Introduction

The Goland wing model used in this work is based on the described model in Beran et al(2004). The model represents a cantilevered wing with a 20ft span and 6ft chord. The aerofoil consists of a 4% thick parabolic arc. Two configurations are available, with or without a tip store. The store has a width of 1ft and a length of 10ft.

The wing structure is modeled by a finite element model of the wing box. The finite element model is built up from shear panels, modeling the spars and ribs, and membrane elements, modeling the wing skins. The spar and rib caps are modeled by rod elements and posts connect the wing skins at every spar/rib intersection. The material properties of every element consist of a Young's modulus of 1.4976x10⁹ slugs/ft², a shear modulus of 5.616x10⁸ slugs/ft², and a structural density of 0.0001 slugs/ft³.

The result of the model is a very flexible wing that can exhibit several different aeroelastic behaviors. The clean case model has been shown to flutter at relative low velocities, Beran et al(2004), Woodgate and Badcock(2007). The wing with store has also been shown to develop an LCO in the transonic regime, Beran et al(2004).

Variability Study

The influence of structural variability on the aerelastic behaviour of aircraft has been receiving increased attention from the community. In the Goland wing case this can play a decisive factor with respect to flutter. In the following example, seven parameters were allowed to vary within +/-5% of their nominal values to perform Monte-Carlo analysis of the aeroelastic stability. The CFD based eigenvalue analysis requires the normal mode shapes and natural frequencies as inputs. By varying the structural parameters, 1000 samples of different mode shapes and natural frequencies were generated. This was implemented in MatLab using MSC. Nastran with the models provided above.

MSC.Nastran and CFD Based Results

Available Resources for Download

CFD Resources

IGES File
ICEM CFD HEXA Project	(Multiblock)
Grid Format	(CGNS), (Tecplot), (Plot3D)

MSC.Nastran Resources

Model	MSC.Nastran F.E.	MSC.Nastran Solution
Goland Clean	(Modal Analysis)	(Modal Solution)
Goland Clean	(Flutter Analysis)	(Flutter Solution)
Goland Store	(Modal Analysis)	(Modal Solution)
Goland Store	(Flutter Analysis)	(Flutter Solution)

Variability Resources

Model	MC Analysis	Sample Test
Goland Clean	(Random Mode Generation)	(Sample Modes)

Solver Input Files

Structural and Model Files

Tecplot CFD Files

Eigenvalue Mode Tracking - Mach 0.50
CFD Inviscid Solution - Mach 0.50

Refereed Journals

• Goland, M., "The Flutter of a Uniform Cantilever Wing," Journal of Applied Mechanics, Vol. 12, No. 4, pag. A197-A208, 1945.
  

• Patil, M.J., Hodges, D.H., and Cesnik, C.E.S, "Nonlinear Aeroelastic Analysis of Complete Aircraft in Subsonic Flow," Journal of Aircraft, Vol. 37, No. 5, pag. 753-760, 2000.
  doi: 10.2514/2.2685

• Beran, P.S., Strganac, T.W., Kim, K., and Nichkawde, C., "Studies of Store-Induced Limit-Cycle Oscillations Using a Model with Full System Nonlinearities," Nonlinear Dynamics, Vol. 37, No. 4, pag. 323-339, 2004.
  doi: 10.1023/B:NODY.0000045544.96418.bf

• Beran, P.S., Khot, N.S., Eastep, F.E., Snyder, R.D., and Zweber, J.V., "Numerical Analysis of Store-Induced Limit-Cycle Oscillation," Journal of Aircraft, Vol. 41, No. 6, pag. 1315-1326, 2004.
  doi: 10.2514/1.404

• Vio, G.A., Dimitriadis, G., Cooper, J.E., Badcock, K.J., Woodgate, M.A., and Rampurawala, A., "Aeroelastic System Identification using Transonic CFD Data for a Wing/Store Configuration," Aerospace Science and Technology, Vol. 11, No. 2-3, pag. 146-154, 2007.
  doi: 10.1016/j.ast.2006.09.003

• Woodgate, M. and Badcock, K.J., "On the fast prediction of Transonic Aeroelastic Stability and Limit Cycles," AIAA Journal, Vol. 45, No. 6, pag. 1370-1381, 2007.
  doi: 10.2514/1.25604

Conference Papers

• Beran, P.S., Khot, N.S., Eastep, F.E., Snyder, R.D., Zweber, J.V., Huttsell, L.J., and Scott, J.N., "The Dependence of Store-Induced Limit-Cycle Oscillation Predictions on Modelling Fidelity," RTO AVT Symposium on "Reduction of Military Vehicle Acquisition Time and Cost through Advanced Modelling and Virtual Simulation", Paris, France, 22-25 Apr. 2002.
  RTO-MP-089 Paper

• Beran, P.S., Khot, N.S., Eastep, F.E., Strganac, T.W., and Zweber, J.V., "Effects of Viscosity on Store-Induced Limit-Cycle Oscillation," ITEA Aircraft-Stores Compatibility Symposium, Destin, Florida, 2003.

• Khot, N., Beran, P., Zweber, J., and Eastep, F., "Influence of Tip Store Mass Location on Wing Limit-Cycle Oscillation," 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Norfolk, Virginia, 7-10 Apr. 2003.
  AIAA-2003-1731 Paper

• Vio, G.A., Dimitriadis, G., Cooper, J.E., Badcock, K.J., Woodgate, M.A., and Rampurawala, A., "Aeroelastic System Identification using Transonic CFD Data for a 3D Wing," IX International Conference on Recend Advances in Structural Dynamics, Southampton, U.K., 17-19 Jul. 2006.
  SD-2006-38 Paper

• Dimitriadis, G., Vio, G.A., Cooper, J.E., and Badcock, K.J., "Flight-Regime Dependent Reduced Order Models of CFD/FE Aeroelastic Systems in Transonic Flow," 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Waikiki, Hawaii, 23-26 Apr. 2007.
  AIAA-2007 Paper

• Vio, G.A., Dimitriadis, G., Cooper, J.E., and Badcock, K.J., "Linear and Non-Linear Transonic Flow Behaviour of the Goland⁺ Wing," International Forum of Aeroelasticity and Structural Dynamics, Stockholm, Sweden, 18-20 Jun. 2007.
  IFASD-2007 Paper

• Marques, S., Badcock, K.J., Khodaparast, H.H., and Mottershead, J.E., "CFD Based Aeroelastic Stability Predictions Under the Influence of Structural Variability," 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Springs, California, 4-7 May 2009.
  AIAA Paper 2009-2324