, Volume 51, Issue 11, pp 2689–2712 | Cite as

Nonlinear dynamics and internal resonances of a planar multi-tethered spherical aerostat in modulated flow

  • La Mi
  • Oded Gottlieb
Nonlinear Dynamics, Identification and Monitoring of Structures


We derive a nonlinear initial boundary value problem for a planar multi-tethered spherical aerostat system employing the extended Hamilton’s principle with geometric constraints, along with a single tether limiting case. We numerically investigate a reduced-order modal dynamical system with harmonic incident flow excitation that is obtained for both single and multi-tether configurations, respectively. The resulting frequency responses reveal superharmonic periodic, period-doubled, quasiperiodic and chaotic-like solutions close to a 3:1 internal resonance and certain combination resonances.


Multi-tethered aerostat Nonlinear dynamics Internal resonance 



This research is supported in part by the Grand Technion Energy Program and the Jordan & Irene Tark Aerospace Structures Research Fund. LM is grateful for the 2015 Irwin and Joan Jacobs Fellowship for excellent achievements in her graduate program at the Technion. We thank the anonymous reviewers for their detailed comments which helped improve the manuscript.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Autonomous Systems and Robotics Program (TASP)Technion—Israel Institute of TechnologyHaifaIsrael
  2. 2.Mechanical Engineering and TASPTechnion—Israel Institute of TechnologyHaifaIsrael

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