Publications

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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.

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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.

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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.

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.

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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.

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