Mindlin's equations of plated, crystal plates for thin-film stress prediction

Abstract

When an electroded, crystal plate is subjected to a steady acceleration and/or a steady, uniform temperature change, stresses are induced due to body forces exerted on the plate and electrodes, and due to the differences in thermal expansions between the plate and electrodes. Based on Mindlin's first-order equations of plated crystal plates [R. D. Mindlin, Progress in Applied Mechanics (Macmillan, New York, 1963), pp. 73–84, Prager Anniversary Volume], a set of six coupled equations is obtained in which the thin-film stresses induced by the body forces and thermal expansions are taken into account. A principle of virtual displacement corresponding to these equations is also obtained. In a partially electroded, circular crystal disk, the stresses due to steady acceleration are calculated, and the changes of thickness-shear frequencies due to these stresses are predicted.