ON THE NORMAL ACCELERATION SENSITIVITY OF CONTOURED QUARTZ RESONATORS RIGIDLY SUPPORTED ALONG RECTANGULAR EDGES

An analysis of the normal acceleration sensitivity of contoured AT- and SC-cut quartz crystal resonators rigidly supported along rectangular edges is performed. The variational principle with all natural conditions for anisotropic static flexure is used in the calculation of the flexural biasing state. However, in this work the biasing shearing stresses with quadratic variation across the thickness of the plate are obtained a posteriori from the flexural solution in the conventional manner. The accompanying quadratically varying biasing shearing strains, which are very important in this work, are obtained from the constitutive equations along with all other quadratically varying strains resulting from the anisotropy. The calculated biasing deformation fields are employed in an existing perturbation equation along with the mode shapes of the contoured resonators to calculate the normal acceleration sensitivities. It is shown that the normal acceleration sensitivity vanishes for many cases and is less than a few parts in 1013 for all cases considered.