Analysis of thickness modes of contoured, doubly-rotated quartzresonators

摘要

It is shown that the theoretical development of D.S. Stevens andH.F. Tiersten (1986) can be used for calculating all three mode familiesof a doubly-rotated, contoured quartz resonator. Their approach uses atransformation of the mechanical displacement vector to the eigenvectortriad of the pure thickness solution. The solution methodology herereorganizes the transformation matrix Q in their formulation tocalculate the other two mode families. Calculations compare well withexperimental results for the three mode families of an SC-cut crystaland an FC-cut crystal and with published calculations for the SBTC-cutmode family with major displacement along the x₃ blank axis.The key constants for the SC-cut are presented for workers to use in thefuture