Application of Viscous and Iwan Modal Damping Models to Experimental Measurements From Bolted Structures

Abstract

Measurements are presented from a two-beam structure with several bolted interfaces in order to characterize the nonlinear damping introduced by the joints. The measurements (all at force levels below macroslip) reveal that each underlying mode of the structure is well approximated by a single degree-of-freedom (SDOF) system with a nonlinear mechanical joint. At low enough force levels, the measurements show dissipation that scales as the second power of the applied force, agreeing with theory for a linear viscously damped system. This is attributed to linear viscous behavior of the material and/or damping provided by the support structure. At larger force levels, the damping is observed to behave nonlinearly, suggesting that damping from the mechanical joints is dominant. A model is presented that captures these effects, consisting of a spring and viscous damping element in parallel with a four-parameter Iwan model. The parameters of this model are identified for each mode of the structure and comparisons suggest that the model captures the stiffness and damping accurately over a range of forcing levels.

Nonlinear modeling of structures with bolted joints: A comparison of two approaches based on a time-domain and frequency-domain solver

“…The four-parameter Iwan model was originally developed after an extensive testing and modeling campaign [2] revealed that the Coulomb model of friction was inadequate for capturing the power-law dissipation exhibited by experimental joints. This power-law relationship continues to be observed in more recent studies [5,6,36], where Iwan models were used successfully to characterize joint behavior.…”

“…The model carries a high degree of epistemic uncertainty due to this limitation, and ongoing research is attempting to address this shortcoming (see [52] for example). Nonetheless, since the dynamics of the structure as a whole is of modeling interest rather than the mechanics occurring in the joint, there is some confidence that the Iwan modal should capture the nonlinearity associated with at least one mode given the achievements of modal Iwan models [5,6]. As a whole-joint model composed of internal sliders, only a single Iwan element is sufficient to represent the hysteresis of the entire contact area.…”

“…Since Segalman's four-parameter Iwan element is one-dimensional, the virtual nodes of a whole joint model would typically be coupled with multiple Iwan elements all oriented in the different translational and rotational directions. In addition, these Iwan elements would be supplemented with springs and dashpots placed in parallel to provide linear sources of joint stiffness and damping [5]. However, it is challenging to determine a unique set of parameters for each of these elements, and, depending on the joint behavior, not all directions my be necessary.…”

“…Specifically, the parameters were tuned to reproduce the measured amplitude-dependent frequency and damping changes observed in the first bending mode from Fig.6. The precedent for tuning Iwan models to modal frequency and damping was set in [5], which also gave a procedure for tuning such models individually to the response of each mode. In this work, however, the Iwan models are in the physical space, so the projection of their nonlinearity onto each mode is not straightforward enough to employ the same tuning procedure.…”

“…However, in structures that contain more than one joint, it becomes difficult to isolate the contribution of each joint to the hysteresis observed in the measurements. As a result, subsequent works have measured the net effect of all of the joints on each mode of vibration and have tuned an Iwan element to model each structural mode, which is assumed to be uncoupled from all other modes [5,6,33]. This approach is often justified in structures that exhibit weak nonlinearities such that there is negligible change in the mode shapes of the structure [5,6] yet the natural frequency and the damping of each mode vary with amplitude.…”