The Sensitivity and Stability of Spinning Process Using Frequency Response Method

Hyun Wook Jung; Joo Sung Lee; L. E. Scriven; Jae Chun Hyun

doi:10.1007/BF02705376

The Sensitivity and Stability of Spinning Process Using Frequency Response Method

Hyun Wook Jung, Joo Sung Lee, L. E. Scriven, Jae Chun Hyun

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

The sensitivity and stability by frequency response of the final filament to several sinusoidal disturbances have been investigated in viscoelastic spinning by using various novel numerical algorithms. Amplitudes, or gains of the spinline cross-sectional area at the take-up, show resonant peaks, which are frequently encountered in hyperbolic systems. To effectively solve the complex system of the frequency response equation, alternative ways have been performed and compared. Interestingly, in the one-dimensional systems considered, integrating the linearized equations over the spinline length to shoot at the take-up boundary condition using two initial guesses ("two-shot" method) proved far more efficient than modal analysis using eigenfunction data or solving the matrix problem from the entire length by a direct method or an iterative one (GMRES). Also, the methodology to determine the stability of the system by using frequency response data, as suggested in Kase and Araki [1982], has been revamped to viscoelastic spinning system.

Original language	English
Pages (from-to)	20-26
Number of pages	7
Journal	Korean Journal of Chemical Engineering
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/BF02705376
Publication status	Published - 2004 Jan

Bibliographical note

Funding Information:
The authors are grateful for being supported by the 3M company at Minneapolis, Minnesota and postdoctoral research program of the Korea Science and Engineering Foundation (KOSEF). This research has also been supported in part by the KOSEF through the Applied Rheology Center (ARC), an official KOSEF-created engineering research center (ERC) at Korea University, Seoul, Korea.

Keywords

Direct Method
Frequency Response
Iterative Method (GMRES)
Modal Analysis
Sensitivity
Stability
Two-shot Method
Viscoelastic Spinning

ASJC Scopus subject areas

General Chemistry
General Chemical Engineering

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10.1007/BF02705376

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title = "The Sensitivity and Stability of Spinning Process Using Frequency Response Method",

abstract = "The sensitivity and stability by frequency response of the final filament to several sinusoidal disturbances have been investigated in viscoelastic spinning by using various novel numerical algorithms. Amplitudes, or gains of the spinline cross-sectional area at the take-up, show resonant peaks, which are frequently encountered in hyperbolic systems. To effectively solve the complex system of the frequency response equation, alternative ways have been performed and compared. Interestingly, in the one-dimensional systems considered, integrating the linearized equations over the spinline length to shoot at the take-up boundary condition using two initial guesses ({"}two-shot{"} method) proved far more efficient than modal analysis using eigenfunction data or solving the matrix problem from the entire length by a direct method or an iterative one (GMRES). Also, the methodology to determine the stability of the system by using frequency response data, as suggested in Kase and Araki [1982], has been revamped to viscoelastic spinning system.",

keywords = "Direct Method, Frequency Response, Iterative Method (GMRES), Modal Analysis, Sensitivity, Stability, Two-shot Method, Viscoelastic Spinning",

author = "Jung, {Hyun Wook} and Lee, {Joo Sung} and Scriven, {L. E.} and Hyun, {Jae Chun}",

note = "Funding Information: The authors are grateful for being supported by the 3M company at Minneapolis, Minnesota and postdoctoral research program of the Korea Science and Engineering Foundation (KOSEF). This research has also been supported in part by the KOSEF through the Applied Rheology Center (ARC), an official KOSEF-created engineering research center (ERC) at Korea University, Seoul, Korea.",

year = "2004",

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doi = "10.1007/BF02705376",

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AU - Hyun, Jae Chun

N1 - Funding Information: The authors are grateful for being supported by the 3M company at Minneapolis, Minnesota and postdoctoral research program of the Korea Science and Engineering Foundation (KOSEF). This research has also been supported in part by the KOSEF through the Applied Rheology Center (ARC), an official KOSEF-created engineering research center (ERC) at Korea University, Seoul, Korea.

PY - 2004/1

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N2 - The sensitivity and stability by frequency response of the final filament to several sinusoidal disturbances have been investigated in viscoelastic spinning by using various novel numerical algorithms. Amplitudes, or gains of the spinline cross-sectional area at the take-up, show resonant peaks, which are frequently encountered in hyperbolic systems. To effectively solve the complex system of the frequency response equation, alternative ways have been performed and compared. Interestingly, in the one-dimensional systems considered, integrating the linearized equations over the spinline length to shoot at the take-up boundary condition using two initial guesses ("two-shot" method) proved far more efficient than modal analysis using eigenfunction data or solving the matrix problem from the entire length by a direct method or an iterative one (GMRES). Also, the methodology to determine the stability of the system by using frequency response data, as suggested in Kase and Araki [1982], has been revamped to viscoelastic spinning system.

AB - The sensitivity and stability by frequency response of the final filament to several sinusoidal disturbances have been investigated in viscoelastic spinning by using various novel numerical algorithms. Amplitudes, or gains of the spinline cross-sectional area at the take-up, show resonant peaks, which are frequently encountered in hyperbolic systems. To effectively solve the complex system of the frequency response equation, alternative ways have been performed and compared. Interestingly, in the one-dimensional systems considered, integrating the linearized equations over the spinline length to shoot at the take-up boundary condition using two initial guesses ("two-shot" method) proved far more efficient than modal analysis using eigenfunction data or solving the matrix problem from the entire length by a direct method or an iterative one (GMRES). Also, the methodology to determine the stability of the system by using frequency response data, as suggested in Kase and Araki [1982], has been revamped to viscoelastic spinning system.

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KW - Frequency Response

KW - Iterative Method (GMRES)

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KW - Stability

KW - Two-shot Method

KW - Viscoelastic Spinning

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The Sensitivity and Stability of Spinning Process Using Frequency Response Method

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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