Finite element method for large-amplitude two-dimensional panel flutter at hypersonic speeds

Gray, C. E.; Mei, Chuh; Shore, C. P.

doi:10.2514/3.10576

Cited by 56 publications

(6 citation statements)

References 20 publications

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“…As this was developed, the nonlinear time functions were approximated such that they were simple harmonic functions by neglecting the higher harmonics. By applying a LUM/NTF approach, the nonlinear time function was linearised, as follows (18)(19)(20) :…”

Section: Formulationmentioning

confidence: 99%

Vibration analyses of an equivalent plate wing with an external store

Na¹,

Kim²,

Shin³

2014

Aeronaut. j. (1968)

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Generally, pylon-mounted external stores significantly affect the aerodynamic characteristics of the aircraft due to their flexibility (1) . Therefore, many investigations upon the dynamic and aeroelastic characteristics of an aircraft wing with external stores have been done over the last few decades (2)(3)(4) Recently, a study was carried out regarding the aeroelastic effects on wings by the engine placement (5) For severe operation conditions, classical linear theory with a small amount of amplitude vibration may not be an appropriate analysis (6) . Nonlinear vibration analysis will be required, especially when the amplitude of the vibration is larger than the wing thickness. Chia (7) performed static, dynamic, and post-buckling analyses of various isotropic and composite plates for that purpose. Dumir and Bhaskar derived finite element formulations to analyse the nonlinear vibration of beams and plates (8) . Moreover, the variational-asymptotic plate formulation (9) and the accompanying equations for the global analysis for the plates (10) have been studied. That approach accounted every possible geometrical non-linearity associated with large displacement and small strain.Paper No. 3992. Manuscript

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Section: Formulationmentioning

confidence: 99%

Vibration analyses of an equivalent plate wing with an external store

Na¹,

Kim²,

Shin³

2014

Aeronaut. j. (1968)

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“…Mei and coworkers [4] developed finite element models to evaluate nonlinear flutter of composite panels considering the von Kàrman large-deflection strain-displacement relations in the time domain. Those authors also evaluated the nonlinear behavior of composite panels for different configurations regarding aspect ratios, lamination angles and number of layers [5]. Afterwards, different approaches were developed to improve design and control instabilities, such as active control based on piezoelectric actuators [6], consideration of stiffeners base as structural elements [7] and the use of electro-rheological fluids as a semi-active approach [8].…”

Section: Introductionmentioning

confidence: 99%

Supersonic Flutter and Buckling Optimization of Tow-Steered Composite Plates

et al. 2019

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The supersonic aeroelastic stability of tow steered carbon reinforced composite panels, in each layer of which the fibers follow curvilinear paths, is assessed. A structural model based on the Rayleigh-Ritz method, combined with the aerodynamic piston theory, is derived to represent the aeroelastic behavior of rectangular plates under different boundary conditions. In this model, the Classical Lamination Theory, considering symmetric stacking sequence and fiber trajectories described by Lagrange polynomials of different orders, is used. In addition, manufacturing constraints, which impose limitations to the feasible fiber trajectories, and the effect of in-plane loads, are also considered in the model. Using a multi-criteria Differential Evolution algorithm, numerical optimization is performed for a variety of scenarios, aiming at increasing the flutter and linear buckling stability margins of tow-steered plates, considering the geometrical parameters defining the fiber trajectories on the layers as design variables. Results obtained for the different optimization scenarios are compared, having a composite plate with unidirectional fibers as the baseline, aiming at evaluating the benefits achieved by the optimum tow-steered plates. Results enable to quantify the stability improvements by exploring fiber steering, which has been shown to be beneficial, even in situations where manufacturing constraints are accounted for.

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“…Two nonlinear aerodynamic terms, ( / ) 2 and ( / )( / ), taken from the third-order piston theory, were added to the linear piston theory to account for the aerodynamic nonlinearity [17]. Using the finite element method, Gray and his coworkers [18,19] presented the large-amplitude LCO with the full third-order piston theory to assess the influence of aerodynamic nonlinearity on the hypersonic panel flutter.…”

Section: Introductionmentioning

confidence: 99%

New Look at Nonlinear Aerodynamics in Analysis of Hypersonic Panel Flutter

Xie

Dai

et al. 2017

Mathematical Problems in Engineering

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A simply supported plate fluttering in hypersonic flow is investigated considering both the airflow and structural nonlinearities. Third-order piston theory is used for nonlinear aerodynamic loading, and von Karman plate theory is used for modeling the nonlinear strain-displacement relation. The Galerkin method is applied to project the partial differential governing equations (PDEs) into a set of ordinary differential equations (ODEs) in time, which is then solved by numerical integration method. In observation of limit cycle oscillations (LCO) and evolution of dynamic behaviors, nonlinear aerodynamic loading produces a smaller positive deflection peak and more complex bifurcation diagrams compared with linear aerodynamics. Moreover, a LCO obtained with the linear aerodynamics is mostly a nonsimple harmonic motion but when the aerodynamic nonlinearity is considered more complex motions are obtained, which is important in the evaluation of fatigue life. The parameters of Mach number, dynamic pressure, and in-plane thermal stresses all affect the aerodynamic nonlinearity. For a specific Mach number, there is a critical dynamic pressure beyond which the aerodynamic nonlinearity has to be considered. For a higher temperature, a lower critical dynamic pressure is required. Each nonlinear aerodynamic term in the full third-order piston theory is evaluated, based on which the nonlinear aerodynamic formulation has been simplified.

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Finite element method for large-amplitude two-dimensional panel flutter at hypersonic speeds

Cited by 56 publications

References 20 publications

Vibration analyses of an equivalent plate wing with an external store

Vibration analyses of an equivalent plate wing with an external store

Supersonic Flutter and Buckling Optimization of Tow-Steered Composite Plates

New Look at Nonlinear Aerodynamics in Analysis of Hypersonic Panel Flutter

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