GYROSCOPICALLY INDUCED VIBRATIONS OF CIRCULAR PLATES

Plates are considered to be spinning at a constant rate while simultaneously undergoing a constant precession at a fixed angle of nutation. The equations of motion are formulated for members mounted either parallel or perpendicular to the spin axis and it is found that these equations contain distributed harmonic inertia forces whose amplitudes and frequencies are dependent on spin and precession. The solutions of these equations, obtained by Fourier-Bessel series expansions, show that the natural frequencies are reduced by the effects of spin and precession and that this effect may become appreciable for appropriate combinations of material properties and geometry. Q