In-plane free vibrations of small-sag inclined cables considering bending stiffness with applications to cable tension identification

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This study proposed an analytical model to characterize in-plane free vibration of a cable considering sags, inclined angles, and non-negligible bending stiffness to enhance the accuracy and efficiency of vibration analysis and health monitoring of cable structures under complex engineering environments. The static equilibrium configuration of the cable is derived, and the singularity at boundary regions is elucidated in detail. The analytical solution of the dynamical control equation is obtained using the successive approximation method. The influences of the sags, inclined angles, and bending stiffness on eigenfrequencies and mode shapes are individualy studied via introducing three non-dimensional parameters. The analytical model is further examined through parametric anaysis. As a typical extension, the model is used to establish a cable tension identification method, in which an inverse problem is solved by the trust-region-dogleg technique. The identification method is verified through comparisons with existing methods established based on classical string vibration theory and various numerical methods, e.g., finite element method and finite difference method. Validations are made by using experimental outcomes, on which the data collected from both an experiment in laboratory and a field experiment in the Poyanghu bridge are used for comparison. It is found that the proposed model along with the method is able to capture precise vibration features and identify cable tensions accurately in favor of the improvement of cable condition monitoring and health management in fields such as bridge engineering.