19. Towards an Understanding of the Transient Behavior of the Five-Parameter Iwan-Type Model

Mignolet (J Sound Vib 349:289–298, 2015) demonstrated mathematically that his proposed five-parameter Iwan-type model weakens the coupling between the change in effective stiffness and change in effective damping of the model as vibration amplitude changes. Several experimental studies on bolted-joint structures have experienced difficulty in fitting a traditional Iwan model to match measurements, so this advantage is sorely needed. However, Mignolet’s work only considered steady-state harmonic motion, and the stiction behavior of the internal sliders was not studied in great detail. In this work, the force-constitutive formulation of the five-parameter Iwan-type model is implemented computationally and then examined to understand its behavior in more general transient scenarios. The five-parameter model is found to have a complicated dependence on its displacement history. If the model reaches a maximum steady-state displacement after a ring-up response (such as occurs when the system is excited at resonance by a shaker), the stiffness and damping it exhibits is consistent with those formulated by Mignolet. When the vibration decays below the maximum-achieved displacement, however, the effective stiffness and damping revert to power-law behavior with amplitude. The power-law behavior is functionally similar to that of the four-parameter Iwan model (on which the five-parameter model is based), so the advantage of the weakened coupling between the stiffness and damping is lost in a ring-down response.