Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible Flow
An airfoil subjected to two-dimensional incompressible inviscid flow is considered. The airfoil is supported via a translational and a torsional springs. The aeroelastic integro-differential equations of motion for the airfoil are reformulated into a system of six first-order autonomous ordinary dif...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Aerospace Engineering |
| Online Access: | http://dx.doi.org/10.1155/2009/248930 |
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| author | H. Alighanbari S. M. Hashemi |
| author_facet | H. Alighanbari S. M. Hashemi |
| author_sort | H. Alighanbari |
| collection | DOAJ |
| description | An airfoil subjected to two-dimensional incompressible inviscid flow is considered.
The airfoil is supported via a translational and a torsional springs. The aeroelastic
integro-differential equations of motion for the airfoil are reformulated into a system of
six first-order autonomous ordinary differential equations. These are the simplest and
least number of ODEs that can present this aeroelastic system. The differential equations are then used for the bifurcation analysis of an airfoil with a structural nonlinearity in the pitch direction. Sample bifurcation diagrams
showing both stable and unstable limit cycle oscillation are presented. The types of
bifurcations are assessed by evaluating the Floquet multipliers. For a specific case, a
period doubling route to chaos was detected, and mildly chaotic behavior in a narrow
range of velocity was confirmed via the calculation of the Lyapunov exponents. |
| format | Article |
| id | doaj-art-3c93fb34ec744f50b3a807c2d4291f1a |
| institution | Kabale University |
| issn | 1687-5966 1687-5974 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Aerospace Engineering |
| spelling | doaj-art-3c93fb34ec744f50b3a807c2d4291f1a2025-02-03T07:26:18ZengWileyInternational Journal of Aerospace Engineering1687-59661687-59742009-01-01200910.1155/2009/248930248930Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible FlowH. Alighanbari0S. M. Hashemi1Department of Aerospace Engineering, Ryerson University, Toronto, ON, M5B 2K3, CanadaDepartment of Aerospace Engineering, Ryerson University, Toronto, ON, M5B 2K3, CanadaAn airfoil subjected to two-dimensional incompressible inviscid flow is considered. The airfoil is supported via a translational and a torsional springs. The aeroelastic integro-differential equations of motion for the airfoil are reformulated into a system of six first-order autonomous ordinary differential equations. These are the simplest and least number of ODEs that can present this aeroelastic system. The differential equations are then used for the bifurcation analysis of an airfoil with a structural nonlinearity in the pitch direction. Sample bifurcation diagrams showing both stable and unstable limit cycle oscillation are presented. The types of bifurcations are assessed by evaluating the Floquet multipliers. For a specific case, a period doubling route to chaos was detected, and mildly chaotic behavior in a narrow range of velocity was confirmed via the calculation of the Lyapunov exponents.http://dx.doi.org/10.1155/2009/248930 |
| spellingShingle | H. Alighanbari S. M. Hashemi Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible Flow International Journal of Aerospace Engineering |
| title | Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible Flow |
| title_full | Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible Flow |
| title_fullStr | Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible Flow |
| title_full_unstemmed | Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible Flow |
| title_short | Derivation of ODEs and Bifurcation Analysis of a Two-DOF Airfoil Subjected to Unsteady Incompressible Flow |
| title_sort | derivation of odes and bifurcation analysis of a two dof airfoil subjected to unsteady incompressible flow |
| url | http://dx.doi.org/10.1155/2009/248930 |
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