The response of a nonlinear oscillator excited by white noise is considered. A truncated Hermite polynomial series is used as an approximation to the probability density function. While this approach has been used before by many authors to obtain statistics such as the time-dependent mean or mean-square values, it has not been noted before that the approach can be extended to obtain the correlation function and spectrum. This series when substituted into the Fokker-Planck equation yields a set of time-dependent moment equations, which can be solved numerically for the correlation functions, or, after a Fourier transform, a set of complex algebraic equations which can be solved for the spectrum. Examples of spectra for the Duffing and van der Pol oscillators are shown.
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June 1992
Technical Briefs
The Response Spectrum of a Nonlinear Oscillator
Huw G. Davies,
Huw G. Davies
Department of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada
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Qiang Liu
Qiang Liu
Department of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada
Search for other works by this author on:
Huw G. Davies
Department of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada
Qiang Liu
Department of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada
J. Appl. Mech. Jun 1992, 59(2): 459-462 (4 pages)
Published Online: June 1, 1992
Article history
Received:
August 23, 1990
Revised:
January 24, 1991
Online:
March 31, 2008
Citation
Davies, H. G., and Liu, Q. (June 1, 1992). "The Response Spectrum of a Nonlinear Oscillator." ASME. J. Appl. Mech. June 1992; 59(2): 459–462. https://doi.org/10.1115/1.2899546
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