On the Spectral Signature of Weakly Bilinear Oscillators

[+] Author and Article Information
P. V. Bayly

Department of Mechanical Engineering, Washington University, St. Louis, MO 63130

J. Vib. Acoust 118(3), 352-361 (Jul 01, 1996) (10 pages) doi:10.1115/1.2888190 History: Received July 01, 1994; Revised January 01, 1995; Online February 26, 2008


An analytical relationship is derived between the strength of a weak stiffness discontinuity and the magnitudes of superharmonic peaks in the Fourier spectrum of a bilinear oscillator. Expressions are obtained for three ranges of forcing frequencies: far from resonances, and near primary and superharmonic resonances. The difference between the two linear stiffness coefficients is used as the small parameter, ε, in a modified perturbation analysis. Closed-form expressions for the extra harmonic components in the spectrum are obtained as functions of the strength of the stiffness discontinuity. These results are relevant to the problem of detecting small cracks in structures and shafts; they suggest that greater sensitivity to small cracks can be obtained by exploiting superharmonic resonance.

Copyright © 1996 by The American Society of Mechanical Engineers
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