The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in-setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.
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April 1998
Research Papers
In-Plane Vibration Modes of Arbitrarily Thick Disks
K. I. Tzou,
K. I. Tzou
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213
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J. A. Wickert,
J. A. Wickert
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213
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A. Akay
A. Akay
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213
Search for other works by this author on:
K. I. Tzou
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213
J. A. Wickert
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213
A. Akay
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213
J. Vib. Acoust. Apr 1998, 120(2): 384-391 (8 pages)
Published Online: April 1, 1998
Article history
Received:
March 1, 1996
Revised:
March 1, 1997
Online:
February 26, 2008
Citation
Tzou, K. I., Wickert, J. A., and Akay, A. (April 1, 1998). "In-Plane Vibration Modes of Arbitrarily Thick Disks." ASME. J. Vib. Acoust. April 1998; 120(2): 384–391. https://doi.org/10.1115/1.2893842
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