Direct calculation of limit cycles of draw resonance and their stability in spinning process

Jang Ho Yun, Dong Myeong Shin, Joo Sung Lee, Hyun Wook Jung, Jae Chun Hyun

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


Draw resonance, known to govern the onset of instability occurring in extension-dominant polymer processes, has been investigated using the bifurcation analysis method. Time-periodic trajectories of draw resonance along the drawdown ratio over the onset point or Hopf point, have been directly obtained by Newton's method implemented with pseudo arc-length continuation scheme. Floquet multipliers of the monodromy matrix to determine the stability of limit cycles have been also computed by time-integration during one period of the oscillation. It has been revealed that the limit cycles over the onset are more stable when drawdown ratio rises for both Newtonian and viscoelastic fluids, so draw resonance is a stable supercritical Hopf bifurcation.

Original languageEnglish
Pages (from-to)133-136
Number of pages4
JournalNihon Reoroji Gakkaishi
Issue number3
Publication statusPublished - 2008


  • Draw resonance
  • Hopf bifurcation
  • Monodromy matrix
  • Newton's method
  • Pseudo arc-length continuation
  • Stability of limit cycles
  • Time-periodic states

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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