NON-LINEAR DYNAMICS OF THE FOLLOWER-LOADED DOUBLE PENDULUM WITH ADDED SUPPORT-EXCITATION

✍ Scribed by J.S. Jensen

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 298 KB
• Volume: 215
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1998.1620

✦ Synopsis

The partially follower-loaded elastic double pendulum subjected to excitation of the support, parallel to the straight upright pendulum position, is studied. The effect of small-amplitude off-resonant (high-frequency) excitation on the linear stability and non-linear behaviour of the pendulum, is examined. By use of the method of direct partition of motion (DPM) [1] (Blekhman, 1994, Vibrational Mechanics), the model equations are transformed into autonomous equations with the high-frequency excitation approximated by equivalent static forces. Linear stability analysis shows that the support-excitation has a stabilizing effect for most system parameters, but can also destabilize the upright pendulum position in certain situations. Local post-and pre-critical non-linear behaviour is analyzed by using centre manifold reduction and normal forms. Support-excitation is seen to change the bifurcational behaviour qualitatively: e.g., supercritical bifurcations may change to become subcritical. Chaotic behaviour of the pendulum is shown to exist for a wider range of system parameters and initial conditions with added support-excitation, compared to the case of a fixed support.