INPLANE VIBRATION MODES OF ARBITRARILY THICK DISKS

The three-dimensional vibration of an arbitrarily thick annular disk i s investigated for two classes of boundary conditions: all surfaces tr action-free, and all free except for the clamped inner radius. These t wo models represent limiting cases of such common engineering componen ts as automotive and aircraft disk brakes, for which existing models f ocus on out-of-plane bending vibration. For a disk of significant thic kness, vibration modes in which motion occurs within the disk's equili brium plane can play a substantial role in setting its dynamic respons e. Laboratory experiments demonstrate that in-plane modes exist at fre quencies comparable to those of out-of-plane bending even for thicknes s-to-diameter ratios as small as 10(-1). The equations for three-dimen sional motion are discretized through the Ritz technique, yielding nat ural frequencies and mode shapes for coupled axial, radial, and circum ferential deformations. This treatment is applicable to ''disks'' of a rbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings and shells. The solutions so obtained converge in th e limiting cases to the values expected from the classical theories, a nd to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the te chnoligcally-important range, the natural frequencies of certain in- a nd out-of-plane modes can be close to one another, or even identically repeated.