Nonuniform Film on the Surface

The surface mass-density of the film can be written in the form 

The shear-mode oscillations in quartz crystal, which are now the solution of the three-dimensional wave equation, can be written in the form 

following the procedure described in Ref. 170, we obtain the equation for the resonance frequency [Eq. (12)] in the text (see Sec. B.2). 

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