On the Vibration of Bolted Plate and Flange Assemblies

The vibration of an annular plate that is free along its outer edge, and that is connected to a flange along its inner edge by bolts that are equally spaced in the circumferential direction, is studied. A disk with this geometry, or a stacked array of such disks, is common in applications involving data storage, rotating machinery, or brake systems. The periodic structural imperfections that are associated with the bolt pattern can have interesting implications for the plate’s dynamic response. Changes that occur in the natural frequencies and mode shapes as a result of such deviations from an ideally clamped inner edge are studied through laboratory measurements, and through an approximate model that captures the rotationally periodic character of the bolted plate and flange system. In the axisymmetric case, the natural frequencies of the plate’s “sine” and “cosine” vibration modes are repeated for a specified number of nodal diameters. Under the influence of a regular bolt pattern, and the resulting local variations of the stiffness and compression at the plate/flange interface, some natural frequencies are repeated and others split. This process depends on the number of bolts used to mount the plate, and on the number of nodal diameters present in a specific vibration mode. A straightforward criterion to predict the split and repeated modes is discussed.