Nonlinear System Identification for Joints Including Modal Interactions

Abstract

Even with the best available simulation tools, it is still not possible to predict the effective stiffness and damping of bolted interfaces. Hence, it is currently necessary to identify models for these non-linear structures experimentally. One approach is to assume that the modes are decoupled and to fit a non-linear model to match the response for each mode in isolation. This modal approach has found to be suitable for systems with very weak non-linearities. However, it has been observed that in many assembled structures, the multiple modes of jointed structures can interact non-linearly and become coupled. This work focuses on the micro-slip regime where the coupling is weak, and investigates ways to extend existing approaches to this more general case. Two methods are proposed: (i) generating multi-modal maps of instantaneous natural frequency and damping as a function of the modal amplitudes; (ii) fitting polynomial models including coupling terms between the modes using the Restoring Force Surface Method. The proposed techniques were tested against data from a simulated 2DOF non-linear system representative of a simple jointed structure with a discrete non-linearity. This analysis was then extended to the particular case of a 3DOF system where only 2 modes are coupled by a non-linearity. It was found that both approaches were able to capture the modal coupling to a suitable accuracy for smooth non-linearities, although the modal-map approach generally performed slightly better than the Restoring Force Surface Method. However, both approaches had considerably higher errors when the non-linearity was discontinuous. This work suggests that both approaches warrant further investigation.