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English: Phase jumps in the frequency response of the Duffing equation, for nonlinear stiffness and damping The graph shows the amplitude of the steady-state periodic response as a function of angular frequency The dashed parts of the frequency response are unstable, i.e. at the corresponding forcing frequency the realized response is on either one of the two amplitudes in the drawn-lines part of the graph.
When the frequency is slowly varying, the response amplitude can exhibit jumps. When the frequency is slowly increased from very low to high, the amplitude jumps down from A to B. But when the frequency is decreased from high to low, the amplitude jumps at C up to D.
The frequency response is obtained through the method of harmonic balance as:
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Author Kraaiennest
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  • D.W. Jordan & P. Smith (2007) Nonlinear ordinary differential equations – An introduction for scientists and engineers (4th ed.), Oxford University Press, pp. 223–233 ISBN: 978-0-19-920824-1.
  • M.J. Brennan, I. Kovacic, A. Carrella & T.P. Waters (2008). "On the jump-up and jump-down frequencies of the Duffing oscillator.". Journal of Sound and Vibration 318 (4–5): 1250–1261. DOI:10.1016/j.jsv.2008.04.032.

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16 November 2016

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Date/TimeThumbnailDimensionsUserComment
current19:07, 12 February 2017Thumbnail for version as of 19:07, 12 February 2017659 × 541 (102 KB)Kraaiennestlighter arrow color
17:49, 16 November 2016Thumbnail for version as of 17:49, 16 November 2016659 × 541 (98 KB)Kraaiennest{{Information |description={{en|1=Phase jumps in the frequency response of the Duffing equation, <math>\ddot{x} + \delta \dot{x} + \alpha x + \beta x^3 = \gamma \cos (\omega t)\,</math> for <math>\alpha...

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