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Complex Modal Extraction for Estimating Wave Parameters in One-Dimensional Media

[+] Author Affiliations
B. F. Feeny

Michigan State University, East Lansing, MI

Paper No. DETC2010-28919, pp. 997-1006; 10 pages
doi:10.1115/DETC2010-28919
From:
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 22nd International Conference on Design Theory and Methodology; Special Conference on Mechanical Vibration and Noise
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4413-7 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME

abstract

A method of complex orthogonal decomposition is applied to the extraction of modes from simulation data of multi-modal traveling waves in one-dimensional continua. The decomposition of a transient wave is performed on a nondispersive pulse. Complex wave modes are then extracted from a two-harmonic simulation of a dispersive medium. The wave frequencies and wave numbers are obtained by looking at the whirl of the complex modal coordinate, and the complex modal function, respectively, in the complex plane. From the frequencies and wave numbers, the wave speeds are then estimated, as well as the group velocity associated with the two waves. The group velocity is also extracted directly from a decomposition of the traveling envelope of the waveform. The observations from the first two examples are used to help interpret the decomposition of a simulation of the traveling waves produced by a Gaussian initial displacement profile in an Euler-Bernoulli beam. While such a disturbance produces a continuous spectrum of wave components, the sampling conditions limit the range of wave components (i.e. mode shapes and modal coordinates) to be extracted. Within this working range, the wave numbers and frequencies are obtained from the extraction, and compared to theory. The frequency distribution is then approximated. The results are robust to random noise.

Copyright © 2010 by ASME
Topics: Waves

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