Examination of the Response of a Flexible Circular Rotor Subjected to Specified Gyroscopic Rates

The natural and forced motion of a rotor configuration comprised of a constant thickness, annular plate fixed at the inner boundary to a rigid core and at the outer boundary to a symmetric, rigid rim is examined here. Natural modes and frequencies are determined for the rotor in the spin mode and numerical results are presented as a function of plate and rim parameters. The forced vibration response of the rotor subjected to constant spin and precession rates is examined with emphasis placed on understanding the boundary conditions imposed on the plate by the dynamic motion of the rim assumed to have a lateral degree of freedom and two rotational degrees of freedom about transverse axes. Free vibration of the rotor in a null gyroscopic state is also examined as a special case. Natural modes and frequencies are determined from the closed form solution obtainable for the governing equation of motion and presented as a function of plate and rim parameters.