The dynamics of a thin piezoelectric cylinder gyroscope

The paper considers the theory of a new type of vibratory rate gyroscope. The design considered is based upon a thin cylindrical shell of radially polarized lead zirconate titanate on which are deposited drive and pick-off electrodes. The equations of motion of the cylindrical shell are derived and the response of the gyroscope to constant and harmonic rates of turn is determined. NOTATION mean radius of cylinder piezoelectric coupling coefficients electric displacement electric field wall thickness gains (i = 1,2) axial coordinates of electrode top and bottom edges natural frequency generalized coordinate elastic compliance coefficients at constant electric field (i, j = 1, 2, 3) mid-surface strains (i, j = 1, 2, 3) direct and shear strains distance z above mid-surface kinetic energy axial, circumferential and shear stresses distance z above mid-surface shell displacements (i = 1, 2, 3) axial mode shape functions voltage strain energy electric potential energy radial distance above mid-surface electrode angle permittivity at constant stress damping factor density forcing frequency angular rate of turn