Some analytical results on piezoelectric gyroscopes

Equations for linear piezoelectricity are formulated in a reference frame rotating at a small, constant angular velocity. Propagation of plane waves in an infinite rotating body is examined. Thickness vibration of infinite plates rotating about their normal are discussed. The equations are then simplified by a perturbation procedure based on the small angular velocity. The perturbation procedure simplifies the problem and shows the mechanism of piezoelectric gyroscopes. Specific gyroscopes of plates in thickness shear-thickness shear motion, beams in flexure-flexure motion, and circular cylindrical shells in torsional-axisymmetric radial motion are studied by equations of piezoelectric beams, plates, and shells in conjunction with the perturbation procedure. Free vibration frequencies and modes as well as conditions for double resonance are obtained. Forced vibration is also studied which yields simple expressions for the sensitivity of the gyroscopes. The propagation of surface waves on a rotating half space is also discussed which suggests the possibility of surface mode piezoelectric gyroscopes.