The modes of vibration of manufactured parts can be good indicators of the overall quality of the manufacturing process. That is, deviations in the modal frequencies or modal vectors of mechanical parts can help to identify outlier or systemic problems in the raw materials or fabrication procedure. A novel method for characterizing nonuniformities in homogeneous symmetric parts using pseudorepeated modal frequencies is discussed in this paper. It is demonstrated that the spacing between pseudorepeated roots in dominantly symmetric manufactured parts is a direct indicator of nonuniformities (i.e., inclusions, voids) in the stiffness or mass distributions. Smaller differences between split-peaks indicate less nonuniformity, and hence, higher quality parts. A simple fourth-order lumped parameter model is used to elaborate on this technique analytically, a representative finite element model is used to further this development, root locus techniques are used to study the sensitivity to nonuniformities, and acceleration response data from impact vibration tests on deep drawn hemispherical shells are used to verify the approach experimentally.
Nondestructive Evaluation of Parts With Degenerate Modes Using Pseudorepeated Roots
Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division December 12, 2003. Associate Editor: J. Tu.
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Jellison, B. J., Kess, H. R., Adams, D. E., and Nelson, D. C. (December 3, 2004). "Nondestructive Evaluation of Parts With Degenerate Modes Using Pseudorepeated Roots ." ASME. J. Dyn. Sys., Meas., Control. September 2004; 126(3): 498–508. https://doi.org/10.1115/1.1789536
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