Modal and Aeroelastic Analysis of A High-Aspect-Ratio Wing with Large Deflection Capability

محورهای موضوعی : Mechanical Engineering

R. Koohi ¹ ( Department of, Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran )
H. Shahverdi ² ( Department of Aerospace Engineering and Center of Excellence in Computational Aerospace, Amirkabir University of Technology, Tehran, Iran )
H. Haddadpour ³ ( Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran )

تاریخ دریافت : 1393/05/28 تاریخ پذیرش : 1393/07/30 تاریخ انتشار : 1393/12/10

کلید واژه: FEM, Jone's Approximate Unsteady Aerodynamics, Wing Aeroelastic Stability, Large Deflection,

چکیده مقاله :

This paper describes a modified structural dynamics model for aeroelastic analysis of high-aspect-ratio wings undergoing large deformation behavior. To gain this aim, a moderate deflection beam model is modified with some important large deflection terms and then coupled with a state space unsteady aerodynamics model. Finite element method is used to discretize the equations of motion. A dynamic perturbation equation about a nonlinear static equilibrium is applied to determine the flutter boundary. The obtained results show good agreement in comparison with the other existing data such as high-altitude long-endurance (HALE) wing and Goland wing. It is found that the present aeroelastic tool have a good agreement in comparison with valid researches and also considering the effect of the geometric structural nonlinearity and higher order nonlinear terms on the flutter boundary determination is very significant.

منابع و مأخذ:

[1]   Hodges, D. H., Dowell, E., “Nonlinear Equations of Motion for the Elastic Bending and Torsion of Twisted Non uniform Rotor Blades”,  NASA TN D-7818, 1974.

[2]   Dowell, E., Traybar, J., and Hodges, D. H., “An Experimental-Theoretical Correlation Study of Nonlinear Bending and Torsion Deformations of a Cantilever beam”, Journal of Sound and Vibration, Vol. 50, 1977, pp. 533-544.

[3]   Hodges, D. H., Crespo da Silva, M., and Peters, D., “Nonlinear Effects in the Static and Dynamic Behavior of Beams and Rotor Blades”, Vertica, Vol. 12, No. 3, 1988, pp. 243-256.

[4]   Rosen, A., Freidmann, P. P., “The Nonlinear Behavior of Elastic Slender Straight Beams Undergoing Small Strains and Moderate Rotations”, Journal of Applied Mechanics, Vol. 46, 1979, pp. 161-168.

[5]   Crespo da Silva, M., Glynn, C., “Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams-I. Equations of Motions”, Journal of Structural Mechanics, Vol. 6, No. 4, 1978, pp. 437-448.

[6]   Crespo da Silva, M., Glynn, C., “Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams-I. Forced Motions”, Journal of Structural Mechanics, Vol. 6, No. 4, 1978, pp. 449-461.

[7]   Pai, P., Nayfeh, A., “Three-Dimensional Nonlinear Vibrations of Composite Beams-I. Equations of Motion”, Nonlinear Dynamics, Vol. 1, 1990, pp. 477-502.

[8]   Hodges, D. H., “A Mixed Variational Formulation Based on Exact Intrinsic Equations for Dynamics of Moving Beams”, International Journal of Solids and Structures, Vol. 26, No. 11, 1990, pp. 1253-1273.

[9]   Tang, D., Dowell, E., “Experimental and Theoretical Study on Aeroelastic Response of High-Aspect-Ratio Wings”, AIAA Journal, Vol. 39, No. 8, 2001, pp. 1430-1441.

[10]     Tang, D., Dowell, E., “Effects of Geometric Structural Nonlinearity on Flutter and Limit Cycle Oscillations of High-Aspect-Ratio Wings”, J Fluid Structure, Vol. 19, 2004, pp. 291-306.

[11]     Patil, M. J., Hodges D. H., and Cesnik, C. E. S., “Nonlinear Aeroelasticity and Flight Dynamics of High-Altitude, Long-Endurance Aircraft”, Journal of Aircraft, Vol. 38, No. 1, 2001, pp. 88-94.

[12]     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, 2000, pp. 753-760.

[13]     Patil, M. J., Hodges, D. H., “Limit-Cycle Oscillations in High-Aspect-Ratio Wings”, J Fluids Structure, Vol. 15, 2001, pp. 107-132.

[14]     Yuan, K. A., Friedmann, P. P., “Aeroelasticity and Structural Optimization of Composite Helicopter Rotor Blades with Swept Tips”, NASA CR 4665, 1995.

[15]     Yuan, K. A., Friedmann, P. P., “Structural Optimization for Vibratory Loads Reduction of Composite Helicopter Rotor Blades with Advanced Geometry Tips”, Journal of the American Helicopter Society, Vol. 43, No. 3, 1998, pp. 246-256.

[16]     Friedmann, P. P., Glaz, B., and Palacios, R., “A Moderate Deflection Composite Helicopter Rotor Blade Model with an Improved Cross-Sectional Analysis”, International Journal of Solids and Structures, Vol. 46, 2009, pp. 2186-2200.

[17]     Hodges, D. H., “Nonlinear Composite Beam Theory”, AIAA, Reston, VA, 2006.

[18]     Hodges, D. H., Yu, W., “A Rigorous, Engineer-Friendly Approach for Modeling Realistic, Composite Rotor Blades”, Wind Energy, Vol. 10, 2007, pp. 179-193.

[19]     Murugan, S., Ganguli, R., and Harursampath, D., “Effects of Structural Uncertainty on Aeroelastic Response of Composite Helicopter Rotor”, 48^th AIAA/ASME/ASCE/AHS/ACS Structures, Structural Dynamics and Materials Conference, Honolulu, HI, AIAA Paper 2298, 2007, pp. 1-18.

[20]     Patil, M. J, Hodges, D. H., “On the Importance of Aerodynamic and Structural Geometrical Nonlinearities in Aeroelastic Behavior of High-Aspect-Ratio Wings”, Journal of Fluids and Structures, Vol. 19, 2004, pp. 905-915.

[21]     Librescu, L., Chiocchia, G., and Marzocca, P., “Implications of Cubic Physical/Aerodynamic Non-linearities on the Character of the Flutter Instability Boundary”, International Journal of Non-linear Mechanics, Vol. 38, 2003, pp. 173-199.

[22]     Ghadiri, B., Razi, M., “Limite Cycle Oscillations of Rectangular Cantilever Wings Containing Cubic Nonlinearity in an Incompressible Flow”, Journal of solid and structures, Vol. 23, 2007, pp. 665-680.

[23]     Hodges, D. H., “Nonlinear Equations for Dynamics of Pretwisted Beams Undergoing Small Strains and Large Rotations”, NASA TP 2470, 1985.

[24]     Razavi Kermanshahi, M., Lotfi Neyestanak, A. A., “Exact Vibration and Buckling Solution of Levy Type Initially Stressed Rectangular Thin Plates”, Int J Advanced Design and Manufacturing Technology, Vol. 6, No. 4, 2013, pp. 65-73.

[25]     Karbaschi, K., Hasanzadeh, H., “Numerical Analysis of Plate’s Vibration Behavior with Non-linear Edge under Various Boundary Conditions”, Int J Advanced Design and Manufacturing Technology, Vol. 1, No. 2, 2008, pp. 52-65.

[26]     Kargarnovin, M. H., Karbaschi, K., and Hasanzadeh, H., “Numerical Study of Increasing Error Order in Finite Difference Method Used for Analyzing the Rectangular Isotropic Plate's Vibration Behavior”, Int J Advanced Design and Manufacturing Technology, Vol. 1, No. 2, 2008, pp. 1-9.

[27]     Greenberg, J. M., “Airfoil in Sinusoidal Motion in a Pulsating Stream”, NACA TN 1326, 1947.

[28]     Peters, D. A., Cao, W. M., “Finite State Induced Flow Models Part I: Two Dimensional Thin Airfoil”, Journal of Aircraft, Vol. 32, No. 2, 1995, pp. 313-322.

[29]     Patil, M. J. “Aeroelastic Tailoring of Composite Box Beams”, In Proceedings of the 35th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 1997.