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Aeroservoelasticity Read chapter Read first chapter

2015 | OriginalPaper | Chapter

4. Finite-State Aeroelastic Modeling

Author : Ashish Tewari

Published in: Aeroservoelasticity

Publisher: Springer New York

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Abstract

Chapter 4 describes the finite-state modeling techniques for deriving a linear, time-invariant state-space model of the aeroservoelastic plant. The linear systems theory is applied to the aeroelastic system in order to convert the frequency domain unsteady aerodynamics to the time domain. This requires the use of rational function approximations (RFA) in the Laplace domain for analytic continuation from harmonic curve-fits to transient response aerodynamics. The chapter presents the various RFA models, which have been developed and optimized by both gradient and non-gradient, nonlinear optimization techniques. Application of the RFA method to both typical wing section, and three-dimensional wing, with control surfaces, is presented. Illustrative finite-state model is presented for the flutter analysis of a real aircraft wing with experimental structural data, and compared with flight-flutter test results.

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previous chapter Unsteady Aerodynamic Modeling
next chapter Linear Aeroelastic Control
Footnotes
1
For the necessary conditions for the existence, and properties of Laplace transform of a function, refer to a textbook on engineering mathematics [88].
 
2
The noncirculatory lift is mainly responsible for a change in the airfoil’s effective mass due to a layer of the fluid being vertically displaced. This effect is termed the apparent inertia . The noncirculatory effects for a gas on stiffness and damping are usually negligible.
 
3
The fit error, ϵ, is divided by the number of elements n 2 as well as by the number M over which the curve fit is carried out, in order to yield an average fit error per element and per frequency point.
 
4
The RFA of Eversman and Tewari [50] is slightly different from Eq. (4.50) in that the lag terms do not have the Laplace variable in their numerators:
$$\begin{aligned} \text{G}(s) = \text{A}_0+\text{A}_1s+\text{A}_2s^2+\sum_{j=1}^{N}{\text{A}_{j+2}\frac{1}{s+b_j}},\end{aligned}$$
An effect of this change is that the coefficient matrix \(\text{A}_\text{0}\) can no longer be regarded as the “aerodynamic stiffness”, which was the case in the original RFA of Sevart [152] and Roger [144].
 
5
Antisymmetric modes have mutually opposite signs of deflections at either side of the wing, and result in a modification of the aerodynamic influence coefficients, such as those computed by the doublet-lattice method (Chap. 3).
 
6
The original DAST-ARW1 wing has two trailing edge control surfaces of approximately 20 % chord each, one inboard, and the other outboard. These are replaced by a single outboard flap here.
 
Metadata
Title
Finite-State Aeroelastic Modeling
Author
Ashish Tewari
Copyright Year
2015
Publisher
Springer New York
Book
Aeroservoelasticity

Print ISBN: 978-1-4939-2367-0

Electronic ISBN: 978-1-4939-2368-7

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-1-4939-2368-7_4

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