Abstract
We present a collection of experimental results on the influence of modal interactions (i.e., internal or autoparametric resonances) on the nonlinear response of flexible metallic and composite structures subjected to a range of resonant excitations. The experimental results are provided in the form of frequency spectra, Poincaré sections, pseudo-phase planes, dimension calculations, and response curves. Experimental observations of transitions from periodic to chaotically modulated motions are also presented. We also discuss relevant analytical results. The current study is also relevant to other internally resonant structural systems.
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References
Nayfeh A. H. and Balachandran B., ‘Modal interactions in dynamical and structural systems’, Applied Mechanics Reviews 42(11), 1989, 175–202.
Nayfeh A. H. and Mook D. T., Nonlinear Oscillations, Wiley-Interscience, New York, 1979.
Haddow A. G., Barr A. D. S., and Mook D. T., ‘Theoretical and experimental study of modal interaction in a two-degree-of-freedom structure’, Journal of Sound and Vibration 97, 1984, 451–473.
Nayfeh A. H. and Zavodney L. D., ‘Experimental observation of amplitude- and phase-modulated responses of two internally coupled oscillators to a harmonic excitation’, Journal of Applied Mechanics 55, 1988, 706–711.
Nayfeh A. H. and Balachandran B., ‘Experimental investigation of resonantly forced oscillations of a two-degree-of-freedom structure’, International Journal of Nonlinear Mechanics 25(2), 1990, 199–209.
Nayfeh A. H., Balachandran B., Colbert M. A., and Nayfeh M. A., ‘An experimental investigation of complicated responses of a two-degree-of-freedom structure’, Journal of Applied Mechanics 56(4), 1989, 960–967.
Balachandran B. and Nayfeh A. H., ‘Nonlinear motions of a beam-mass structure’, Nonlinear Dynamics 1, 1990, 39–61.
Balachandran B. and Nayfeh A. H., ‘Nonlinear oscillations of a harmonically excited composite structure’, Composite Structures 16(4), 1990, 323–339.
Balachandran, B., ‘A theoretical and experimental study of modal interactions in resonantly forced structures’, Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, U.S.A., 1990.
Sethna P. R., ‘Vibrations of dynamical systems with quadratic nonlinearities’, Journal of Applied Mechanics 32, 1965, 576–582.
Nayfeh A. H., Mook D. T., and Marshall L. R., ‘Nonlinear coupling of pitch and roll modes in ship motions’, Journal of Hydronautics 7, 1973, 145–152.
Miles J. W., ‘Resonantly forced motion of two quadratically coupled oscillators’, Physica 13D, 1984, 247–260.
Nayfeh A. H. and Raouf R. A., ‘Non-linear oscillation of circular cylindrical shells’, International Journal of Solids and Structures 23, 1987, 1625–1638.
Nayfeh A. H., ‘Application of the method of multiple scales to nonlinearly coupled oscillators’, In Lasers, Molecules, and Methods, edited by J. O. Hirschfelder, R. E. Wyatt, and R. D. Coalson, Wiley, New York, 1989, 137–196.
Nayfeh A. H., ‘On the undesirable roll characteristics of ships in regular seas’, Journal of Ship Research 32, 1988, 92–100.
Mook D. T., Plaut R. H., and HaQuang N., ‘The influence of an internal resonance on non-linear structural vibrations under subharmonic resonance conditions’, Journal of Sound and Vibration 102, 1985, 473–492.
Nayfeh A. H., ‘Parametric excitation of two internally resonant oscillators’, Journal of Sound and Vibration 119, 1987, 95–109.
Nayfeh, A. H., Raouf, R. A., and Nayfeh, J. F., ‘Nonlinear response of infinitely long circular cylindrical shells to subharmonic radial loads’, Journal of Applied Mechanics, 1991, in press.
Nayfeh A. H. and Nayfeh J. F., ‘Surface waves in closed basins under principal and autoparametric resonances’, Physics of Fluids A 2, 1990, 1635–1648.
Nayfeh, A. H. and Zavodney, L. D., ‘The response of two-degree-of-freedom systems with quadratic non-linearities to a combination parametric resonance’, Journal of Sound and Vibration 107, 329–350.
Mook D. T., HaQuang N., and Plaut R. H., ‘The influence of an internal resonance on non-linear structural vibrations under combination resonance conditions’, Journal of Sound and Vibration 104, 1985, 229–241.
Streit D. A., Bajaj A. K., and Krousgrill C. M., ‘Combination parametric resonance leading to periodic and chaotic response in two-degree-of-freedom systems with quadratic non-linearities’, Journal of Sound and Vibration 124, 1988, 297–314.
Moon F. C., Chaotic Vibrations: An Introduction for Applied Scientists and Engineers, Wiley-Interscience, New York, 1987.
Nayfeh A. H. and Raouf R. A., ‘Nonlinear forced response of infinitely long circular cylindrical shells’, Journal of Applied Mechanics 54, 1987, 571–577.
Froehling H., Crutchfield J. P., Farmer D., Packard N. H., and Shaw R., ‘On determining the dimension of chaotic flows’, Physica 3D, 1981, 605–617.
Roux J. C., Simoyi R. H., and Swinney H. L., ‘Observation of a strange attractor’, Physica 8D, 1983, 257–266.
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Balachandran, B., Nayfeh, A.H. Observations of modal interactions in resonantly forced beam-mass structures. Nonlinear Dyn 2, 77–117 (1991). https://doi.org/10.1007/BF00053831
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DOI: https://doi.org/10.1007/BF00053831