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Observation and evolution of chaos for a cantilever plate in supersonic flow

Publication ,  Journal Article
Xie, D; Xu, M; Dai, H; Dowell, EH
Published in: Journal of Fluids and Structures
October 1, 2014

For a wing-like plate in supersonic flow cantilevered at its root, chaotic motions are studied in this paper. Prior literature has mainly focused on a simply supported plate or the limit cycle oscillations (LCOs) of a cantilever plate. The governing equations are constructed using von Karman plate theory and first-order piston theory. The Rayleigh-Ritz approach is adopted to discretize (and reduce the order of) the partial differential equations of the plate, and the resulting ordinary differential equations (ODEs) are solved numerically by the fourth-order Runge-Kutta (RK4) method. Numerical simulations demonstrate that the evolution of chaos is very complex, and the route to chaos depends on the panel's length-to-width ratio a/b. For a/b=1, a period-doubling of periodic motion occurs before transition to chaos. Another route to chaos is via quasi-periodic response directly for a/b=2. The most complicated prechaos and postchaos pattern is for a/b=0.5, which shows the presence of chaos regions with periodicity windows. Additionally, bifurcation diagrams show that certain features of the aeroelastic system such as quasi-periodic motions may be missed with too few Rayleigh-Ritz modes. Time histories, phase plane portraits, Poincaré maps and frequency spectra are used for identifying periodic and chaotic motions.

Duke Scholars

Published In

Journal of Fluids and Structures

DOI

EISSN

1095-8622

ISSN

0889-9746

Publication Date

October 1, 2014

Volume

50

Start / End Page

271 / 291

Related Subject Headings

  • Fluids & Plasmas
  • 40 Engineering
  • 09 Engineering
 

Citation

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Xie, D., Xu, M., Dai, H., & Dowell, E. H. (2014). Observation and evolution of chaos for a cantilever plate in supersonic flow. Journal of Fluids and Structures, 50, 271–291. https://doi.org/10.1016/j.jfluidstructs.2014.05.015
Xie, D., M. Xu, H. Dai, and E. H. Dowell. “Observation and evolution of chaos for a cantilever plate in supersonic flow.” Journal of Fluids and Structures 50 (October 1, 2014): 271–91. https://doi.org/10.1016/j.jfluidstructs.2014.05.015.
Xie D, Xu M, Dai H, Dowell EH. Observation and evolution of chaos for a cantilever plate in supersonic flow. Journal of Fluids and Structures. 2014 Oct 1;50:271–91.
Xie, D., et al. “Observation and evolution of chaos for a cantilever plate in supersonic flow.” Journal of Fluids and Structures, vol. 50, Oct. 2014, pp. 271–91. Scopus, doi:10.1016/j.jfluidstructs.2014.05.015.
Xie D, Xu M, Dai H, Dowell EH. Observation and evolution of chaos for a cantilever plate in supersonic flow. Journal of Fluids and Structures. 2014 Oct 1;50:271–291.
Journal cover image

Published In

Journal of Fluids and Structures

DOI

EISSN

1095-8622

ISSN

0889-9746

Publication Date

October 1, 2014

Volume

50

Start / End Page

271 / 291

Related Subject Headings

  • Fluids & Plasmas
  • 40 Engineering
  • 09 Engineering