On the Spectral Signature of Weakly Bilinear Oscillators-Reference-Cited by-同舟云学术

On the Spectral Signature of Weakly Bilinear Oscillators

Published:1996-07-01 Issue:3 Volume:118 Page:352-361
ISSN:1048-9002
Container-title:Journal of Vibration and Acoustics
language:en
Short-container-title:

Author:

Bayly P. V.¹

Affiliation:

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

Abstract

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.

Publisher

ASME International

Subject

General Engineering

Link

http://asmedigitalcollection.asme.org/vibrationacoustics/article-pdf/118/3/352/5625916/352_1.pdf

Reference9 articles.

1. Actis, R., and Dimarogonas, A., 1989, “Nonlinear Effects due to Closing Cracks in Vibrating Beams,” ASME Des. Div. Publ. DE, Vol. 18, No. 3, pp. 99–104.

2. Bayly, P., and Virgin, L., 1991, “Chaotic Rattling of a Piece-wise Nonlinear Oscillator,” ASME Publication 91-WA-DSC-17, pp. 1–6.

3. Bayly P. , and VirginL., 1993, “An Experimental Study of an Impacting Pendulum,” Journal of Sound and Vibration, Vol. 164, No. 2, pp. 364–374.

4. Bender, C., and Orszag, S., 1978, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York.

5. Chu Y. , and ShenM.-H. H., 1992, “Analysis of Forced Bilinear Oscillators and the Application to Cracked Beam Dynamics,” AIAA Journal, Vol. 30, No. 10, pp. 2512–2519.

Cited by 19 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Nonlinear Vibration Analysis of a Beam with a Breathing Crack;Applied Sciences;2019-09-15

2. Development of Polynomial Model for Cantilever Beam with Breathing Crack;Procedia Engineering;2016

3. A wavelet-based method for the forced vibration analysis of piecewise linear single- and multi-DOF systems with application to cracked beam dynamics;Journal of Sound and Vibration;2015-12

4. A novel approach to detecting breathing-fatigue cracks based on dynamic characteristics;Journal of Sound and Vibration;2013-01

5. Analysis of Breathing Cracks Using Vibrations;Experimental Techniques;2012-02-28