Nonlinear dynamics and internal resonances of a planar multi-tethered spherical aerostat in modulated flow
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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.
KeywordsMulti-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.
- 13.Lee CL, Perkins NC (1992) Nonlinear oscillations of suspended cables containing a two-to-one internal resonance. Nonlinear Dyn 3:465–490Google Scholar
- 19.Shoshani O, Gottlieb O (2011) The nonlinear bifurcation structure of a wake oscillator model for self-excited vortex-induced vibration of a spherical pendulum. In: Proceedings of the 7th EUROMECH nonlinear dynamics conference, Rome, Italy, MS-19, pp 1–2Google Scholar