Analysis of stationary impact vibration in continuous system with asymmetrical hysteresis loop characteristics

Shigeru Aoki, Yasunori Sakai

Research output: Contribution to journalArticlepeer-review


This paper deals with impact vibration in beam system excited by periodic displacement with cosine function. The analytical model is steady impact vibration for a cantilever beam. The beam collides elastically to clamped steel of unsymmetric faces at an arbitrary point of span. Tried to analyze by applying the Fourier series method for this system with assuming force of restitution has a triangle hysteresis loop characteristics. For verification of the analytical method, experiments are performed. The analytical results are in a fairly good agreement with the experimental ones. After that tried to analyze the infinitesimal stabilities for the approximate solution by Fourier series method by applying variation equation. As the result, experimental result appear at the stable solution region in the analytical solution.

Original languageEnglish
Pages (from-to)1692-1699
Number of pages8
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Issue number767
Publication statusPublished - 2010 Jul
Externally publishedYes


  • Approximate solution
  • Collision vibration
  • Forced vibration
  • Hysteresis damping
  • Method of vibration analysis
  • Nonlinear vibration
  • Stability
  • Steady-State response
  • Vibration of continuous system

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering


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