Bolted joints are prevalent in most assembled structures; however, predictive models for their behavior do not exist. Calibrated models, such as the Iwan model, are able to predict the response of a jointed structure over a range of excitations once calibrated at a nominal load. The Iwan model, though, is not widely adopted due to the high computational expense of implementation. To address this, an analytical solution of the Iwan model is derived under the hypothesis that for an arbitrary load reversal, there is a new distribution of dry friction elements, which are now stuck, that approximately resemble a scaled version of the original distribution of dry friction elements. The dry friction elements internal to the Iwan model do not have a uniform set of parameters and are described by a distribution of parameters, i.e., which internal dry friction elements are stuck or slipping at a given load, that ultimately governs the behavior of the joint as it transitions from microslip to macroslip. This hypothesis allows the model to require no information from previous loading cycles. Additionally, the model is extended to include the pinning behavior inherent in a bolted joint. Modifications of the resulting framework are discussed to highlight how the constitutive model for friction can be changed (in the case of an Iwan–Stribeck formulation) or how the distribution of dry friction elements can be changed (as is the case for the Iwan plasticity model). The reduced Iwan plus pinning model is then applied to the Brake–Reuß beam in order to discuss methods to deduce model parameters from experimental data.
Brake, Matthew R.; Ewins, Daniel J.; Segalman, Daniel J.; Bergman, Lawrence A.; Quinn, D.D.
The Fourth International Workshop on Jointed Structures was held from October 19-21, 2015, in Dartington, UK. Forty-five 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 new roadmap for the evolution of joints research from academic to industrial applications over the next five to ten years. The workshop itself was organized around four themes: applications that can benefit from joints research (applicability), repeatability and variability issues in experiments (repeatability), challenges in developing predictive models (predictability), and potential paths forward (way forward). The outcomes of the workshop are still in progress as the joints community develops a new roadmap for joints research; however, there are many aspects that are related here within. The ultimate goal of this research community is to develop a validated method for the design and analysis of dynamically loaded structures with frictional joints.
This report analyzes the results of a study on culture and its capability to influence research. The study occurred during the 2016 Nonlinear Mechanics and Dynamics Summer Research Institute, a six-week research program sponsored by Sandia National Laboratories and the University of New Mexico consisting of 27 graduate students participating in ten different projects. Two separate surveys were administered at the beginning and end of the Institute, in addition to interviews and observation, in order to study the effects of various cultural factors on engineering processes and maintaining professional interactions. The results of this study indicate that cultural differences are not a significant barrier to engineering progress and most cultural issues are minor. A variety of cultures instead provide new perspectives, advancing universal understanding.
This paper presents a method for predicting how sensitive a frictional contact’s steady-state behavior is to its initial conditions. Previous research has proven that if a contact is uncoupled, i.e. if slip displacements do not influence the contact pressure distribution, then its steady-state response is independent of initial conditions, but if the contact is coupled, the steady-state response depends on initial conditions. In this paper, two metrics for quantifying coupling in discrete frictional systems are examined. These metrics suggest that coupling is dominated by material dissimilarity due to Dundurs’ composite material parameter β when β ≥ 0.2, but geometric mismatch becomes the dominant source of coupling for smaller values of β. Based on a large set of numerical simulations with different contact geometries, material combinations, and friction coefficients, a contact’s sensitivity to initial conditions is found to be correlated with the product of the coupling metric and the friction coefficient. For cyclic shear loading, this correlation is maintained for simulations with different contact geometries, material combinations, and friction coefficients. Furthermore, for cyclic bulk loading, the correlation is only maintained when the contact edge angle is held constant.
The Reduced Order Modeling Unlimited Localized Interface Simulator (ROMULIS) is a set of toolbox scripts in MATLAB designed to perform nonlinear transient integration on a system of reduced order structural models that interact with each other at localized interfaces. ROMULIS is meant to provide a user-friendly interface for applying the latest developments in numerical techniques and modeling in structural dynamics analysis while also giving the freedom to implement new technologies from forthcoming research. This report documents how to use and interpret the toolbox scripts. The theory behind the code is given, followed by a manual for interacting with the scripts to perform simulations. Lastly, a high-level introduction that explains how the scripts interact with each other is given for aspiring developers.
The 2016 Parameterized Reduced Order Modeling (PROM) Workshop was held in June, 2016, in Albuquerque, NM. This workshop included 30 researchers who took part in a two day discussion regarding the state of the art for PROMs, complimentary reduced order modeling (ROM) theories, and discussion of the future directions of PROM research. The goals of the workshop were three-fold: to assess the relative accuracy, efficiency, and merits of the different PROM methods; to discuss the state of the art for ROMs and how PROMs can benefit from these advances; and to define the pressing challenges for PROMs and a path for future research collaborations.
A novel, experimental method is presented for measuring the coefficient of restitution during impact events. These measurements are used to indirectly validate a new model of elastic-plastic contact. The experimental setup consists of a stainless steel sphere that is attached at the bottom of a 2.2 m long pendulum. The test materials are of the form of 1 inch diameter pucks that the sphere strikes over a range of velocities. Digital image correlation is used to measure the displacement and velocity of the ball. From this data the coefficient of restitution is calculated as a function of velocity. This report details the experimental setup, experimental process, the results acquired, as well as the future work.
The Nonlinear Mechanics and Dynamics (NOMAD) Research Institute is a six week long collaborative research program for graduate students from across the world. The 2015 NOMAD Research Institute was hosted jointly by Sandia National Laboratories and the University of New Mexico, and featured 24 graduate students working on seven different research projects. These projects included: developing experimental strategies for studying the dynamics of nonlinear systems, a numerical round robin for predicting the response of a jointed system, quantification of uncertainty in a lap joint, assessment of experimental substructuring methods, a study of stress waves propagating through jointed interfaces, structural design optimization with joints, and the nonlinear system identification of MEMS devices. This report details both the technical research and the programmatic organization of the 2015 NOMAD Research Institute.
Broadband impact excitation in structural dynamics is a common technique used to detect and characterize nonlinearities in mechanical systems since it excites many frequencies of a structure at once. Non-stationary time signals from transient ring-down measurements require time-frequency analysis tools to observe variations in frequency and energy dissipation as the response evolves. This work uses the short-time Fourier transform to estimate the instantaneous parameters from measured or simulated data. By combining the discrete Fourier transform with an expanding or contracting window function that moves along the time axis, the resulting spectra are used to estimate the instantaneous frequencies, damping ratios and complex Fourier coefficients. This method is demonstrated on a multi-degree-of-freedom beam with a cubic spring attachment. The amplitude-frequency dependence in the damped response is compared to the undamped nonlinear normal modes. A second example shows the results from experimental ring-down measurements taken on a beam with a lap joint, revealing how the mechanical interface introduces nonlinear frequency and damping parameters.
Motivated by the current demands in high-performance structural analysis, and by a desire to better model systems with localized nonlinearities, analysts have developed a number of different approaches for modelling and simulating the dynamics of a bolted-joint structure. However, the types of conditions that make one approach more effective than the others remains poorly understood due to the fact that these approaches are developed from fundamentally and phenomenologically different concepts. To better grasp their similarities and differences, this research presents a numerical round robin that assesses how well three different approaches predict and simulate a mechanical joint. These approaches are applied to analyze a system comprised of two linear beam structures with a bolted joint interface, and their strengths and shortcomings are assessed in order to determine the optimal conditions for their use.
Experimental dynamic substructuring is a means whereby a mathematical model for a substructure can be obtained experimentally and then coupled to a model for the rest of the assembly to predict the response. Recently, various methods have been proposed that use a transmission simulator to overcome sensitivity to measurement errors and to exercise the interface between the substructures; including the Craig-Bampton, Dual Craig-Bampton, and Craig-Mayes methods. This work compares the advantages and disadvantages of these reduced order modeling strategies for two dynamic substructuring problems. The methods are first used on an analytical beam model to validate the methodologies. Then they are used to obtain an experimental model for structure consisting of a cylinder with several components inside connected to the outside case by foam with uncertain properties. This represents an exceedingly difficult structure to model and so experimental substructuring could be an attractive way to obtain a model of the system.
The quantification of model form uncertainty is very important for engineers to understand when using a reduced order model. This quantification requires multiple numerical simulations which can be computationally expensive. Different sampling techniques, including Monte Carlo and Latin Hypercube, are explored while using the maximum entropy method to quantify the uncertainty. The maximum entropy method implements random matrices that maintain essential properties. This is explored on a planar frame using different types of substructure representations, such as Craig-Bampton. Along with the model form uncertainty of the substructure representation, the effect of component mode synthesis for each type of substructure representation on the model form uncertainty is studied.
Conference Proceedings of the Society for Experimental Mechanics Series
Stender, M.; Papangelo, A.; Allen, M.; Brake, Matthew R.; Schwingshackl, C.; Tiedemann, M.
Many engineered structures are assembled using different kinds of joints such as bolted, riveted and clamped joints. Even if joints are often a small part of the overall structure, they can have a massive impact on its dynamics due to the introduction of nonlinearities. Thus, joints are considered a design liability. Significant effort has been spent in joint characterization and modelling, but a predictive joint model is still non-existent. To overcome these uncertainties and ensure certain safety standards, joints are usually overdesigned according to static considerations and their stiffness. Especially damping and nonlinearity are not considered during the design process. This can lead to lower performance, lower payload, and as result of the joints structural dynamic models often do a poor job of predicting the dynamic response. However, it is well-known that, particularly for metal structures, joints represent the main source of energy dissipation. In this work a minimal model is used to show how structural performance can be improved using joints as a design variable. Common optimization tools are applied to a nonlinear joint model in order to damp undesired structural vibrations. Results illustrate how the intentional choice of joint parameters and locations can effectively reduce vibration level for a given operating point of a jointed structure.
The focus of this paper is on continuing the experimental/modeling investigation of the Brake-Reuß beam which was initiated a year ago as part of the NOMAD program at Sandia National Labs. The ultimate goal of the overall effort is to (1) determine the parameters of joint models, in particular the Iwan model in its modal form, from well delineated tests and (2) extend this approach to identify statistical distributions of the model parameters to account for joint uncertainty. The present effort focused on free response of the beam resulting from an impact test. The use of this data in conjunction with the Hilbert transform is shown to provide a straightforward framework for the identification of the joint model parameters at the contrary of the forced response data used earlier. The resulting frequency and damping vs. amplitude curves are particularly conducive to a Iwan-type modeling which is demonstrated. The curves also show the effect of the bolt torque on the joint behavior, i.e.,increase in natural frequency, linear limit, and macroslip threshold. Macroslip is shown to have occurred in some of the tests and it is concluded from ensuing testing that this event changed the nature of the jointed beams. Specifically, the linear natural frequency (observed under very low level impact test) shifted permanently by 20 Hz and, in one case, the linear natural frequency was observed to decrease with increasing bolt torque level in opposition to other beams and physical expectations. An analysis of the joint surface strongly suggest that a significant plastic zone developed during the macroslip phase which induced the above unusual behaviors.
Assembled mechanical systems often contain a large number of bolted connections. These bolted connections (joints) are integral aspects of the load path for structural dynamics, and, consequently, are paramount for calculating a structure's stiffness and energy dissipation prop- erties. However, analysts have not found the optimal method to model appropriately these bolted joints. The complexity of the screw geometry causes issues when generating a mesh of the model. This report will explore different approaches to model a screw-substrate connec- tion. Model parameters such as mesh continuity, node alignment, wedge angles, and thread to body element size ratios are examined. The results of this study will give analysts a better understanding of the influences of these parameters and will aide in finding the optimal method to model bolted connections.