Abstract
This paper describes the shear coefficient K of transverse vibration for trigonal crystals such as quartz crystal, lithium tantalate and lithium niobate which are anisotropic materials. In this paper, we derive the shear coefficient K for rectangular cross section of the trigonal crystals 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^^^(SUB)44, c'66. In addition, A value of K for quartz crystal, lithium tantalate and lithium niobate versus a cut angle is calculated so that K has a value of 0. 796-0. 867 for quartz crystal, 0. 834-0. 857 for lithium tantalate and 0. 831-0. 863 for lithium niobate, respectively, when a Z-plate of the crystals is rotated with a cut angleθof 0-180°about the x-axis. The values of K for quartz crystal are then compared with those for an isotropic material obtained by other authors.
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