Abstract
A nonlinear model of cable, able to twist, is formulated. For small sag-to-length ratios (e.g. 1/10) and technical parameter values proper to electrical transmission lines, the motion is ruled by the classical equations of the perfectly flexible cable, plus a further equation governing the twist evolution. A two degree-of-freedom system is successively obtained via a Galerkin procedure. The relevant nonlinear ODE’s are dealt with a Multiple Scale approach, under 2:1 internal resonance condition and no resonance conditions, in order to investigate Hopf bifurcations and post-critical behaviors. All the numerical results are compared with those furnished by the flexible model, and the influence of twist is discussed.
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