Abstract
The results of an experimental and theoretical investigation of the dynamics of a thin elastic rod are presented. Regular, planar motions of the rod are observed to become unstable in wedge-shaped regions of the forcing frequency-forcing amplitude parameter plane. Inside of these wedges, motions are nonplanar and generally chaotic. Fractal dimension calculations from experimental data indicate that the dynamics of the rod may be modelled by between two and six degrees of freedom. A family of asymmetric bending-torsion nonlinear modes are discovered experimentally, and their frequency-amplitude characteristic is obtained. A two degree-of-freedom system is derived by starting with a geometrically exact linearly elastic rod theory and projecting onto the first bending and torsional modes. Numerical simulations indicate that this two-mode model exhibits much of the behavior observed experimentally.
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