Application of the Centre Manifold Theory in Non-Linear Aeroelasticity

Liu, Lili; Wong, Yau Shu; Lee, B.H.K.

doi:10.1006/jsvi.1999.2895

Cited by 114 publications

(61 citation statements)

References 10 publications

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“…2(a). The crossing happens for U * L = 6.285, which is the same value reported by Liu et al 18 For the dynamic aeroelastic results presented in the following sections, the freestream speed is U * = 0.95 U * L and the corresponding root locus is illustrated in Fig. 2(b).…”

Section: A Linear Stability Analysissupporting

confidence: 80%

Nonlinear Model Reduction for Flexible Aircraft Control Design

Ronch

Badcock

Wang

et al. 2012

AIAA Atmospheric Flight Mechanics Conference

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The paper describes a systematic approach to the model reduction of large dimension fluid-structure-flight models, and the subsequent flight control design of very flexible aircraft. System nonlinearities may be due to the large wing deformations, the coupling between flexible and rigid body dynamics and/or flow separation at large angles of incidence. A nonlinear reduced order model is used to reduce the computational cost and dimension of the large-order nonlinear system for a practical control law design. The approach uses information on the eigenspectrum of the coupled system Jacobian matrix and projects the system through a series expansion onto a small basis of eigenvectors representative of the full-order dynamics. For a pitch-plunge aerofoil with structural nonlinearities, a controller based on reduced models was designed to alleviate gust loads. The approach to model reduction was also demonstrated for a two-dimensional problem with aerodynamics modelled using the computational fluid dynamics equations, and a flexible wing modelled using the geometrically-exact nonlinear beam equations. In all cases, the model reduction was found adequate to predict the large order system dynamics at a neglegible cost compared to that incurred by solving the nonlinear full-order system.

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Section: A Linear Stability Analysissupporting

confidence: 80%

Nonlinear Model Reduction for Flexible Aircraft Control Design

Ronch

Badcock

Wang

et al. 2012

AIAA Atmospheric Flight Mechanics Conference

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“…Therefore, the presented HAM fails in seeking the solution after the secondary point. In order to do so, one could give the initial solution guess (i.e., (11)) with the third harmonics, so that the initial solution can be determined. In addition, both Figure 8 and Table 4 show that the presented technique can indeed save a large amount of computational effort.…”

Section: Discussionmentioning

confidence: 99%

“…Let a 0 , h 0 , ω 0 , β 0 , and x 0 (τ) denote the initial approximations of a, h, ω, β, and x(τ), respectively. Due to solution expression (12) and initial conditions (11), the initial guess of solution can be chosen as…”

Section: Homotopy Analysis Methodsmentioning

confidence: 99%

“…Recently, Chung et al proposed a new incremental method and applied it to solve aeroelastic problems with freeplay [9] and hysteresis [10] structural nonlinearities, respectively. In addition, the center manifold theory, originally developed to qualitatively analyze nonlinear vibrations, was employed to obtain the approximations of airfoil LCOs [11,12].…”

Section: Introductionmentioning

confidence: 99%

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Highly Accurate Solution of Limit Cycle Oscillation of an Airfoil in Subsonic Flow

Zhang

Chen

Liu

et al. 2011

Advances in Acoustics and Vibration

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The homotopy analysis method (HAM) is employed to propose a highly accurate technique for solving strongly nonlinear aeroelastic systems of airfoils in subsonic flow. The frequencies and amplitudes of limit cycle oscillations (LCOs) arising in the considered systems are expanded as series of an embedding parameter. A series of algebraic equations are then derived, which determine the coefficients of the series. Importantly, all these equations are linear except the first one. Using some routine procedures to deduce these equations, an obstacle would arise in expanding some fractional functions as series in the embedding parameter. To this end, an approach is proposed for the expansion of fractional function. This provides us with a simple yet efficient iteration scheme to seek very-high-order approximations. Numerical examples show that the HAM solutions are obtained very precisely. At the same time, the CPU time needed can be significantly reduced by using the presented approach rather than by the usual procedure in expanding fractional functions.

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“…Semi-empirical procedures combined with experimental data were used to predict the joint strength as a function of basic laminate properties and joint geometrical parameters. Studies reported in the literature address the importance of joint allowables [27,28], selection of optimum ply stacking sequence [8], washer size, effects of clamping force or bolt preload on joint strength and failure modes [9,29,30]. Yet, some of these questions remain unanswered.…”

Section: Design Analysis and Characterization Of Jointsmentioning

confidence: 99%

Simple Questions for Interactive Information Retrieval

Kumaran

Allan

2006

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Application of the Centre Manifold Theory in Non-Linear Aeroelasticity

Cited by 114 publications

References 10 publications

Nonlinear Model Reduction for Flexible Aircraft Control Design

Nonlinear Model Reduction for Flexible Aircraft Control Design

Highly Accurate Solution of Limit Cycle Oscillation of an Airfoil in Subsonic Flow

Simple Questions for Interactive Information Retrieval

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