A non-linear oscillator with history dependent force

Roger Fosdick, Yohannes Ketema, Jang Horng Yu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We study the dynamics of a non-linear damped one-degree-of-freedom oscillator whose response force is dependent on the history of the motion and is of the relaxing type. Such an oscillator may serve as a simple model for mechanical applications where viscoelastic materials are used for the purpose of vibration damping and/or isolation. In the simplest cases history dependent forces are characterized by two parameters: the relaxation modulus ΦO and the relaxation time γ. Through the use of a version of Melnikov's method we show how the two parameters govern the existence of non-linear subharmonic orbits. We suggest an experimental method for determining both parameters.

Original languageEnglish (US)
Pages (from-to)447-459
Number of pages13
JournalInternational Journal of Non-Linear Mechanics
Issue number3
StatePublished - May 1998


  • History material
  • Melnikov's method
  • Oscillator
  • Subharmonic orbits
  • Vibration damping
  • Viscoelasticity


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