Abstract
Catastrophe theory was successfully applied to the analysis of draw resonance phenomena. It was shown that the potential of cusp catastrophe was appropriate to the analysis of oscillating viscoelasticity appearing in the above-mentioned phenemena. Moreover, basic behavior such as stress relaxation is discussed in regard to this potential. In these analyses, no relaxation spectrum is introduced. However, an apparent spectrum can be obtained if the results of stress relaxation are analyzed by a procedure similar to that used in the analysis of linear viscoelasticity. But a spectrum may not always exist even if derived analytically.
Similar content being viewed by others
Article PDF
References
For example, J. D. Ferry, “Visco elastic Properties of Polymers,” 2nd ed, John Wiley, New York, N.Y., 1970.
A. Odajima, J. Sohma, and M. Koike, J. Phys. Soc. Jpn., 12, 272 (1957).
K. Fujimoto and T. Nishi, J. Soc. Rubber Ind. Jpn., 34, 828 (1972).
K. Fujimoto, T. Nishi, and R. Kado, Polym. J., 3, 448 (1972).
Y. Inoue, A. Nishioka, and R. Chûjô, Makromol. Chem., 168, 163 (1973).
T. Matsumoto, Y. Segawa, Y. Warashina, and S. Onogi, Trans. Soc. Rheol., 17, 47 (1973).
V. Volterra, “Leçon sur la Théorie Mathématique de la Lutte pour la Vie,” Gauthier-Villars, Paris, 1931.
H. Ishihara and S. Kase, J. Appl. Polym. Sci., 20, 169 (1976).
R. J. Fischer and M. M. Denn, Appl. Polym. Symp., 27, 103 (1975).
R. Thom, “Stabilité Structurelle et Morphogénèse,” W. A. Benjamin Inc., Menlo Park, Calif., (1972).
J. M. T. Thompson and P. A. Shorrock, J. Mech. Phys. Solids, 23, 21 (1975).
G. Doetsch, “Theorie und Anwendung der Lapalace-Transformation”, Springer, Berlin, (1973).
E. C. Zeeman, Towards Theor. Biol., 4, 8 (1972).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chûjô, R., Tsuyama, K. Application of Catastrophe Theory to Draw Resonance. Polym J 11, 879–887 (1979). https://doi.org/10.1295/polymj.11.879
Issue Date:
DOI: https://doi.org/10.1295/polymj.11.879