Mathematical and numerical evaluation of the damping behaviour for a multi-strand bar

Multi-strand systems include, but are not limited to, electrical wire conductors, structural cables, and some composite reinforcements. These systems (apart from composite reinforcements) are generally metallic for a variety of reasons. One often overlooked advantage is that dry friction between metal contacts can provide damping over significantly wider temperature ranges than is typical for common damping materials such as viscoelastic polymers. This paper, proposes a mathematical model that describes the hysteretic vibrational behaviour of a frictionally constrained multi-strand bar constructed from strands that have a circular cross-section. The mathematical model analytically predicts the frictional system stiffness under simply supported boundary conditions. The assembled strands are numerically simulated using finite elements and hysteresis behaviour is compared to that obtained from the mathematical model. This shows that the mathematical model is capable of predicting the stiffness and the force-displacement hysteresis response of the system for a variety of conditions.