Computational Study of Aeroelastic Limit Cycles due to Localized Structural Nonlinearities

Padmanabhan, Madhusudan A.; Dowell, Earl H.; Pasiliao, Crystal L.

doi:10.2514/1.c034645

Cited by 12 publications

(5 citation statements)

References 15 publications

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“…The equations of the motion of an aeroelastic system with freeplay can generally be expressed in the form of a set of piecewise linear state space equations (e.g., Equation ( 5) in [3], Equation (8) in [4], and Equation (1) in [13]):…”

Section: State Space Equations Of An Aeroelastic System With Freeplaymentioning

confidence: 99%

“…The most widely adopted process is to assign only one principal system state a series of non-zero values and study the LCO behaviors case by case. For example, Padmanabhan and Dowell [8] studied an all-moving surface model and a wing-store model with various structural nonlinearities, such as cubic stiffness, cubic damping, and freeplay. In their study, less than one hundred I.C.s were tested in time integrations for the second model, while that number for the first model was only one.…”

Section: Introductionmentioning

confidence: 99%

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Integration of Freeplay-Induced Limit Cycles Based On a State Space Iterating Scheme

Wang

Chao

2021

Applied Sciences

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Time integration is commonly used to obtain accurate system responses, such as the limit cycle oscillations (LCOs) for an aeroelastic system with freeplay. However, the integrations that start with various initial conditions (I.C.s) are usually studied case by case, so only a few system states can possibly be focused on. This paper proposes a state space iterating (SSI) scheme to find LCO solutions using time integration by using another method. First, a large number of arbitrary I.C. cases are used for time integrations, but only a very short integration time is required for each I.C. case. Second, system behaviors are depicted visually through a method that combines a modified Poincaré map and Lorenz map, in which the LCO solutions are found as fixed points via visual inspections. To verify the SSI scheme’s ability to find LCOs, a typical plunge–pitch wing section is established numerically. Time integrations with both the classic scheme and the proposed SSI scheme are carried out. The LCO results of the SSI scheme are well-aligned with those from the classic scheme. The SSI scheme visualizes the patterns of system responses using arbitrary I.C. cases and analyzes the LCO stability, which provides more mathematical insights into an aeroelastic system with freeplay.

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Section: State Space Equations Of An Aeroelastic System With Freeplaymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Integration of Freeplay-Induced Limit Cycles Based On a State Space Iterating Scheme

Wang

Chao

2021

Applied Sciences

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“…Here, only the slip motion is considered, and therefore, the transitions between stick-slip are not included in the model. Similar assumption was done in Padmanabhan et al (2018). A smooth approximation in terms of the hyperbolic tangent function is used.…”

Section: Structural Nonlinearity Modelingmentioning

confidence: 99%

“…The most used concentrated structural nonlinearity representations are the hardening or softening stiffness (Lee et al, 2005), free play (Conner et al, 1997), and hysteresis (Malher et al, 2017). It is also possible to find concentrated nonlinear dissipative effects, such as dry friction (Padmanabhan et al, 2018) and quadratic damping (Dimitriadis, 2017).…”

Section: Introductionmentioning

confidence: 99%

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Characterization of typical aeroelastic sections under combined structural concentrated nonlinearities

Silva

Marques

2021

Journal of Vibration and Control

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Structural nonlinearities are usually present in aeroelastic systems. The analysis of this system commonly comprises a study involving only one type of nonlinearity, influencing a particular motion of the airfoil. However, practical applications of aeroelastic systems can be affected by different types of structural nonlinearities. It becomes essential to study the stability of the aeroelastic system under these conditions to assess more real operational flight procedures. In this context, this article presents an investigation of a typical aeroelastic section response with trailing edge control surface subjected to combinations of concentrated structural nonlinearities. Different nonlinear scenarios involving cubic hardening stiffness in pitching and free play, free play with preload, and slip dry friction in the trailing edge control surface motion are analyzed. The mathematical model is based on linear unsteady aerodynamics coupled to a three-dof typical aeroelastic section. Hopf bifurcations diagrams are obtained from direct time integration of the equation of motion. The post-flutter limit cycle oscillations are investigated, revealing supercritical and subcritical bifurcations. A complete parametric study of the nonlinear parameters is carried out, thereby allowing a sensitivity analysis of each nonlinear scenario. The results show that aeroelastic tailoring considering the mild post-flutter behavior can be achieved through an appropriate choice of combined nonlinear effects. Moreover, combined nonlinearities can mitigate the undesired subcritical aeroelastic responses caused by free play.

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Supercritical and subcritical aeroelastic behaviors of a three-dimensional wing coupled with a nonlinear energy sink

Huang,

Zheng,

Nie

et al. 2024

International Journal of Non-Linear Mechanics

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Computational Study of Aeroelastic Limit Cycles due to Localized Structural Nonlinearities

Cited by 12 publications

References 15 publications

Integration of Freeplay-Induced Limit Cycles Based On a State Space Iterating Scheme

Integration of Freeplay-Induced Limit Cycles Based On a State Space Iterating Scheme

Characterization of typical aeroelastic sections under combined structural concentrated nonlinearities

Supercritical and subcritical aeroelastic behaviors of a three-dimensional wing coupled with a nonlinear energy sink

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