Aircraft performance can be improved using morphing wing technologies, in which the wing can be deployed and folded under flight conditions, providing a wide flight envelope, good fuel efficiency, and reducing the space required to store the aircraft. Because the deployment of the wing is a nonlinear-coupled motion comprising large rigid body motion and large elastic deformation, a nonlinear folding-wing model is required to perform the necessary time-domain deployment simulation, while a linear model is required to perform the frequency-domain flutter analysis. The objective of this paper is to propose a versatile model that can be applied to both the time-domain and frequency-domain analyses of a folding wing, based on flexible multibody dynamics (MBD) using absolute nodal coordinate formulation (ANCF) and unsteady aerodynamics. This new versatile model expands the application range of the flexible MBD using ANCF in time-domain simulation, allowing it to express the coupled motion of extremely large elastic deformations and large rigid body motions that arise in next-generation aircraft. The time-domain deployment simulation conducted using the proposed model is useful for parametric deployment-system design because the model has improved calculation time. In the frequency-domain flutter analysis of a folding wing, the flutter speed obtained from the proposed model agrees with that obtained from an experiment, with an error of 4.0%, showing promise for application in next-generation aircraft design.
Issue Section:
Research Papers
References
1.
Weisshaar
, T. A.
, 2013
, “Morphing Aircraft Systems: Historical Perspectives and Future Challenges
,” J. Aircr.
, 50
(2
), pp. 337
–353
.2.
Wang
, Y.
, Wynn
, A.
, and Palacios
, R.
, 2016
, “Nonlinear Modal Aeroservoelastic Analysis Framework for Flexible Aircraft
,” AIAA J.
, 54
(10
), pp. 3075
–3090
.3.
NASA
, 2016
, “NASA to Test in-Flight Folding Spanwise Adaptive Wing to Enhance Aircraft Efficiency
,” National Aeronautics and Space Administration, Washington, DC, accessed Feb. 1, 2018, https://www.nasa.gov/feature/nasa-to-test-in-flight-folding-spanwise-adaptive-wing-to-enhance-aircraft-efficiency4.
Shabana
, A. A.
, 1997
, “Flexible Multibody Dynamics: Review of past and Recent Developments
,” Multibody Syst. Dyn.
, 1
(2
), pp. 189
–222
.5.
Dibold
, M.
, Gerstmayr
, J.
, and Irschik
, H.
, 2009
, “A Detailed Comparison of the Absolute Nodal Coordinate and the Floating Frame Reference Formulation in Deformable Multibody Systems
,” ASME J. Comput. Nonlinear Dyn.
, 4
(2
), p. 021006
.6.
Schiehlen
, W.
, 1997
, “Multibody System, Dynamics: Roots and Perspectives,” Multibody Syst. Dyn.
, 1
(2
), pp. 149
–188
.7.
Zhao
, Y.
, and Hu
, H.
, 2013
, “Prediction of Transient Responses of a Folding Wing During the Morphing Process
,” Aerosp. Sci. Technol.
, 24
(1
), pp. 89
–94
.8.
Hu
, W.
, Ynag
, Z.
, and Gu
, Y.
, 2016
, “Aeroelastic Study for Folding Wing During the Morphing Process
,” J. Sound Vib.
, 365
(17
), pp. 216
–229
.9.
Otsuka
, K.
, and Makihara
, K.
, 2016
, “Aeroelastic Deployable Wing Simulation Considering Rotation Hinge Joint Based on Flexible Multibody Dynamics
,” J. Sound Vib.
, 369
, pp. 147
–167
.10.
Otsuka
, K.
, Wang
, Y.
, and Makihara
, K.
, 2017
, “Deployable Wing Model Considering Structural Flexibility and Aerodynamic Unsteadiness for Deployment System Design
,” J. Sound Vib.
, 408
, pp. 105
–122
.11.
Otsuka
, K.
, and Makihara
, K.
, 2018
, “Deployment Simulation Using Absolute Nodal Coordinate Plate Element for Next-Generation Aerospace Structures
,” AIAA J.
, 56
(3
), pp. 1266
–1276
.12.
Shabana
, A. A.
, 1998
, “Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics
,” Nonlinear Dyn.
, 16
, pp. 293
–306
.13.
Escalona
, J. L.
, Hussien
, H. A.
, and Shabana
, A. A.
, 1998
, “Application of the Absolute Nodal Co-Ordinate Formulation to Multibody System Dynamics
,” J. Sound Vib.
, 214
(5
), pp. 833
–851
.14.
Lan
, P.
, and Shabana
, A. A.
, 2010
, “Rational Finite Elements and Flexible Body Dynamics
,” ASME J. Vib. Acoust.
, 132
(4
), p. 021006
.15.
Liu
, L.
, Shan
, J.
, and Zhang
, Y.
, 2016
, “Dynamics Modeling and Analysis of Spacecraft With Large Deployable Hoop-Truss Antenna
,” J. Spacecr. Rockets
, 53
(3
), pp. 471
–479
.16.
Li
, P.
, Liu
, C.
, Tian
, W.
, and Hu
, H.
, 2016
, “Dynamics of a Deployable Mesh Reflector of Satellite Antenna: Form-Finding and Modal Analysis
,” ASME J. Comput. Nonlinear Dyn.
, 11
(4
), p. 041017
.17.
Fan
, W.
, and Zhu
, W. D.
, 2016
, “An Accurate Singularity-Free Formulation of a Three-Dimensional Curved Euler-Bernoulli Beam for Flexible Multibody Dynamic Analysis
,” ASME J. Vib. Acoust.
, 138
(5
), p. 051001
.18.
Ren
, H.
, Fan
, W.
, and Zhu
, W. D.
, 2018
, “An Accurate and Robust Geometrically Exact Curved Beam Formulation for Multibody Dynamic Analysis
,” ASME J. Vib. Acoust.
, 140
(1
), p. 011012
.19.
Wang
, I.
, Gibbs
, S. C.
, and Dowell
, E. H.
, 2011
, “Structural Dynamics Model of Multisegmented + and Experiment
,” J. Aircr.
, 48
(6
), pp. 2149
–2160
.20.
Wang
, I.
, Gibbs
, S. C.
, and Dowell
, E. H.
, 2012
, “Aeroelastic Model of Multisegmented Folding Wings: Theory and Experiment
,” J. Aircr.
, 49
(3
), pp. 911
–921
.21.
Hafeez
, M. M. A.
, and El-Badawy
, A. A.
, 2018
, “Flutter Limit Investigation for a Horizontal Axis Wind Turbine Blade
,” ASME J. Vib. Acoust.
, 140
(4
), p. 041014
.22.
Song
, Z. G.
, Yang
, T. Z.
, Li
, F. M.
, Carrera
, E.
, and Hagedorn
, P.
, 2018
, “A Method of Panel Flutter Suppression and Elimination for Aeroelastic Structures in Supersonic Airflow
,” ASME J. Vib. Acoust.
, 140
(6
), p. 064501
.23.
Zhao
, Y.
, and Hu
, H.
, 2012
, “Parameterized Aeroelastic Modeling and Flutter Analysis for a Folding Wing
,” J. Sound Vib.
, 331
(2
), pp. 308
–324
.24.
Zhang
, W.
, Hu
, W. H.
, Cao
, D. X.
, and Yao
, M. H.
, 2016
, “Vibration Frequencies and Modes of a Z-Shaped Beam With Variable Folding Angles
,” ASME J. Vib. Acoust.
, 138
(4
), p. 041004
.25.
Romero
, I.
, 2008
, “A Comparison of Finite Elements for Nonlinear Beams: The Absolute Nodal Coordinate and Geometrically Exact Formulations
,” Multibody Syst. Dyn.
, 20
(1
), pp. 51
–68
.26.
Bauchau
, O. A.
, Han
, S.
, Mikkola
, A.
, and Matikainen
, M. K.
, 2014
, “Comparison of the Absolute Nodal Coordinate and Geometrically Exact Formulations for Beams
,” Multibody Syst. Dyn.
, 32
(1
), pp. 67
–85
.27.
Bauchau
, O. A.
, Betsch
, P.
, Cardona
, A.
, Gerstmayr
, J.
, Jonker
, B.
, Masarati
, P.
, and Sonneville
, V.
, 2016
, “Validation of Flexible Multibody Dynamics Beam Formulations Using Benchmark Problems
,” Multibody Syst. Dyn.
, 37
(1
), pp. 29
–48
.28.
Simo
, J. C.
, 1985
, “A Finite Strain Beam Formulation. The Three-Dimensional Dynamic Problem—Part I
,” Comput. Methods Appl. Mech. Eng.
, 49
(1
), pp. 55
–70
.29.
Simo
, J. C.
, and Vu-Quoc
, L.
, 1986
, “A Three-Dimensional Finite-Strain Rod Model. Part II: Computational Aspects
,” Comput. Methods Appl. Mech. Eng.
, 58
(1
), pp. 79
–116
.30.
Borri
, M.
, and Merlini
, T.
, 1986
, “A Large Displacement Formulation for Anisotropic Beam Analysis
,” Meccanica
, 21
(1
), pp. 30
–37
.31.
Bauchau
, O. A.
, and Hong
, C. H.
, 1987
, “Large Displacement Analysis of Naturally Curved and Twisted Composite Beams
,” AIAA J.
, 25
(11
), pp. 1469
–1475
.32.
Hodges
, D. H.
, 1990
, “A Mixed Variational Formulation Based on Exact Intrinsic Equations for Dynamics of Moving Beams
,” Int. J. Solids Struct.
, 26
(11
), pp. 1253
–1273
.33.
Palacios
, R.
, Murua
, J.
, and Cook
, R.
, 2010
, “Structural and Aerodynamic Models in Nonlinear Flight Dynamics of Very Flexible Aircraft
,” AIAA J.
, 48
(11
), pp. 2648
–2659
.34.
Hodges
, D. H.
, and Yu
, W.
, 2007
, “A Rigorous, Engineer-Friendly Approach for Modelling Realistic, Composite Rotor Blades
,” Wind Energy
, 10
(2
), pp. 179
–193
.35.
Ng
, B. F.
, Hesse
, H.
, Palacios
, R.
, Graham
, J. M. R.
, and Kerrigan
, E. C.
, 2015
, “Aeroservoelastic State-Space Vortex Lattice Modeling and Load Alleviation of Wind Turbine Blades
,” Wind Energy
, 18
(7
), pp. 1317
–1331
.36.
Abbas
, L. K.
, Rui
, X.
, and Marzocca
, P.
, 2012
, “Panel Flutter Analysis of Plate Element Based on the Absolute Nodal Coordinate Formulation
,” Multibody Syst. Dyn.
, 27
(2
), pp. 135
–152
.37.
Kim
, S. S.
, and Vanderploeg
, M. J.
, 1986
, “A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations
,” ASME J. Mech., Trans. Autom. Des.
, 108
(2
), pp. 176
–182
.38.
Maraniello
, S.
, and Palacios
, R.
, 2017
, “Optimal Rolling Maneuvers With Very Flexible Wings
,” AIAA J.
, 55
(9
), pp. 2964
–2979
.39.
Mei
, G.
, Zhang
, J.
, and Kang
, C.
, 2017
, “Analysis of Curved Panel Flutter in Supersonic and Transonic Airflows Using a Fluid–Structure Coupling Algorithm
,” ASME J. Vib. Acoust.
, 139
(4
), p. 041004
.40.
Takahashi
, Y.
, and Shimizu
, N.
, 1999
, “Study on Elastic Forces of the Absolute Nodal Coordinate Formulation for Deformable Beams
,” ASME
Paper No. DETC99/VIB-8203.41.
Wright
, J. R.
, and Cooper
, J. E.
, 2015
, Introduction to Aircraft Aeroelasticity and Loads
, Wiley
, Chichester, UK
.Copyright © 2019 by ASME
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