Asymptotic analysis of passive nonlinear suppression of aeroelastic instabilities of a rigid wing in subsonic flow

O. V. Gendelman, A. F. Vakakis, Lawrence Bergman, D. M. McFarland

Research output: Contribution to journalArticle

Abstract

We study theoretically passive suppression of aeroelastic instabilities of a rigid wing in subsonic flow with an essentially nonlinear attachment. The analysis is performed by constructing a reduced-order model, applying complexification/averaging and slow-fast partition of the dynamics. The resulting slow-flow dynamics is then analyzed by singular perturbation. We fully recover computational and experimental results for this system reported in previous works and prove the existence of trivial/nontrivial stable attractors as well as relaxation oscillations in the slow-flow dynamics. These, in turn, correspond to complete/partial instability suppression, and (periodic or quasi-periodic) strongly modulated responses in the full-order dynamics. Moreover, we demonstrate the existence of Shilnikov bifurcations in the dynamics. The analysis of the slow-flow dynamics is confirmed by numerical simulations of the full-order system. The methodology developed in this work can be used in a predictive capacity when applying lightweight essentially nonlinear attachments to passive aeroelastic instability suppression of in-flow wings.

Original languageEnglish (US)
Pages (from-to)1655-1677
Number of pages23
JournalSIAM Journal on Applied Mathematics
Volume70
Issue number5
DOIs
StatePublished - 2010

Keywords

  • Essential nonlinearity
  • Passive aeroelastic instability suppression
  • Shilnikov bifurcation

ASJC Scopus subject areas

  • Applied Mathematics

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