Abstract
The influence of two-to-one internal or autoparametric resonances on the nonlinear response of metallic and composite structures subjected to a harmonic excitation has been investigated theoretically and experimentally. The experimental observations are in good agreement with the theoretical predictions. When the excitation frequency is near the natural frequency of the second flexural mode, the autoparametric resonance gives rise to the saturation phenomenon and two-period quasi-periodic and chaotically modulated motions.
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References
Nayfeh, A. H.; Balachandran, B.: Modal Interactions in dynamical and structural systems. Appl. Mech. Rev. (in press).
Sethna, P. R.: Vibrations of dynamical systems with quadratic nonlinearities. J. Appl. Mech. 32 (1965) 576–582.
Nayfeh, A. H.; Mook, D. T.; Marshall, L. R.: Nonlinear coupling of pitch and roll modes in ship motions. J. Hydronautics 7 (1973) 145–152.
Yamamoto, T.; Yasuda, k.; Nagasaka, I.: On the internal resonance in a nonlinear two-degree-of-freedom system (forced vibrations near the high resonance point when the natural frequencies are in the ratio 1:2). Bull. Jap. Soc. Mech. Engg. 20 (1977) 1093–1101.
Hatwal, H.; Mallik, A. K.; Ghosh, A.: Forced nonlinear oscillations of an autoparametric system - Part 2: Chaotic responses. J. Appl. Mech. 50 (1983) 663–668.
Haddow, A. G.; Barr, A. D. S.; Mook, D. T.: Theoretical and experimental study of modal interaction in a two-degree-of-freedom structure. J. Sound and Vib. 97 (1984) 451–473.
Miles, J. W.: Resonantly forced motion of two quadratically coupled oscillators. Physica D. 13 (1984) 247–260.
Nayfeh, A. H.; Zavodney, L. D.: Experimental observation of amplitude-and phase-modulated responses of two internally coupled oscillators to a harmonic excitation. J. Appl. Mech. 55 (1988) 706–711.
Nayfeh, A. H.: Application of the method of multiple scales to nonlinearly coupled oscillators, In Lasers, Molecules and Methods, Hirschfelder, J. O.; Wyatt, R. E.; Coalson, R. D. (eds.), New York: Wiley 1989.
Nayfeh, A. H.; Raouf, R. A.: Nonlinear forced response of infinitely long circular cylindrical shells. J. Appl. Mech. 54 (1987) 571–577.
Nayfeh, A. H.; Balachandran, B.; Colbert, M. A.; Nayfeh, M. A.: An experimental investigation of complicated responses of a two-degree-of-freedom structure. J. Appl. Mech. (in press).
Nayfeh, A. H.; Balachandran, B.: Experimental investigation of resonantly forced oscillations of a two-degree-of-freedom structure. Int. J. Non. Mech. (in press)
Balachandran, B; Nayfeh, A. H.: Nonlinear oscillations of a harmonically excited composite structure, submitted to Journal of Composite Structures.
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© 1990 Springer-Verlag Berlin Heidelberg
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Nayfeh, A.H., Balachandran, B. (1990). A Theoretical and Experimental Investigation of the Influence of Modal Interactions on the Nonlinear Response of Structures. In: Schiehlen, W. (eds) Nonlinear Dynamics in Engineering Systems. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83578-0_28
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DOI: https://doi.org/10.1007/978-3-642-83578-0_28
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