications to blanks areto be evaluated for sensitive applications. Such questions have beenencountered in other materials and structures with property variations eitheron purpose or as the effect of environmental or natural processes commonlyreferred to as functionally graded materials, or FGMs. Analyses have been donein applications as part of studies on FGMs in structural as well as in acousticwave device applications. A procedure based on series solutions has beendeveloped in the evaluation of frequency changes and features in an infinitequartz crystal plate of AT-cut with the symmetric material variation patterngiven in a cosine function with the findings that the vibration modes are nowclosely coupled. These results can be used in the evaluation of surface damageand corrosion of quartz crystal blanks of resonators in sensor applications ordevelopment of new structures of resonators.