VIBRATION AND COUPLING PHENOMENA IN ASYMMETRIC DISK-SPINDLE SYSTEMS

This paper analytically treats the free vibration of coupled, asymmetr ic disk-spindle systems in which both the disk and spindle are continu ous and flexible. The disk and spindle are coupled by a rigid clamping collar. The asymmetries derive from geometric shape imperfections and nonuniform clamping stiffness at the disk boundaries. They appear as small perturbations in the disk boundary conditions. The coupled syste m eigenvalue problem is cast in terms of ''extended'' eigenfunctions t hat are vectors of the disk, spindle, and clamp displacements. With th is formulation, the eigenvalue problem is self-adjoint and the eigenfu nctions are orthogonal. The conciseness and clarity of this formulatio n are exploited in an eigensolution perturbation analysis. The amplitu de of the disk boundary condition asymmetry is the perturbation parame ter. Exact eigensolution perturbations are derived through second orde r. For general boundary asymmetry distributions, simple rules emerge s howing how asymmetry couples the eigenfunctions of the axisymmetric sy stem and how the degenerate pairs of axisymmetric system eigenvalues s plit into distinct eigenvalues. Additionally, properties of the formul ation are ideal for use in modal analyses, Ritz-Galerkin discretizatio ns, and extensions to gyroscopic or nonlinear analyses.