A two-sided interface model for dissipation in structural systems with frictional joints
Introduction
Complex engineering structures are often composed of a multitude of components, connected by mechanical joints and interfaces, which are often give rise to a significant fraction of the overall dissipation observed in the response. This damping is associated with interfacial frictional slip, known as microslip, and is strongly amplitude dependent and hence nonlinear [1], [2], [3]. Predictive structural models therefore require an accurate representation of the behavior at and near the interface, giving rise to the experimentally observed nonlinear stiffness and damping characteristics.
The most direct method to represent microslip in a larger structural model is to resolve the interface in a finite element model [4]. Unfortunately, the small length scales required to capture the mechanics of microslip lead to a problem for which the time required to generate a computational solution is prohibitively long [5]. Thus, one is led to search for alternative representations of the dissipation induced by mechanical interfaces with larger structural models. One common technique is to incorporate the observed dissipation into a linear joint model with effective mass, damping and stiffness parameters, which must then be estimated to match experimentally observed results. However, the identified parameters are thus tied to the response of a particular test. As the forcing levels vary the identified parameters can change significantly because of the nonlinear nature of the interface dissipation—the joint model is no longer predictive.
The role of friction and microslip has been incorporated into several nonlinear reduced-order models for the joint based on descriptions of the slip interface in the joint. Menq, Bielak, and Griffin [6] develop a continuum model representing the microslip that arises in frictional dampers. Quinn and Segalman [7] consider a similar model and show that by varying the spatial distribution of the frictional intensity the predicted dissipation is representative of experimentally observed scalings. Discrete models of the interface are often based on combinations of spring-slider elements, as considered by Iwan [8], [9]. Sengalman [10] has developed a four parameter Iwan model that is capable of reproducing the qualitative properties of the joint dynamics. Meanwhile, Song, Hartwigsen, McFarland, Vakakis, and Bergman [11] have developed an adjusted Iwan beam element based on a parallel-series Iwan model that can be naturally incorporated into an existing finite element framework. With the proper identification of the model parameters, the adjusted Iwan beam element can be used to capture experimentally observed profiles for the response of jointed structures.
The present work considers a two-sided interface model based on a series-series Iwan model in which the parameters are physically motivated [7]. The model is shown to naturally decompose into an elastic and dissipative component that decouple for time-dependent external forces applied to the joint. This interface model is then incorporated into a larger structural model, following the approach taken in Song, Hartwigsen, McFarland, Vakakis, and Bergman [11]. Once embedded in the structural model the elastic and dissipative components of the joint model couple together through the forces acting on the interface. Finally, this joint model is shown to qualitatively reproduce response features of jointed structures observed experimentally.
Section snippets
A two-sided interface model
To begin consider a single series of Iwan elements, made up of interfaces and masses as shown in Fig. 1. In this model each element is assumed to be identical, with a mass , and a stiffness , respectively. The forces and , represent the shear loading applied to the masses in the component, while and ( and ) describe the forces acting on the left (right) edge of the interface. In addition, each interface is described through the frictional force . For
Characteristic scales
While the proposed interface model described above is able to represent states of partial slip, its explicit numerical solution is nonetheless restricted by prohibitively small time steps. The characteristic time and length scales of the above interface model serve to guide the model reduction.
To compare interface models of varying size, we scale the inter-element stiffness and mass by the overall static stiffness and total mass of the elastic chain, and , so that
Structural response
The ability of this interface model to represent structural damping can best be evaluated within a larger structural system. As illustrated in Fig. 13, a frictional interface joining the two rods undergoing longitudinal deformation is considered. In the monolithic structure (no joint), we consider the system to be represented by an elastic chain of discrete spring–mass elements. Here each spring and mass is assumed to be identical, with mass and stiffness , so that the total mass
Conclusions
An interface model has been presented that naturally allows for both energy dissipation and elasticity in the joint, and has been shown to capture the structural damping that arises from microslip. The model can be decomposed into a series-series Iwan system, together with an elastic chain subject to tangential loads. Based on this novel decomposition, a reduced-order model was formulated that exhibits significant computational advantages, yet nonetheless captures the energy dissipation within
Acknowledgments
This material is based upon work supported by Sandia National Laboratories through Contract number 193122, Dr. Daniel Segalman, Project Director. The authors would like to thank Dr. Segalman and Prof. Ed Berger of the University of Virginia for many helpful discussions. Finally, comments made by the reviewers and editors have greatly enhanced the clarity of the presentation.
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