New Frontiers in Cable Mechanics: Modeling and Design of a Smart Cable

The galloping instability of a suspended shallow flexible cable (possibly ice-accreted) has been studied via a linear continuum model. The cable is suspended from the same level of two supports and modeled as a linear one-dimensional structure embedded in a three-dimensional space. External and internal damping are considered according to the Rayleigh model of damping, and the aerodynamic forces are modeled under the assumption of quasi-steady theory. Two critical galloping modes, in-plane and out-of-plane components, have been studied through an exact analysis by solving a boundary value problem. An analytical analysis, through a straight-forward perturbation method has been applied to analyze the galloping phenomenon in three resonance conditions: non-resonant, one-one resonant and one-one-one resonant cases. Lastly, two numerical approaches have also been employed, and the outcomes have been compared with the exact and analytical solutions, presented with figures and tables. The insight is that the coupling leads to either lower or higher critical velocities compared with the prediction made by the simplified planar model. Parallelly, a piezoelectric damper has been designed to control the vibration of a straight single cable structure, tuned with the shunt circuits. The optimal placement of the damper, and optimization of geometrical and mechanical parameters have been described. The control procedure and performance of the damper in terms of longitudinal and transversal vibrations are presented. It is noticed that the LR and NC-R shunts show remarkable suppression of vibrations. An energy harvester has also been designed and the energy has been harvested from the structure as electric power. The harvester has been analyzed in terms of frequency, electric load resistance, and acceleration dependence. The amount of energy extracted from the PVDF energy harvester is low as the input mechanical energy is low due to the hardness of the flexible cable to transfer deformation to the piezoelectric tube and the dissipation of energy through the circuit.