Abstract
Although the study of internal resonance in mechanical systems has been given significant consideration, minimal attention has been given to internal resonance for systems which consider the presence of aerodynamic forces. Herein, the investigators examine the possible existence of internal resonances, and the related nonlinear pathologies that such responses may have, for an aeroelastic system which possesses nonlinear aerodynamic loads. Evidence of internal resonance is presented for specific classes of aeroelastic systems, and such adverse response indicates nonlinearities may lead to aeroelastic instabilities that are not predicted by traditional (linear) approaches.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Nayfeh, A. H. and Mook, D. T., Nonlinear Oscillations, Wiley, New York, 1979.
Nayfeh, A. H. and Balachandran, B., ‘Modal interactions in dynamical and structural systems’, ASME Applied Mechanics Review 42(11) Part 2, 1989, S175–S201.
Tuer, K. L., Golnaraghi, M. F., and Wang, D., ‘Development of a generalized active vibration suppression strategy for a cantilever beam using internal resonance’, Nonlinear Dynamics 5, 1994, 131–151.
Nayfeh, A. H., ‘Parametric excitation of two internally resonant oscillators’, Journal of Sound and Vibration 119(1), 1987, 95–109.
Tuer, K. L., Duquette, A. P., and Golnaraghi, M. F., ‘Vibration control of a flexible beam using a rotational internal resonance controller, Part I: Theoretical development and analysis’, Journal of Sound and Vibration 167(1), 1993, 41–62.
Bajaj, A. K., Davies, P., and Chang, S. I., ‘On internal resonances in mechanical systems’, in Nonlinear Dynamics and Stochastic Mechanics, CRC Mathematical Modeling Series, W. Kliemann and N. Namachchivaya (eds.), CRC Press, Boca Raton, FL, 1995, pp. 69–94.
Cheung, Y. K. and Xu, Z., ‘Internal resonance of strongly nonlinear autonomous vibrating systems with many degrees-of-freedom’, Journal of Sound and Vibration 180(2), 1995, 229–238.
Nayfeh, A. H. and Balachandran, B., Applied Nonlinear Dynamics, Wiley, New York, 1995.
Cole, S. R., ‘Effects of spoiler surfaces on the aeroelastic behavior of a low-aspect ratio wing’, in Proceedings of the 31st AIAA Structures, Structural Dynamics, and Materials Conference, AIAA, New York, 1990, AIAA Paper 90-0981, pp. 1455–1463.
Oh, K., Nayfeh, A. H., and Mook, D. T., ‘Modal interactions in the forced vibration of a cantilever metallic plate’, Nonlinear and Stochastic Dynamics, ASME 78, 1994, 237–247.
O'Neil, T. G. and Strganac, T. W., ‘An experimental investigation of nonlinear aeroelastic response’, AIAA Journal of Aircraft 35(4), 1998, 616–622.
O'Neil, T., Gilliatt, H. C., and Strganac, T. W., ‘Investigations of aeroelastic response for a system with continuous structural nonlinearities’, in Proceedings of the 37th AIAA Structures, Structural Dynamics, and Materials Conference, AIAA, New York, 1996, AIAA Paper 96-1390.
Woolston, D. S., Runyan, H. L., and Andrews, R. E., ‘An investigation of effects of certain types of structural nonlinearities on wing and control surface flutter’, Journal of Aeronautical Sciences 24(1), 1957, 57–63.
Price, S. J., Alighanbari, H., and Lee, B. H. K., ‘The aeroelastic response of a two-dimensional airfoil with bilinear and cubic structural nonlinearities’, in Proceedings of the 35th AIAA Structures, Structural Dynamics, and Materials Conference, AIAA, New York, 1994, AIAA Paper 94-1546, pp. 1771–1780.
Jones, D. J. and Lee, B. H. K., ‘Time marching numerical solution of the dynamic response of nonlinear systems’, National Aeronautical Establishment, Aeronautical Note 25, National Research Council (Canada) No. 24131, Ottawa, Ontario, Canada, 1985.
Hauenstein, J., Laurenson, R. M., Eversman, W., Galecki, G., Qumei, I., and Amos, A. K., ‘Chaotic response of aerosurfaces with structural nonlinearities’, in Proceedings of the 31st AIAA Structures, Structural Dynamics, and Materials Conference, AIAA, New York, 1990, AIAA Paper 90-1034, pp. 1530–1539.
Price, S. J., Alighanbari, H., and Lee, B. H. K., ‘Postinstability behavior of a two-dimensional airfoil with a structural nonlinearity’, Journal of Aircraft 31(6), 1994, 1395–1401.
Zhao, L. C. and Yang, Z. C., ‘Chaotic motions of an airfoil with non-linear stiffness in incompressible flow’, Journal of Sound and Vibration 138(2), 1990, 245–254.
Tang, D. M. and Dowell, E. H., ‘Flutter and stall response of a helicopter blade with structural nonlinearity’, Journal of Aircraft 29, 1992, 953–960.
Tang, D. M. and Dowell, E.H., ‘Comparison of theory and experiment for non-linear flutter and stall response of a helicopter blade’, Journal of Sound and Vibration 165(2), 1993, 251–276.
Dowell, E. H., Curtiss, H. C., Jr., Scanlon, R. H., and Sisto, F., A Modern Course in Aeroelasticity, Kluwer, Dordrecht, 1989.
Fung, Y. C., An Introduction to the Theory of Aeroelasticity, Wiley, New York, 1955.
Sheldahl, R. E. and Klimas, P. C., ‘Aerodynamic characteristics of seven airfoil sections through 180 degrees of attack for use in aerodynamic analysis of vertical axis wind turbines, SAND80-2114’, Sandia National Laboratories, Albuquerque, NM, 1981.
Nayfeh, A. H., Perturbation Methods, Wiley, New York, 1973.
Gilliatt, H. C., ‘Investigations of internal resonance phenomena and related nonlinear pathologies in aeroelastic systems’, M.S. Thesis, Texas A&M University, 1997.
Craig, R. R., Structural Dynamics: An Introduction to Computer Methods, Wiley, New York, 1981.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gilliatt, H.C., Strganac, T.W. & Kurdila, A.J. An Investigation of Internal Resonance in Aeroelastic Systems. Nonlinear Dynamics 31, 1–22 (2003). https://doi.org/10.1023/A:1022174909705
Issue Date:
DOI: https://doi.org/10.1023/A:1022174909705