Vibrations of ballooning elastic strings

Fang Zhu, Rajiv Sharma, Christopher D. Rahn

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper investigates the nonlinear dynamic response of a linearly elastic string fixed at one boundary and undergoing constant speed circular motion at the other boundary. The response divides into nonlinear, steady state ballooning that is fixed relative to a rotating coordinate system and linearized vibration about the steady state. Single loop balloons have high tension and purely imaginary eigenvalues. The single loop vibration frequencies generally decrease with increasing balloon length. Highly extensible strings whirl in first and higher modes with forward whirling modes having lower frequencies. Axially stiff strings exhibit whirling only in higher modes. If the nondimensional string stiffness is larger than 1000 then the inextensible steady state solutions and the lowest six vibration frequencies match the extensible results to within 3%. One and a half loop balloons are divergently unstable. Long and/or sufficiently extensible strings form low tension double loop balloons. Inextensible double balloons are coupled mode flutter unstable. The steady state balloons, steady state eyelet tension, and balloon stability are experimentally verified.

Original languageEnglish (US)
Title of host publication16th Biennial Conference on Mechanical Vibration and Noise
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791880432
StatePublished - 1997
EventASME 1997 Design Engineering Technical Conferences, DETC 1997 - Sacramento, United States
Duration: Sep 14 1997Sep 17 1997

Publication series

NameProceedings of the ASME Design Engineering Technical Conference


ConferenceASME 1997 Design Engineering Technical Conferences, DETC 1997
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation


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