On the modeling of vibration transmission over a spatially curved cable with casing

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We propose an approach to the vibration modeling of spatially curved steel wires with a casing and a contact between the outer casing and the inner steel wire. For the mathematical model of the steel wire and the outer casing, the Euler–Bernoulli beam theory with no axial pre-load is used, and for the discretisation, finite elements are used. The excitation of the steel wire and the outer casing is in the form of random kinematic excitation. For the energy dissipation the proportional viscous damping model and the structural damping model are used. The damping parameters are identified from the Nyquist diagram and from the continuous wavelet transform. For the identification of the frequency dependence of the dynamic modulus of elasticity a method is proposed that uses the measured natural frequencies and the experimentally determined natural modes. The contact between the steel wire and the outer casing is modelled using the penalty method with the friction in a tangential direction. We show that higher values of the friction coefficient have a significant influence on lowering the level of vibration transmission. The model also predicts that the dynamic modulus of the elasticity of a steel wire does not have a major influence on the level of vibration transmission, which was also validated by experiment. On the basis of an experimental validation the model of a steel wire with an outer casing proved to be suitable for the prediction of the vibration transmission.