Non-linear normal modes of plane cable trusses

•Non-linear dynamic model for plane cable-truss, based on sinusoidal shape functions.•Harmonic approach to describe periodic orbits of generalised coordinates.•Non-linear normal modes calculated as a continuation of linear modes.•Numerical experiments provide: the evolution of generalised coordinates in the phase-space, non– linear behaviour in configuration space and frequency-displacement relationships. A model for the non-linear dynamic behaviour of pre-stressed cable trusses is presented. The model provides the basis for a simplified description of the (in-plane) non-linear dynamical behaviour of biconcave and bi-convex cable structures (as well as of single cables) subject to different loading (and mass distribution) conditions. The simplicity of the proposed approach is coupled with its ability to schematically represent a wide range of actual structures, including light pedestrian suspended cable bridges and cable roofs with vertical harnesses, under different vertical loading conditions. Although aiming at the needs of the practitioner, in search for a simplified and intuitive understanding of the effects of nonlinearities on the dynamic response of cable structures (to confirm and explain results from more detailed FEM models), the proposed approach also paves the way for the investigation in the extensive taxonomy of the non-linear dynamic behaviour of cable structures. The present paper focuses on non-linear normal modes (NNMs) arising as a continuation of linear vibration modes of the structure when energy is increased. The identification of non-linear normal modes is achieved through harmonic balance; a time-integration analysis is then performed on the same model, with initial conditions derived from the harmonic balance approach, demonstrating consistent results. To further test the model, its behaviour is compared to simulations on a 66-degrees of freedom finite element truss model, with satisfactory results.