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Dynamics of traveling, inextensible cables. (English) Zbl 1121.74306

Summary: The closed-form solution for rigid-body motions of two-dimensional traveling, sagged cables with a nonlinear geometrical constraint is developed. This closed-form solution shows that the rigid-body motions are always stable even if the translation speed is over the critical speed. With increasing translation speed, the translation motion effects on the cable increase accordingly. When the translation speed is much greater than the critical speed, the vibration effects compared to the translation motion effects can be ignored. Therefore, for an infinite translation speed, the initial and dynamic configurations for the inextensible cable are identical. The dynamic configuration of the inextensible cables is obtained in this paper, which provides a basis to get the dynamic responses of sagged, elastic cables.

MSC:

74H05 Explicit solutions of dynamical problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
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