Dynamic Response Of Two Interacting Extensible Barsin Frictional Contact

Abstract

In this paper, a new model is developed to describe the nonlinear dynamics of twoaxially deformable bars sliding relative to each other in which the interaction is governed byfriction. The first bar is fixed at one end and is subjected to a distributed normal force perpen-dicular to its axis to activate friction at the common interface, while the second bar is allowed toslide relative to the fixed one. A semi-analytical solution method is developed in which only thenonlinear interaction is addressed numerically. The dynamic behaviour of the bars is expressedas a summation of vibration modes including the necessary rigid body mode to allow for thepermanent sliding of one bar relative to the other. This results in a computationally efficientscheme without compromising the accuracy of the solutions. The developed model can be usedin pile driveability studies. In this case the fixed bar resembles the soil column while the secondbar describes the dynamics of the driven pile.