Mathematical modeling of linearly-elastic non-prestrained cables based on a local reference frame

Cables are widely used and serve different purposes in engineering. This paper aims to formulate a general dynamic model on extensible non-prestrained cables under external forces. In terms of the Hamilton's principle, the governing equation and boundary conditions are achieved according to the variation of action integral. Meanwhile, the local reference frame of the cable curve is illustrated which is composed of four vectors. In the presented model, it is shown that the external force along the binormal direction could not be balanced by the internal tensile force of the cable itself. And the curved cable will result in an elastic force in the normal direction which is in a linear relationship with the curvature of the cable. Further, this approach is applied to cables under uniformly distributed loads or self-weights. The contours and internal tensile forces of the cables are figured out by means of numerical methods. The developed model is evaluated by means of experimental data in published literature. The good agreement between the numerical and experimental results shows that the presented method is feasible in theory.