A harmonic balance approach for large-scale problems in nonlinear structural dynamics

Computers and Structures

Volumn 88, Issue 17-18, 2010, Pages 1002-1014

  LaBryer, A ^a   Attar, P J ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

Aliasing; Flapping flight; Harmonic balance; Nonlinear finite elements; Time periodic

Indexed keywords

ALIASING; FINITE ELEMENT SOLVER; FLAPPING FLIGHT; HARMONIC BALANCE; HARMONIC BALANCE APPROACH; HARMONIC BALANCE METHOD; HIGH-DIMENSIONAL; LARGE-SCALE PROBLEM; NON-LINEAR FINITE ELEMENTS; NONLINEAR STRUCTURAL DYNAMICS; ORDERS OF MAGNITUDE; STEADY STATE SOLUTION; TIME DOMAIN; TIME MARCHING; TIME-PERIODIC SOLUTIONS;

DYNAMICAL SYSTEMS; FINITE ELEMENT METHOD; FLIGHT DYNAMICS; NONLINEAR DYNAMICAL SYSTEMS; STRUCTURAL DYNAMICS; TIME DOMAIN ANALYSIS;

HARMONIC ANALYSIS;

EID: 77955429434     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2010.06.003     Document Type: Article

References (47)

1. N. Kryloff, and N. Bogoliuboff Introduction to nonlinear mechanics 1947 Princeton University Press Princeton, NJ
2. T.J. Aprille, and T.N. Trick Steady-state analysis of nonlinear circuits with periodic inputs Proc IEEE 60 1 1972 108 114
3. Nastov O. Spectral methods for circuit analysis. PhD thesis, Massachusetts Institute of Technology; 1999.
4. Beran P, Petit C. A direct method for quantifying limit cycle oscillation response characteristics in the presence of uncertainties. AIAA paper 2004-1695.
5. Y. Kim, S. Noah, and Y. Choi Periodic response of multi-disk rotors with bearing clearances J Sound Vibr 144 3 1991 381 395
6. McMullen M, Jameson A, Alonso J. Acceleration of convergence to a periodic steady state in turbomachinery flows. AIAA paper 2001-0152.
7. McMullen M. The application of nonlinear frequency domain methods to the Euler and Navier-Stokes equations. PhD thesis, Stanford University; 2001.
8. Gopinath AK, Beran PS, Jameson A. Comparative analysis of computational methods for limit-cycle oscillations. AIAA paper 2006-2076.
9. G. Dimitriadis Continuation of higher-order harmonic balance solutions for nonlinear aeroelastic systems J Aircraft 45 2 2008 523 537
10. K.C. Hall, J.P. Thomas, and W.S. Clark Computation of unsteady nonlinear flows in cascades using a harmonic balance technique AIAA J 40 5 2002 879 886
11. J.P. Thomas, J.P. Dowell, and K.C. Hall Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit cycle oscillations AIAA J 40 4 2002 638 646
12. L. Liu, J.P. Thomas, E.H. Dowell, and P. Attar A comparison of classical and high dimensional harmonic balance approaches for a duffing oscillator J Comput Phys 215 2006 298 320 (Pubitemid 43574493)
13. A. LaBryer, and P.J. Attar High dimensional harmonic balance dealiasing techniques for a duffing oscillator J Sound Vibr 324 2009 1016 1038
14. W. Cheney, and D. Kincaid Numerical mathematics and computing 2004 Brooks/Cole Belmont, CA
15. R.C. Maple, P.I. King, P.D. Orkwis, and J.M. Wolff Adaptive harmonic balance method for nonlinear time-periodic flows J Comput Phys 193 2004 620 641
16. J.C. Tannehill, D.A. Anderson, and R.H. Pletcher Computational fluid mechanics and heat transfer second ed. 1997 Taylor and Francis Philadelphia, PA
17. R.W. Hamming Numerical methods for scientists and engineers 1973 McGraw-Hill New York
18. J.P. Boyd Chebyshev and Fourier spectral methods 1989 Springer-Verlag Berlin
19. C. Canuto, M.Y. Haussaini, A. Quarteroni, and T.A. Zang Spectral methods in fluid dynamics 1987 Springer-Verlag Berlin
20. S.A. Orszag On the elimination of aliasing in finite difference schemes by filtering high-wavenumber components J Atmos Sci 28 1971 1074
21. T.Y. Hou, and R. Li Computing nearly singular solutions using pseudo-spectral methods J Comput Phys 226 2006 379 397
22. S.K. Lele Compact finite difference schemes with spectral-like resolution J Comput Phys 103 1992 16 42
23. T. Belytschko, W.K. Liu, and B. Moran Nonlinear finite elements for continua and structures 2000 John Wiley and Sons
24. T. Weis-Fogh Quick estimates of flight fitness in hovering animals including novel mechanisms for lift production J Exp Biol 59 1973 169 230
25. J. Rayner Thrust and drag in flying birds: applications to birdlike micro air vehicles Fixed and flapping wing aerodynamics for micro air vehicle applications vol. 195 2001 AIAA Reston, VA 217 230
26. Lee JS. Numerical study on flapping-airfoil design and unsteady mechanism of two-dimensional insect wing. PhD thesis, Seoul National University; 2006.
27. K. Isogai, Y. Shinmoto, and Y. Watanabe Effects of dynamic stall on propulsive efficiency and thrust of flapping airfoil AIAA J 37 10 1999 1145 1151
28. K. Hall, and S. Hall A rational engineering analysis of the efficiency of flapping flight Fixed and flapping wing aerodynamics for micro air vehicle applications vol. 195 2001 AIAA Reston, VA 217 230
29. S. Heathcote, Z. Wang, and I. Gursul Effect of spanwise flexibility on flapping wing propulsion J Fluid Struct 24 2008 183 199
30. S. Heathcote, and I. Gursul Flexible flapping airfoil propulsion AIAA J 45 5 2007 1066 1079
31. Y. Lian, W. Shyy, D. Viieru, and B. Zhang Membrane wing aerodynamics for micro air vehicles Prog Aerospace Sci 39 2003 425 465
32. W. Shyy, P. Ifju, and D. Viieru Membrane wing-based micro air vehicles Appl Mech Rev 58 2005 283 301
33. Gordnier R, Visbal M. High fidelity computational simulation of a membrane wing airfoil (Invited). AIAA paper 2008-0614.
34. R.O. O'Reilly, and P.J. Holmes Non-linear, non-planar and non-periodic vibrations of a string J Sound Vibr 153 3 1992 413 435
35. T.C. Molteno, and N.B. Tufillaro An experimental investigation into the dynamics of a string Am J Phys 72 9 2004 413 435
36. M.R. Rubin, and O. Gottlieb Numerical solutions of forced vibration and whirling of a non-linear string using the theory of a Cosserat point J Sound Vibr 197 1 1996 85 101
37. Attar PJ, Gordnier R. High fidelity computational aeroelastic analysis of a plunging membrane airfoil. AIAA paper 2009-2472.
38. LaBryer A, Attar PJ. Modeling the nonlinear structural dynamics of a plunging membrane airfoil using a high dimensional harmonic balance approach. AIAA paper 2009-2474.
39. Rojratsirikul P, Wang Z, Gursul I. Unsteady aerodynamics of membrane airfoils. AIAA paper 2008-0613.
40. J.V. Ferreira, and A.L. Serpa Application of the arc-length method in nonlinear frequency response J Sound Vibr 284 1 2005 133 149
41. A.L.R. Thomas, G.K. Taylor, R.B. Srgley, R.L. Nudds, and R.J. Bomphrey Dragonfly flight: free-flight and tethered flow visualizations reveal a diverse array of unsteady lift-generating mechanisms, controlled primarily via angle of attack J Exp Biol 207 2004 4299 4323
42. P.J. Attar Some results for approximate strain and rotation tensor formulations in geometrically non-linear Reissner-Mindlin plate theory Int J Non-Linear Mech 43 2 2008 81 99
43. L. Bao, J. Hu, Y.L. Yu, P. Cheng, B.Q. Xu, and B.G. Tong Viscoelastic constitutive model related to deformation of insect wing under loading in flapping motion J Appl Math Mech 26 6 2006 741 748
44. M.A. Crisfield Nonlinear finite element analysis of solids and structures vol. 1 1991 John Wiley and Sons
45. E.H. Dowell Aeroelasticity of plates and shells 1975 Noordhoff International Publishing Leyden, The Netherlands
46. R.D. Cook, D.S. Malkus, M.E. Plesha, and R.J. Witt Concepts and applications of finite element analysis fourth ed. 2002 John Wiley and Sons
47. U. Adelfinger, and E. Ramm EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements Int J Numer Methods Eng 36 1993 1311 1337