Michael James Starr

Handbook on dynamics of jointed structures.

The problem of understanding and modeling the complicated physics underlying the action and response of the interfaces in typical structures under dynamic loading conditions has occupied researchers for many decades. This handbook presents an integrated approach to the goal of dynamic modeling of typical jointed structures, beginning with a mathematical assessment of experimental or simulation data, development of constitutive models to account for load histories to deformation, establishment of kinematic models coupling to the continuum models, and application of finite element analysis leading to dynamic structural simulation. In addition, formulations are discussed to mitigate the very short simulation time steps that appear to be required in numerical simulation for problems such as this. This handbook satisfies the commitment to DOE that Sandia will develop the technical content and write a Joints Handbook. The content will include: (1) Methods for characterizing the nonlinear stiffness and energy dissipation for typical joints used in mechanical systems and components. (2) The methodology will include practical guidance on experiments, and reduced order models that can be used to characterize joint behavior. (3) Examples for typical bolted and screw joints will be provided.

Application of viscous and Iwan modal damping models to experimental measurements from bolted structures

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. As a result, 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.

Relationships among certain joint constitutive models.

In a recent paper, Starr and Segalman demonstrated that any Masing model can be represented as a parallel-series Iwan model. A preponderance of the constitutive models that have been suggested for simulating mechanical joints are Masing models, and the purpose of this discussion is to demonstrate how the Iwan representation of those models can yield insight into their character. In particular, this approach can facilitate a critical comparison among numerous plausible constitutive models. It is explicitly shown that three-parameter models such as Smallwoods (Ramberg-Osgood) calculate parameters in such a manner that macro-slip is not an independent parameter, yet the model admits macro-slip. The introduction of a fourth parameter is therefore required. It is shown that when a macro-slip force is specified for the Smallwood model the result is a special case of the Segalman four-parameter model. Both of these models admit a slope discontinuity at the inception of macro-slip. A five-parameter model that has the beneficial features of Segalmans four-parameter model is proposed. This model manifests a force-displacement curve having a continuous first derivative.

New Approximations for Elastic Spheres Under an Oscillating Torsional Couple

The Lubkin solution for two spheres pressed together and then subjected to a monotonically increasing axial couple is examined numerically. The Deresiewicz asymptotic solution is compared to the full solution and its utility is evaluated. Alternative approximations for the Lubkin solution are suggested and compared. One approximation is a Pade rational function which matches the analytic solution over all rotations. The other is an exponential approximation that reproduces the asymptotic values of the analytic solution at infinitesimal and infinite rotations. Finally, finite element solutions for the Lubkin problem are compared with the exact and approximate solutions.

Investigation of modal iwan models for structures with bolted joints

Structures with mechanical joints are difficult to accurately model; even when the natural frequencies of the system remain essentially constant, the damping introduced by the joints is often observed to depend nonlinearly on amplitude. Although models for individual joints have been employed with some success, the modeling of a structure with many joints remains a significant obstacle. This work explores whether nonlinear damping can be applied in a modal framework, where instead of modeling each discrete joint within a structure, a nonlinear damping model is used for each mode of interest. This approach assumes that the mode shapes of the structure do not change significantly with amplitude and that there is negligible coupling between modes. The nonlinear Iwan joint model has had success in modeling the nonlinear damping of individual joints and is used as a modal damping model in this work. The proposed methodology is first evaluated by simulating a structure with a small number of discrete Iwan joints (bolted joints) in a finite element code. A modal Iwan model is fit to simulated measurements from this structure and the accuracy of the modal model is assessed. The methodology is then applied to actual experimental hardware with a similar configuration and a modal damping model is identified for the first few modes of the system. The proposed approach seems to capture the response of the system quite well in both cases, especially at low force levels when macro-slip does not occur.

Modeling of threaded joints using anisotropic elastic continua

Using fine material meshes in structural dynamics analysis is often impractical due to time step considerations. Unfortunately, fine meshes are typically required to capture the inherent physics in jointed connections. This is especially true in threaded connections which feature numerous contact interfaces and stress singularities. A systematic method is presented here for representing the threaded volume by a continuous, homogeneous, linear elastic, anisotropic equivalent material. The parameters of that equivalent material depend on thread geometry and the assumed contact condition between adjacent threads and are derived from detailed finite element simulations of a characteristic thread-pair unit cell. Numerical simulations using the equivalent material closely match the local stiffness through the load path calculated from the finely meshed thread models and also reproduce classical theoretical and experimental results from the literature.

Iwan Models and Their Provenance

Iwan models have had some exposure recently in modeling the nonlinear response of individual joints. This popularity can be ascribed to their mathematical simplicity, their versatility, and their ability to capture the important responses of mechanical joints under unidirectional loads. There is a lot of history to this category of model. Masing explored kinematic hardening of metals with a model consisting of ten Jenkins elements in series. Soon after, Prandtl explored the behavior of a continuous distribution of such elements. Ishlinskii explored the mathematical structure of such continuous distributions. Much more recently, Iwan demonstrated practical application of such models in capturing various sorts of metal plasticity.Among the features that make such models interesting is a simple relationship between the asymptotic nature of the integral kernel at small values and the power-law relation between force amplitude and dissipation per cycle in harmonic loading. Iwan provided several differential equations for deducing the kernel from force-displacement relations. Segalman and Starr devised methods for deducing kernels from force-displacement curves of arbitrary Masing models. This is illustrated to generate a BPII model equivalent to the Ramberg-Osgood plasticity model. The Segalman-Starr relationship is used to find relationships among several other plasticity models.Copyright

Modal Analysis to Accommodate Slap in Linear Structures

The generalized momentum balance (GMB) methods, explored chiefly by Shabana and his co-workers, treat slap or collision in linear structures as sequences of impulses, thereby maintaining the linearity of the structures throughout. Further, such linear analysis is facilitated by modal representation of the structures. These methods are discussed here and extended. Simulations on a simple two-rod problem demonstrate how this modal impulse approximation affects the system both directly after each impulse as well as over the entire collision. Furthermore, these simulations illustrate how the GMB results differ from the exact solution and how mitigation of these artifacts is achieved. Another modal method discussed in this paper is the idea of imposing piecewise constant forces over short, yet finite, time intervals during contact. The derivation of this method is substantially different than that of the GMB method, yet the numerical results show similar behavior, adding credence to both models. Finally, a novel method combining these two approaches is introduced. The new method produces physically reasonable results that are numerically very close to the exact solution of the collision of two rods. This approach avoids most of the non physical, numerical artifacts of interpenetration or chatter present in the first two methods.

Proceedings of the Third International Workshop on Jointed Structures.

The Third International Workshop on Jointed Structures was held from August 16th to 17th, 2012, in Chicago Illinois, following the ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Thirty two researchers from both the United States and international locations convened to discuss the recent progress of mechanical joints related research and associated efforts in addition to developing a roadmap for the challenges to be addressed over the next five to ten years. These proceedings from the workshop include the minutes of the discussions and follow up from the 2009 workshop [1], presentations, and outcomes of the workshop. Specifically, twelve challenges were formulated from the discussions at the workshop, which focus on developing a better understanding of uncertainty and variability in jointed structures, incorporating high fidelity models of joints in simulations that are tractable/efficient, motivating a new generation of researchers and funding agents as to the importance of joint mechanics research, and developing new insights into the physical phenomena that give rise to energy dissipation in jointed structures. The ultimate goal of these research efforts is to develop a predictive model of joint mechanics.

Approximate Constitutive Relation for Lap Joints Using a Tribo-Mechanical Approach

Energy dissipation in mechanical joints occurs as a result of micro-slip motion between contacting rough surfaces. An account of this phenomenon is especially challenging due to the vast differences in the length and time scale differences between the macro-mechanical structure and the micron-scale events at the joint interface. This paper considers the contact between two nominally flat surfaces containing micron-scale roughness. The rough surface interaction is viewed as a multi-sphere elastic interaction subject to a periodic tangential force. It combines the Mindlin’s formulation [1, 2] for the elastic interaction of two spheres with the Greenwood and Williamson’s [3] statistical approach for the contact of two nominally flat rough surfaces so as to develop a model for multi-sphere problem in which sphere radii, contact load and the number of spheres in contact can only be known in a statistical sense and not deterministically.Copyright