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Calculation of Aeroelastic Limit Cycles due to Localized Nonlinearity and Static Preload

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The presence of a static preload can significantly alter the limit cycle oscillation response of nonlinear aeroelastic systems. This paper reports a numerical study of two distinct types of preload, mechanical (i.e., independent of flow velocity) and aerodynamic (i.e., dependent on flow velocity), and their effects on limit cycle behavior. Simulations are carried out on models of a wing-with-store and an all-moving surface, respectively, with linear potential flow aerodynamics and a localized structural nonlinearity. Novel, computationally efficient methods based on dual-input describing functions are proposed and employed for calculating limit cycles, thereby generalizing earlier work that used single-input describing functions for the no-preload situation. Results are presented for a smooth nonlinearity (cubic hardening) and a nonsmooth one (classical freeplay), along with selected time marching responses. Finally, the feasibility of including nonlinear aerodynamics in the present framework is discussed.


  • [1] Norton W. J., “Limit Cycle Oscillation and Flight Flutter Testing,” Proceedings of 21st Annual Symposium, Soc. of Flight Test Engineers, Garden Grove, CA, 1990, p. 3. Google Scholar

  • [2] Denegri C. M., “Limit Cycle Oscillation Flight Test Results of a Fighter with External Stores,” Journal of Aircraft, Vol. 37, No. 5, 2000, pp. 761–769. doi: LinkGoogle Scholar

  • [3] Goodman C., Hood M., Reichenbach E. and Yurkovich R., “An Analysis of the F/A-18C/D Limit Cycle Oscillation Solution,” AIAA Paper  2003-1424, 2003. LinkGoogle Scholar

  • [4] Luber W. G., “Flutter Prediction on a Combat Aircraft Involving Backlash on Control Surfaces,” 16th International Modal Analysis Conference, Vol. 1, Soc. for Experimental Mechanics, Bethel, CT, 1998, pp. 291–299. Google Scholar

  • [5] Anderson W. and Mortara S., “Maximum Control Surface Freeplay, Design and Flight Testing Approach on the F-22,” AIAA Paper  2007-1767, 2007. LinkGoogle Scholar

  • [6] Conner M. D., Tang D. M., Dowell E. H. and Virgin L. N., “Nonlinear Behavior of a Typical Airfoil Section with Control Surface Freeplay: A Numerical and Experimental Study,” Journal of Fluids and Structures, Vol. 11, No. 1, 1997, pp. 89–109. doi: 0889-9746 CrossrefGoogle Scholar

  • [7] Lee B. H. K., Price S. J. and Wong Y. S., “Nonlinear Aeroelastic Analysis of Airfoils: Bifurcation and Chaos,” Progress in Aerospace Sciences, Vol. 35, No. 3, 1999, pp. 205–334. doi: PAESD6 0376-0421 CrossrefGoogle Scholar

  • [8] Dowell E. H., Thomas J. P., Hall C. H. and Denegri C. M., “Theoretical Predictions of F-16 Fighter Limit Cycle Oscillations for Flight Flutter Testing,” Journal of Aircraft, Vol. 46, No. 5, 2009, pp. 1667–1672. doi: LinkGoogle Scholar

  • [9] Denegri C. M., Sharma V. K. and Northington J. S., “F-16 Limit-Cycle Oscillation Analysis Using Nonlinear Damping,” Journal of Aircraft, Vol. 53, No. 1, 2016, pp. 243–250. doi: LinkGoogle Scholar

  • [10] Tang D. and Dowell E. H., “Aeroelastic Airfoil with Free Play at Angle of Attack with Gust Excitation,” AIAA Journal, Vol. 48, No. 2, 2010, pp. 427–442. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [11] Tang D. and Dowell E. H., “Aeroelastic Response Induced by Free Play, Part 1: Theory,” AIAA Journal, Vol. 49, No. 11, 2011, pp. 2532–2542. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [12] Tang D. and Dowell E. H., “Aeroelastic Response Induced by Free Play, Part 2: Theoretical/Experimental Correlation Analysis,” AIAA Journal, Vol. 49, No. 11, 2011, pp. 2543–2554. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [13] Tang D. and Dowell E. H., “Computational/Experimental Aeroelastic Study for a Horizontal-Tail Model with Free Play,” AIAA Journal, Vol. 51, No. 2, 2013, pp. 341–352. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [14] Padmanabhan M. A., Pasiliao C. L. and Dowell E. H., “Simulation of Aeroelastic Limit-Cycle Oscillations of Aircraft Wings with Stores,” AIAA Journal, Vol. 52, No. 10, 2014, pp. 2291–2299. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [15] Padmanabhan M. A., Dowell E. H., Thomas J. P. and Pasiliao C. L., “Store-Induced Limit-Cycle Oscillations due to Nonlinear Wing-Store Attachment,” Journal of Aircraft, Vol. 53, No. 3, 2016, pp. 778–789. doi: LinkGoogle Scholar

  • [16] Howcroft C., Lowenberg M., Neild S. and Krauskopf B., “Effects of Freeplay on Dynamic Stability of an Aircraft Main Landing Gear,” Journal of Aircraft, Vol. 50, No. 6, 2013, pp. 1908–1922. doi: LinkGoogle Scholar

  • [17] Laurenson R. M. and Trn R. M., “Flutter of Control Surfaces with Structural Nonlinearities,” McDonnell Douglas Astronautics Co. Technical Rept.  MDC-E1734, St. Louis, MO, 1977. Google Scholar

  • [18] Price S. J., Alighanbari H. and Lee B. H. K., “The Aeroelastic Response of a Two-Dimensional Airfoil with Bilinear and Cubic Structural Nonlinearities,” Journal of Fluids and Structures, Vol. 9, No. 2, 1995, pp. 175–193. doi: 0889-9746 CrossrefGoogle Scholar

  • [19] Hall K. C., “Eigenanalysis of Unsteady Flows About Airfoils, Cascades, and Wings,” AIAA Journal, Vol. 32, No. 12, 1994, pp. 2426–2432. doi: AIAJAH 0001-1452 LinkGoogle Scholar

  • [20] Padmanabhan M. A., “A Theoretical and Computational Study of Limit Cycle Oscillations in High Performance Aircraft,” Ph.D. Thesis, Duke Univ., Durham, NC, 2015, pp. 8–20, Chap. 2. Google Scholar

  • [21] Gelb A. and Vander Velde W. E., Multiple-Input Describing Functions and Nonlinear System Design, McGraw–Hill, 1968. Google Scholar

  • [22] Kholodar D. B., “Aircraft Control Surface and Store Freeplay-Induced Vibrations in Aeroelastic Stability Envelope,” Journal of Aircraft, Vol. 53, No. 5, 2016, pp. 1538–1548. doi: LinkGoogle Scholar

  • [23] Desmarais R. N. and Reed W. H., “Wing/Store Flutter with Nonlinear Pylon Stiffness,” Journal of Aircraft, Vol. 18, No. 11, 1981, pp. 984–987. doi: LinkGoogle Scholar