Simulation of Nonlinear Systems Having Series and Parallel Friction Elements

The numerical response of a SDOF oscillator with a friction element and spring in series is investigated. The connection between the friction element and the spring is massless resulting in an ideal “Iwan element,” also termed an elastic/perfectly-plastic element. A methodology is proposed that avoids the complications caused by hysteresis, allowing the system to be simulated using relatively simple programming logic. A notable feature of the technique is that it yields a functional relation for the friction force that depends on the present value of the state vector, rather than on prior history of the motion. The method introduces a small, “fictitious” slider mass within the Iwan element. Simulations are presented to show how the relative size of the slider mass affects the trade off between accuracy and computational costs. It is seen that the results of the method are very accurate and easy to implement. It is also shown that the added numerical stiffness associated with the high-frequency dynamics of the slider mass can be alleviated through use of a switchable viscous damping term. The viscous damping term decreases the number of timesteps required for simulation without adversely affecting the accuracy. The paper considers SDOF systems having a single Iwan-element as well as multiple Iwan elements.