Non-Gaussian Response of Nonlinear Oscillators with Fourth-Order Internal Resonance

  • R. A. Ibrahim
  • A. Soundararajan
Conference paper
Part of the IUTAM Symposium book series (IUTAM)


The random response of a nonlinear two-degree-of-freedom oscillator subjected to wide band excitations is analyzed. The oscillator involves cubic nonlinear inertia coupling between its normal modes. The random excitations appear as non-homogeneous and parametric terms in the equations of motion. In the neighborhood of fourth-order internal resonance condition the response statist ics are determined by using the Fokker-Planck equation approach and a non-Gaussian closure scheme based on the properties of higher-order cumulants. Contrary to the Gaussian closure solution, the non-Gaussian closure yields a strictly stationary response in the time domain. It is found that unbounded response statistics take place at certain regions which are located above or below the exact internal resonance.


Fatigue Autocorrelation Acoustics 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • R. A. Ibrahim
    • 1
  • A. Soundararajan
    • 2
  1. 1.Dept. of Mechanical EngineeringTexas Tech UniversityLubbockUSA
  2. 2.Dept. of Mechanical EngineeringWestern Michigan UniversityKalamozooUSA

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