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. (C) 1998 Academic Press. [References: 23]
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