Research Papers

Multiparameter Spectral Analysis for Aeroelastic Instability Problems

[+] Author and Article Information
Arion Pons

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

Stefanie Gutschmidt

Department of Mechanical Engineering,
University of Canterbury,
Christchurch 8041, New Zealand

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 1, 2017; final manuscript received March 16, 2018; published online April 5, 2018. Assoc. Editor: George Kardomateas.

J. Appl. Mech 85(6), 061011 (Apr 05, 2018) (10 pages) Paper No: JAM-17-1661; doi: 10.1115/1.4039671 History: Received December 01, 2017; Revised March 16, 2018

This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of significant new solution and analysis algorithms for aeroelastic flutter problems; including direct solvers for polynomial problems of arbitrary order and size, and a pseudospectral method for characterizing the nature of the flutter point and its local modal damping gradient. Two variants of the flutter point direct solver are presented, their computational characteristics are compared, and an efficient hybrid method of direct spectral solution and iterative pseudospectral solution is developed. This method is well suited to the analysis of problems arising in reduced-order modeling and preliminary design optimization and has the advantage of computing all the system flutter points and their characteristics with minimal user oversight. The aeroelastic inverse problem, with applications in parameter identification and system optimization, is also shown to be solvable via multiparameter analysis. Extensions and improvements to this new conceptual framework and associated solvers are discussed.

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Fig. 1

Diagram of the system of section models

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Fig. 3

Modal damping plot for the single section model (Υ–ω form), including the modeshape bending-torsion ratio, compared with the multiparameter solutions

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Fig. 2

Characterization of flutter points based on two pseudospectral evaluations

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Fig. 4

Modal damping plot a set of couples section models (N=5, Υ–ω form), including the modeshape bending–torsion ratio, compared with the multiparameter solutions

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Fig. 5

Wall-clock computation times for MEP and modal damping analyzes of the system of section models (Υ–ω form)

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Fig. 6

Fractions of total wall-clock analysis time for components of the MEP analysis process, for both linearization methods

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Fig. 7

Wall-clock computation times for the hybrid operator determinant-ICP analysis, ICP-only analysis, and modal damping analysis of the system of section models (Υ–ω form)



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