Parametric excitation of subharmonic oscillations
- 73 Downloads
Subharmonic oscillations of order one-half for a single-degree-of-freedom system with quadratic, cubic, and quartic nonlinearities under parametric excitation are investigated. Two approximate methods (multiple scales and generalized synchronization) are used for comparison. The modulation equations (reduced equations) of the amplitudes and the phases are obtained. Steady-state solutions (periodic solutions) and their stability are determined. Numerical solutions are carried out, and graphical representations of the results are presented and discussed. The results obtained by the two methods are in excellent agreement.
KeywordsPeriodic Solution Multiple Scale Parametric Excitation Generalize Synchronization Jump Phenomenon
Unable to display preview. Download preview PDF.
- Evan-Iwanowski, R. M. (1976).Resonance Oscillations in Mechanical Systems, Elsevier, New York.Google Scholar
- Gerald, C. F. (1980).Applied Numerical Analysis. Addison-Wesley, Reading, Massachusetts.Google Scholar
- Haag, J. (1962).Oscillatory, Motions, Wadsworth.Google Scholar
- Ibrahim, R. A. (1985).Parametric Random Vibration Wiley-Interscience, New York.Google Scholar
- Nayfeh, A. H., and Mook, D. T. (1979).Nonlinear Oscillations, Wiley-Interscience, New York.Google Scholar
- Schmidt, G., and Tondl, A. (1986).Nonlinear Vibrations, Akademie-Verlag, Berlin.Google Scholar
- Zavodney, L. D. (1987). A theoretical and experimental investigation of parametrically excited nonlinear mechanical systems, Ph. D. Dissertation, Virgnia Polytechnic Institute and State University.Google Scholar