Vibration of an Eccentrically Clamped Annular Plate

Abstract

Small amplitude vibration of an eccentric annular plate, which is free along its outer edge and clamped along the interior, is investigated through experimental and analytical methods. A disk with this geometry, or a stacked array in which the clamping and symmetry axes of each disk are nominally coincident, is common in data storage and brake systems applications. In the present case, the geometric imperfections on the boundary can have important implications for the disk’s dynamic response. Changes that occur in the natural frequency spectrum, the mode shapes, and the free response under eccentric mounting are studied through laboratory measurements and an approximate discrete model of the plate. The natural frequencies and modes are found through global discretization of the Kamke quotient for a classical thin plate. For the axisymmetric geometry, the natural frequencies of the “sine” and “cosine” vibration modes for a specified number of nodal diameters are repeated. With increasing eccentricity, on the other hand, each pair of repeated frequencies splits at a rate that depends on the number of nodal diameters. Over a range of clamping and eccentricity ratios, the model’s predictions are compared to the measured results.