Lyapunov inverse iteration for stability analysis using computational fluid dynamics

S. Timme; K. J. Badcock; M. Wu; A. Spence

doi:10.2514/6.2012-1563

Lyapunov inverse iteration for stability analysis using computational fluid dynamics

S. Timme, K. J. Badcock, M. Wu, A. Spence

Research output: Chapter in Book/Entry/Poem › Conference contribution

1 Scopus citations

Abstract

The recently developed inexact Lyapunov inverse iteration method is presented for the analysis of aeroelastic and fluid stability problems with Hopf bifurcations when using computational fluid dynamics in the modelling. The idea is to take the Jacobian matrix and its derivative with respect to an independent parameter, both evaluated at an equilibrium point, to obtain estimates of the critical eigenpair in addition to the critical value of the independent parameter. Prior knowledge of a frequency estimate, required as shift in standard inverse iteration, is not needed. The test cases presented include a two-degrees- of-freedom aerofoil and a flexible wing encountering flutter, and unsteady vortex shedding behind a circular cylinder in low Reynolds number flow.

Original language	English (US)
Title of host publication	53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012
Publisher	American Institute of Aeronautics and Astronautics Inc.
ISBN (Print)	9781600869372
DOIs	https://doi.org/10.2514/6.2012-1563
State	Published - 2012
Externally published	Yes
Event	53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012 - Honolulu, HI, United States Duration: Apr 23 2012 → Apr 26 2012

Publication series

Name	53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012

Other

Other	53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012
Country/Territory	United States
City	Honolulu, HI
Period	4/23/12 → 4/26/12

ASJC Scopus subject areas

Aerospace Engineering
Mechanical Engineering
General Materials Science
Surfaces and Interfaces

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10.2514/6.2012-1563

Cite this

Timme, S., Badcock, K. J., Wu, M., & Spence, A. (2012). Lyapunov inverse iteration for stability analysis using computational fluid dynamics. In 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012 (53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012). American Institute of Aeronautics and Astronautics Inc.. https://doi.org/10.2514/6.2012-1563

Lyapunov inverse iteration for stability analysis using computational fluid dynamics. / Timme, S.; Badcock, K. J.; Wu, M. et al.
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012. American Institute of Aeronautics and Astronautics Inc., 2012. (53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012).

Research output: Chapter in Book/Entry/Poem › Conference contribution

Timme, S, Badcock, KJ, Wu, M & Spence, A 2012, Lyapunov inverse iteration for stability analysis using computational fluid dynamics. in 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012, American Institute of Aeronautics and Astronautics Inc., 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012, Honolulu, HI, United States, 4/23/12. https://doi.org/10.2514/6.2012-1563

Timme S, Badcock KJ, Wu M, Spence A. Lyapunov inverse iteration for stability analysis using computational fluid dynamics. In 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012. American Institute of Aeronautics and Astronautics Inc. 2012. (53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012). doi: 10.2514/6.2012-1563

Timme, S. ; Badcock, K. J. ; Wu, M. et al. / Lyapunov inverse iteration for stability analysis using computational fluid dynamics. 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012. American Institute of Aeronautics and Astronautics Inc., 2012. (53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012).

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abstract = "The recently developed inexact Lyapunov inverse iteration method is presented for the analysis of aeroelastic and fluid stability problems with Hopf bifurcations when using computational fluid dynamics in the modelling. The idea is to take the Jacobian matrix and its derivative with respect to an independent parameter, both evaluated at an equilibrium point, to obtain estimates of the critical eigenpair in addition to the critical value of the independent parameter. Prior knowledge of a frequency estimate, required as shift in standard inverse iteration, is not needed. The test cases presented include a two-degrees- of-freedom aerofoil and a flexible wing encountering flutter, and unsteady vortex shedding behind a circular cylinder in low Reynolds number flow.",

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AU - Timme, S.

AU - Badcock, K. J.

AU - Wu, M.

AU - Spence, A.

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N2 - The recently developed inexact Lyapunov inverse iteration method is presented for the analysis of aeroelastic and fluid stability problems with Hopf bifurcations when using computational fluid dynamics in the modelling. The idea is to take the Jacobian matrix and its derivative with respect to an independent parameter, both evaluated at an equilibrium point, to obtain estimates of the critical eigenpair in addition to the critical value of the independent parameter. Prior knowledge of a frequency estimate, required as shift in standard inverse iteration, is not needed. The test cases presented include a two-degrees- of-freedom aerofoil and a flexible wing encountering flutter, and unsteady vortex shedding behind a circular cylinder in low Reynolds number flow.

AB - The recently developed inexact Lyapunov inverse iteration method is presented for the analysis of aeroelastic and fluid stability problems with Hopf bifurcations when using computational fluid dynamics in the modelling. The idea is to take the Jacobian matrix and its derivative with respect to an independent parameter, both evaluated at an equilibrium point, to obtain estimates of the critical eigenpair in addition to the critical value of the independent parameter. Prior knowledge of a frequency estimate, required as shift in standard inverse iteration, is not needed. The test cases presented include a two-degrees- of-freedom aerofoil and a flexible wing encountering flutter, and unsteady vortex shedding behind a circular cylinder in low Reynolds number flow.

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Lyapunov inverse iteration for stability analysis using computational fluid dynamics

Abstract

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