Abstract
A uniform, free-free, Euler-Bernoulli beam, transporting a concentrated mass with rotary and transverse inertia, is driven by a follower force with controlled direction. A finite element model of the beam transverse motion in the plane is formulated through the extended Hamilton's principle. The stability of the model is investigated with respect to (i) the axial location and the inertia of the concentrated mass, (ii) the location of the follower force direction control sensor, (iii) the sensor gain, and (iv) the magnitude of the constant follower force. Both divergence and flutter instabilities can occur over the range of beam models examined. The analysis predicts the location and the magnitude of the additional mass, and the location and the gain of the follower force direction sensor that permits the follower force magnitude to be maximized for stable transverse motion of the beam.
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