Timoshenkoの横振動棒理論による矩形断面水晶のせん断係数

概要

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This paper describes the shear coefficient K of transverse vibration for quartz crystal that is an anisotropic material. In this paper, we derive the shear coefficient K for quartz crystal of rectangular cross section in Timoshenko's beam theory of three dimensional elasticity. The theoretical result gives K as a function of the transformed elastic stiffness constants C'_<22>, C^^^_<44>, C'_<66>. For an isotropic material it agrees completely with that derived by G.R.Cowper^<(2)>. In addition, A value of K and its temperature coefficient versus a cut angle is calculated, so that K has a value of 0.796 to 0.867 and its temperature coefficient of the first order varies from-15.3 × 10^<-6>/℃ to + 13.2 × 10^<-6>/℃, when a Z-plate of quartz crystal is rotated with a cut angle θ of 0 to 180 degrees about the x-axis. The values of K are then compared with those obtained by other authors.
社団法人日本時計学会の論文
1996-12-20