Abstract
Coulomb friction is common in many engineering systems. This friction introduces a non-linearity that makes analysis of these systems more challenging. Recently, there has been an increased interest in developing new efficient analysis tools that can predict the steady-state response of mechanical systems with friction. The purpose of this work is to address the large computational time required by current techniques by introducing an alternative computation-ally efficient method. The proposed methodology deconstructs the overall nonlinear response into different time intervals, where in each response is linear. Compatibility constraints are used to couple each linear response to obtain a full nonlinear vibration response cycle. This new technique is called the friction response approximation method and is applied to a single degree of system, and a three degree of freedom system. The results show an accurate prediction of the vibration response in comparison with time integration, while requiring much less computational time.