Normal form representation of the aeroelastic response of the Goland wing

Nayfeh, Ali H.; Ghommem, Mehdi; Hajj, Muhammad R.

doi:10.1007/s11071-011-0111-6

Cited by 21 publications

(7 citation statements)

References 12 publications

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“…This equation is driven by the deviation term DC z , which is the discrepancy between the specified nonlinear force curve and the linear curve (typically a oz Á a), defined as positive for a decrease in the force (Peters, 1985). Two stall curves are frequently seen in the literature: piecewise-linear (Dunn and Dugundji, 1992;Patil et al, 2001;Tang and Dowell, 2001) and cubic (Ghommem et al, 2010;Nayfeh et al, 2012;Nichkawde et al, 2006). Both are utilized here ( Fig.…”

Section: Aeroelastic Modeling Frameworkmentioning

confidence: 99%

“…The local behavior predicted by MMS, however, will be sufficient to optimize wing structures as described above, converting dangerous subcritical behavior into supercritical LCOs. Multiple-scale analysis of aeroelastic systems can be found in Chandiramani et al (1996), Beran (1999), Ghommem et al (2010), Gilliatt et al (2003), Paolone et al (2006), and Nayfeh et al (2012), and a similar reduction of the limit cycle behavior to a few critical parameters is conducted by Librescu et al (2002) (the Lyapunov first quantity) and Woodgate and Badcock (2007) (center manifold theory). To the best of the authors' knowledge, it has not been used for design optimization, aero-structural or otherwise.…”

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confidence: 99%

“…Most researchers build models of highly flexible wings by coupling nonlinear beam models to strip theory aerodynamics (Nayfeh et al, 2012;Nichkawde et al, 2006;Patil et al, 2001;Shearer and Cesnik, 2007;Tang andDowell, 2001, 2002) or panel methods (Demasi and Livne, 2009;Palacios et al, 2010;Patil and Hodges, 2004;Wang et al, 2010). The former option is utilized here; both subcritical and supercritical LCOs have been observed, and are ''dependent on a delicate balance between stall aerodynamics and the structural nonlinear forces'' (Tang and Dowell, 2001).…”

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confidence: 99%

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Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization

Stanford

Beran

2013

Journal of Fluids and Structures

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a b s t r a c tThe usefulness of flutter as a design metric is diluted for wings with destabilizing (softening) nonlinearities, as a stable high-amplitude limit cycle (subcritical) may exist for flight speeds well below the flutter point. It is thus desired to design aeroelastic structures such that the post-flutter behavior is as benign (i.e., supercritical) as possible, among the other constraints commonly considered in the optimization process. In order to account for these metrics in an accurate and efficient manner, direct tools are utilized to first locate the Hopf-point (flutter speed), and then to obtain a nonlinear perturbation solution via the method of multiple scales. The latter scheme provides a scalar variable whose sign and magnitude dictate the nature of the limit cycle. The accuracy of these methods is demonstrated with a high-aspect-ratio highly flexible wing, modeled with nonlinear beam finite elements and the ONERA dynamic stall tool. Stiffness and inertial design variables are allowed to vary spatially throughout the wing, in order to conduct gradient-based optimization of the limit cycle under flutter and mass constraints. The resulting wing structure demonstrates strongly supercritical behavior, as well as several design conflicts between linear (flutter) and nonlinear (limit cycles) sensitivities, which are not present in the uniform baseline wing.Published by Elsevier Ltd.

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Section: Aeroelastic Modeling Frameworkmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization

Stanford

Beran

2013

Journal of Fluids and Structures

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“…Thus, a simple yet realistic model and analysis framework that can accurately assess the flight performances of a largely deformed highly flexible aircraft, and can fully account for the coupling between flight dynamics and both structural nonlinearity and unsteady aerodynamics, which play a key role in the vehicle's static and dynamic characteristics, are of paramount importance in the analysis and design of these highly flexible aircrafts [3][4][5]. Such models are typically built using nonlinear beam representations of the structure [6][7][8], with either unsteady strip theory [9][10][11][12][13] or unsteady vortex lattice aerodynamics [14,15].…”

Section: Introductionmentioning

confidence: 99%

A Comprehensive Framework for Coupled Nonlinear Aeroelasticity and Flight Dynamics of Highly Flexible Aircrafts

et al. 2020

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A framework to model and analyze the coupled nonlinear aeroelasticity and flight dynamics of highly flexible aircrafts is presented. The methodology is based on the dynamics of 3D co-rotational beams. The coupling of axial, bending and torsional effects is added to the stiffness and mass matrices of Euler-Bernoulli beam to capture the most relevant characteristics of a real wing structure. The finite-state aerodynamic model is coupled with the structural model to simulate the unsteady aerodynamics. A scheme of mixed end-point and mid-point time-marching algorithms is proposed and applied into the implicit predictor-corrector integration, where the end-point algorithm is used in the predictor step for efficiency and mid-point algorithm in corrector step for accuracy. The ground, body and airflow axes for flight dynamics are re-defined by the global and elemental ones for structural dynamics, followed by the redefinitions of local Euler angles and airflow angles of each element. The framework can be used for quick analyses of flexible aircrafts in conceptual and preliminary design phases, including linear and nonlinear trim, aerodynamic load estimation, stability assessment, time-domain simulations and flight performance evaluations. The results show the payload mass and its distributions will significantly affect the trim state and longitudinal stability of highly flexible aircrafts.

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“…Several methods have been proposed for deriving this form and then analyzing the nature of Hopf bifurcation. For instance, Nayfeh et al (2012) and Abdelkefi et al (2013) applied the method of multiple scales to construct an approximation to the response of different wings near the Hopf bifurcation. Dimitriadis et al (2004) used the center manifold theorem to a nonlinear aeroelastic system to reduce its dimensionality and predict its bifurcation and post-bifurcation behavior.…”

Section: Introductionmentioning

confidence: 99%

Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

Abdelkefi

Ghommem²

2013

JMSIC

Self Cite

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In this paper, we employ the normal form to derive a reduced-order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two-dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic system near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self-excited oscillator governed by a time-delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.

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Normal form representation of the aeroelastic response of the Goland wing

Cited by 21 publications

References 12 publications

Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization

Direct flutter and limit cycle computations of highly flexible wings for efficient analysis and optimization

A Comprehensive Framework for Coupled Nonlinear Aeroelasticity and Flight Dynamics of Highly Flexible Aircrafts

Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

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