NONLINEAR VIBRATION OF A CENTRALLY CLAMPED ROTATING-DISK

Deflection profiles were calculated for vibration modes with up to four nodal diameters. Strain energy at large amplitudes was calculated. When vibrating with a particular number of nodal diameters, a disc of slightly imperfect axial symmetry has two normal modes with slightly different natural frequencies. When vibration amplitude becomes large, elastic coupling affects the way in which the two vibrations combine to form two traveling waves. Calculated frequency-response curves compared well with experimental curves. For low values of damping, a regular regime was found, giving a simple relation between frequency interval and the minimum vibration amplitude required for producing a relatively pure traveling wave. The predicted relation was numerically confirmed by tests on steel discs having accentuated frequency intervals. The results have significance in self-excited vibration which derives excitation from a single traveling wave. © 1979.