When a structure deviates from axisymmetry because of circumferentially varying model features, significant changes can occur to its natural frequencies and modes, particularly for the doublet modes that have non-zero nodal diameters and repeated natural frequencies in the limit of axisymmetry. Of technical interest are configurations in which inertia, dissipation, stiffness, or domain features are evenly distributed around the structure. Aside from the well-studied phenomenon of eigenvalue splitting, whereby the natural frequencies of certain doublets split into distinct values, modes of the axisymmetric structure that are precisely harmonic become contaminated with certain additional wavenumbers. From analytical, numerical, and experimental perspectives, this paper investigates spatial modulation of the doublet modes, particularly those retaining repeated natural frequencies for which modulation is most acute. In some cases, modulation can be sufficiently severe that a mode shape will “beat” spatially as harmonics with commensurate wavenumbers combine, just as the superposition of time records having nearly equal frequencies leads to classic temporal beating. An algebraic relation and a diagrammatic method are discussed with a view towards predicting the wavenumbers present in modulated eigenfunctions given the number of nodal diameters in the base mode and the number of equally spaced model features. [S0739-3717(00)01501-4]
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January 2000
Technical Papers
Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures
M. Kim,
M. Kim
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890
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J. Moon,
J. Moon
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890
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J. A. Wickert
J. A. Wickert
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890
Search for other works by this author on:
M. Kim
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890
J. Moon
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890
J. A. Wickert
Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received Aug, 1996; revised July 1997. Associate Technical Editor: C. Pierre.
J. Vib. Acoust. Jan 2000, 122(1): 62-68 (7 pages)
Published Online: July 1, 1997
Article history
Received:
August 1, 1996
Revised:
July 1, 1997
Citation
Kim , M., Moon , J., and Wickert , J. A. (July 1, 1997). "Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures ." ASME. J. Vib. Acoust. January 2000; 122(1): 62–68. https://doi.org/10.1115/1.568443
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