Three dimensional vibration of a ballooning string

Kevin J. Hall, Fang Zhu, Christopher D. Rahn

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Scopus citations

Abstract

In many textile manufacturing processes, yarn is rotated at high speed forming a balloon. In this paper, Hamilton's principle is used to derive the nonlinear partial differential equations of a ballooning string. Jacobian elliptical sine functions satisfy the nonlinear steady state equations. The steady state eyelet tension is related to the string length for a constant balloon height. For high tension and low string length cases, single loop balloons occur. As the string length increases, tension decreases and multiple loop solutions are obtained. The nonlinear partial differential equations are linearized about the steady state solutions, resulting in three coupled equations with spatially varying coefficients. The equations involve a positive definite mass matrix operator, skew symmetric gyroscopic matrix operator, and symmetric stiffness matrix operator. It is shown using a Galerkin approach that only single loop balloons are stable for practical yarn elasticity. The natural frequencies of the single loop balloon increase with decreasing balloon size and increasing yarn stiffness. The effect of yarn elasticity on the first three vibration modes of a single loop balloon is analyzed. The steady state and stability analyses are experimentally verified.

Original languageEnglish (US)
Title of host publication15th Biennial Conference on Mechanical Vibration and Noise
EditorsK.W. Wang, B. Yang, J.Q. Sun, K. Seto, K. Yoshida, al et al
Pages1411-1418
Number of pages8
Edition3 Pt B/2
StatePublished - Dec 1 1995
EventProceedings of the 1995 ASME Design Engineering Technical Conference. Part C - Boston, MA, USA
Duration: Sep 17 1995Sep 20 1995

Publication series

NameAmerican Society of Mechanical Engineers, Design Engineering Division (Publication) DE
Number3 Pt B/2
Volume84

Other

OtherProceedings of the 1995 ASME Design Engineering Technical Conference. Part C
CityBoston, MA, USA
Period9/17/959/20/95

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All Science Journal Classification (ASJC) codes

  • Engineering(all)

Cite this

Hall, K. J., Zhu, F., & Rahn, C. D. (1995). Three dimensional vibration of a ballooning string. In K. W. Wang, B. Yang, J. Q. Sun, K. Seto, K. Yoshida, & A. et al (Eds.), 15th Biennial Conference on Mechanical Vibration and Noise (3 Pt B/2 ed., pp. 1411-1418). (American Society of Mechanical Engineers, Design Engineering Division (Publication) DE; Vol. 84, No. 3 Pt B/2).