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Vibrations of an Axial Bar Experiencing Periodic Unilateral Contact Using the Wavelet Balance Method

[+] Author Affiliations
Simon Jones

Rose-Hulman Institute of Technology, Terre Haute, IN

Mathias Legrand

McGill University, Montreal, QC, Canada

Paper No. DETC2014-34725, pp. V008T11A028; 13 pages
doi:10.1115/DETC2014-34725
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 26th Conference on Mechanical Vibration and Noise
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4641-4
  • Copyright © 2014 by ASME

abstract

Efficiently predicting the vibratory responses of flexible structures which experience unilateral contact is becoming of high engineering importance. An example of such a system is a rotor blade within a turbine engine; small operating clearances and varying loading conditions often result in contact between the blade and the casing.

The method of weighted residuals is a effective approach to simulating such behaviour as it can efficiently enforce time-periodic solutions of lightly damped, flexible structures experiencing unilateral contact. The Harmonic Balance Method (HBM) based on Fourier expansion of the sought solution is a common formulation, though it is hypothesized wavelet bases that can sparsely define nonsmooth solutions may be superior. This is investigated herein using an axially vibrating rod with unilateral contact conditions. A distributional formulation in time is introduced allowing periodic, square-integrable trial functions to approximate the second-order equations. The mixed wavelet Petrov-Galerkin solutions are found to yield consistent or better results than HBM, with similar convergence rates and seemingly more accurate contact force prediction.

Copyright © 2014 by ASME
Topics: Vibration , Wavelets

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