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Research Papers

Aeroelastic Flutter of Continuous Systems: A Generalized Laplace Transform Method

[+] Author and Article Information
Arion Pons

Department of Engineering,
University of Cambridge,
Trumpington Street,
Cambridge CB2 1PZ, UK
e-mail: adp53@cam.ac.uk

Stefanie Gutschmidt

Department of Mechanical Engineering,
University of Canterbury,
Private Bag 4800,
Christchurch 8140, New Zealand
e-mail: stefanie.gutschmidt@canterbury.ac.nz

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 8, 2016; final manuscript received May 6, 2016; published online May 24, 2016. Assoc. Editor: George Kardomateas.

J. Appl. Mech 83(8), 081005 (May 24, 2016) (8 pages) Paper No: JAM-16-1075; doi: 10.1115/1.4033597 History: Received February 08, 2016; Revised May 06, 2016

This paper presents a generalization of the Laplace transform method (LTM) for determining the flutter points of a linear ordinary-differential aeroelastic system—a linear system involving a spatial derivative as well as a time-eigenvalue parameter. Current implementations of the LTM have two major problems: they are unable to solve systems of arbitrary size, order, and boundary conditions, and they require certain key operations to be performed by hand or with symbolic manipulation libraries. Our generalized method overcomes both these problems. We also devise a new method for solving and visualizing the algebraic system that arises from the LTM procedure. We validate our generalized LTM and novel solution method against both the Goland wing model and a large system of high differential order, as a demonstration of their effectiveness for solving such systems.

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References

Figures

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Fig. 1

det(D) against χ for the Goland wing, in vacuo

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Fig. 2

Contour plot of the Goland wing system with modal frequency paths superimposed

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Fig. 3

Modal damping paths of the Goland wing

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Fig. 4

Contour plot of the higher-order test system

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Fig. 5

Modal frequency and damping paths of the higher-order test system in the vicinity of the flutter point

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