BIFURCATIONS OF APPROXIMATE HARMONIC BALANCE SOLUTIONS AND TRANSITION TO CHAOS IN AN OSCILLATOR WITH INERTIAL AND ELASTIC SYMMETRIC NONLINEARITIES
✍ Scribed by A.A. AL-QAISIA; M.N. HAMDAN
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 516 KB
- Volume
- 244
- Category
- Article
- ISSN
- 0022-460X
No coin nor oath required. For personal study only.
✦ Synopsis
The local stability of approximate periodic solutions and period-doubling bifurcations in a harmonically forced non-linear oscillator with symmetric elastic and inertia non-linearities are studied analytically and numerically. Approximate principal resonance solutions are "rst obtained using a two-term harmonic balance and then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict zones of symmetry breaking leading to period-doubling bifurcation and chaos. The results of the present work, which follows the analysis approach presented by Szemplinska-Stupnika (1986 International Journal of Nonlinear Mechanics 23, 257}277; 1987 Journal of Sound and <ibration 113, 155}172) are veri"ed for selected system parameters by numerical simulations using methods of qualitative theory, and good agreement was obtained between the analytical and numerical results. Finally, a criterion for the period-doubling bifurcation is proposed analytically, for this type of oscillator, and compared with computer simulation results that predict the true period-doubling bifurcation and chaos boundaries.