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

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

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

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
Volume36
Issue number3
DOIs
Publication statusPublished - 2008 Oct 20

Fingerprint

metal spinning
cycles
Newton methods
Hopf bifurcation
Newtonian fluids
multipliers
Newton-Raphson method
Polymers
arcs
Trajectories
trajectories
oscillations
Fluids
fluids
polymers
matrices

Keywords

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

ASJC Scopus subject areas

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

Cite this

Direct calculation of limit cycles of draw resonance and their stability in spinning process. / Yun, Jang H.; Shin, Dong Myeong; Lee, Joo Sung; Jung, Hyun Wook; Hyun, Jae Chun.

In: Nihon Reoroji Gakkaishi, Vol. 36, No. 3, 20.10.2008, p. 133-136.

Research output: Contribution to journalArticle

Yun, Jang H. ; Shin, Dong Myeong ; Lee, Joo Sung ; Jung, Hyun Wook ; Hyun, Jae Chun. / Direct calculation of limit cycles of draw resonance and their stability in spinning process. In: Nihon Reoroji Gakkaishi. 2008 ; Vol. 36, No. 3. pp. 133-136.
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