Rotating cable structures
experiment and theory
Springer Online Journal Archives 1860-2000
Abstract The combined effect of gravity and a centrifugal field on the dynamics of a heavy cable with negligible bending stiffness is treated. The inextensible length of the cable is preassigned in such a way that the cross-sectional shape of the cable structure is circular if the contiguration rotates about its central axis with a constant speed and no external forces act. Under the additional influence of gravity, complicated nonlinear weight-excited vibrations occur. To understand the variety of vibrational phenomena. The dynamic system is studied by some experiments first. In order to explain the experimental results theoretically, the governing nonlinear boundary value problem is derived next. Subsequently, an appropriate variational formulation for application of a Rayleigh Ritz procedure is suggested. The resulting nonlinear ordinary differential equations approximately deseribe a part of the observed vibrational behaviour. Both the experiments and the calculations demonstrate that, for high speeds, nonlinear weight-excited vibrations about the circular reference configuration occur. On the other hand, for low velocitites, periodie and even chaos-like snap-through phenomena appear.
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