The shear coefficient for quartz crystal of rectangular crosssection 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 C₂₂ ^', c?₄₄, C₆₆'. For an isotropic material it agrees completely with that derived by G.R. Cowper (1966). 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 -15.3×10 ^-6/°C to +13.2×10^-6/°C, when a Z-plate of quartz crystal is rotated with a cut angle &thetas; of 0-180° about the x axis. The values of K are then compared with those for isotropic materials obtained by other authors