Free vibration and stability analysis of a cantilever beam axially loaded by an intermittently attached tendon

Free vibration and stability analysis of the system consisting of the Euler–Bernoulli beam axially loaded by a tendon is studied in the paper. The tendon is attached to the cantilever beam at the tip as well as in several spanwise locations using mechanical attachment points. This novel beam-tendon system is modelled using a set of partial differential equations and the coupling between the beam and the tendon is ensured by the boundary and continuity conditions. Computational free vibration analysis is conducted using a boundary value problem solver and the results are thoroughly experimentally validated using a bench-top experiment. In particular, the effect of the number of the attachment points and their location on the frequency-loading diagram of the beam-tendon system is investigated for the first time. It is found that the applied axial load causes a frequency shift of beam-dominated natural frequencies, and frequency loci veering between beam-dominated and tendon-dominated modes. Both of these features are shown to be dependent on a number and location of the attachment points. In addition, the effect of the attachment points on the structural stability of the system is numerically studied and it is observed that the critical force of the system with the intermittently attached tendon is always higher than for the system with no attachment points.