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

摘要

In this paper, we derive the shear coefficient K for quartzncrystal of rectangular cross section in Timoshenko's beam theory ofnthree-dimensional (3-D) elasticity. The theoretical result gives K as anfunction of the transformed elastic stiffness constants C22n', cˆ44, C66'. For an isotropicnmaterial it agrees completely with that derived by G.R. Cowper (1966).nIn addition, a value of K and its temperature coefficient versus cutnangle is calculated so that K has a value of 0.796-0.867 and itsntemperature coefficient of the first order varies from -15.3×10n-6/°C to +13.2×10-6/°C, when anZ-plate of quartz crystal is rotated with a cut angle Θ ofn0-180° about the x axis. The values of K are then compared withnthose for isotropic materials obtained by other authors