Dynamic augmentation of geometrically nonlinear beams via guided axially elastic tendons

This paper develops a geometrically nonlinear mathematical model of a flexible cantilevered beam hosting a guided axially elastic tendon. The model is intended as an enabling tool to explore the guided tendon-based dynamic enhancement methods in application to highly flexible and lightweight structures. To both validate the model and to generate further insights, an experiment-guided study is performed on a beam-tendon configuration. Uniquely, this is done with moderately large beam deformations used to exercise nonlinearity. The model-based study of the problem identifies and reflects on the individual stiffness-modulating terms corresponding to various geometrical and axial elasticity-driven mechanisms. The susceptibility to these individual modulating mechanisms is shown to vary between different groups of modes. These are systematically identified using contrasting frequency variations created by the different mechanisms. The second novel aspect of this research is the treatment of the resistive effects posed by the guides on the tendon’s axial movement. It is shown that the progressive locking of the tendon’s motion with increased guide impedance results in higher extents of stiffening due to the segmented activation of the tendon’s elasticity. It is further demonstrated that the effective tailoring of the impedance posed by the guides can be used to generate dynamically optimal conditions. This is illustrated for the specific case of modal damping maximisation, assuming guide-impedance originating in the form of viscous damping. Given these insights, this research recognises potential extensions of the axially activated tendon for vibration suppression applications.