Abstract
We study frequency shifts in a crystal resonator of arbitrary shape due to the addition of a mass layer to its surface by variational method. In addition to the layer inertia and membrane extensional stiffness which have been considered in the literature before, the present analysis generalizes existing results by considering the layer thickness-shear and bending deformations. The inclusion of the layer thickness-shear deformation can describe the situation when the layer is not following the crystal perfectly.
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