The shear coefficient for quartz crystal of rectangular cross section in Timoshenko's beam theory

In this paper, we derive the shear coefficient K for quartz crystal of rectangular cross section in Timoshenko's beam theory of three-dimensional (3-D) elasticity. The theoretical result gives K as a function of the transformed elastic stiffness constants c(22)', (c) over cap(44), c(66)'. For an isotropic material it agrees completely with that derived by Cowper. In addition, a value of K and its temperature coefficient versus cut angle is calculated so that K has a value of 0.796-0.867 and its temperature coefficient of the first order varies from -15.3 x 10(-6)/degrees C to +13.2 x 10(-6)/degrees C, when a Z-plate of quartz crystal is rotated with a cut angle theta of 0-180 degrees about the x axis. The values of K are then compared with those for isotropic materials obtained by other authors.