An analysis of a vibratory angular-rate gyroscope using polarized piezoceramic bimorph plates. Part 1: derivation of variational equations in the absence of angular velocity

A variational equation is derived for the in-plane and out-of-plane motions of a configuration composed of two rectangular and annular sector piezoceramic bimorph plates arranged in the shape of one half of a single tuning fork. The required variational equation for the structure is obtained by means of a low order expansion in the three-dimensional variational equation. The elements that connect any of the two bimorph plates, which are at right angles with respect to each other, are modelled as rigid bodies in the continuity conditions at the interface edges of the connected bimorphs.