An exact solution of torsional quartz crystal resonators of free-free bar-type.
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概要
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An exact solution of a partial differential equation including elastic compliance constant <I>S</I><SUB>56</SUB>', with respect to stress function Ψ has been found for torsional modes of vibration of an arbitrary (singly, doubly, triply) rotated quartz crystal beam with a pair of parallel, free edges. The solution is obtained by relaxing the condition that the edge planes are perpendicular to the main faces of the beam. That is, the edges are off perpendicular by the angle θ=arctan (-<I>S</I><SUB>56</SUB>'/<I>S</I><SUB>55</SUB>'). The exact solution can reduce the difference of the calculatedand measured values of frequency constant for a thickness-to-width ratio. Also, a comparatively large-inclination of the edge cuts is required to reduce the unwanted, complicated mode shapes to simple ones.
- 一般社団法人 日本音響学会の論文
一般社団法人 日本音響学会 | 論文
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