Three-Dimensional Dynamic Modelling and Validation for Vibration of a Beam-Cable System

In order to understand and to predict cable effects on structures, three-dimensional numerical models for a stranded cable and a beam–cable system consisting of a cantilever beam and two connected cables are presented. The multibond graph formalism is used to model the coupled cable–beam system, with the cable and beam substructures using 3D rigid lumped segments. The stranded cables are modelled considering the bending stiffness, tension and sag due to self-weight. The generally applicable cable-structure modelling approach in this paper is applied to vibration-based non-destructive evaluation of electrical utility poles, where simulated modal testing of the pole-conductor system is required. Experimental parametrization of a stranded cable is carried out using specially designed apparatus to accurately measure the bending stiffness at different tensions, and to measure the axial stiffness and axial damping. A reduced-scale lab set-up and finite element models are developed for verification of the numerical models. Experimental free and forced vibration testing is performed on individual cantilever beam and stranded cable subsystems, and on the coupled cable–beam system to verify the numerical models in the frequency and time domains. It is concluded that the 3D bond graph models can be used to understand the interaction between cable and structure, allowing prediction of the in-plane and out-of-plane natural frequencies and time response of the connected pole. It is also concluded that by adding the cable to the pole structure, some modes emerge in the eigenvalue solution of the system which may be categorized as cable-dominated modes, pole-dominated or hybrid modes.