Publications

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A number of methods for non-linear system identification in the time and frequency domain have been developed in the past. These methods have been applied to many systems, ranging from micro-scale devices to macro-scale systems, sometimes with uncertain results. The aim of this paper is to assess the efficiency of a subset of methods and understand their range of usability. The methods considered in this study are the restoring force surface (RFS), Hilbert transform (HT), zero-crossing (ZC), direct quadrature (DQ), short-time Fourier transform (SFT) and zero-crossing for systems with asymmetric restoring forces (ZCA). The accuracy and robustness of the methods against measured noise were evaluated using simulated data from a SDOF system. The application of the selected methods to a simulated non-linear MDOF system was also investigated. It could be shown that under certain conditions these methods may still provide reliable results for MDOF systems although generally their use should be avoided. The methods were also applied to data from a micro-electro-mechanical-systems (MEMS). Unfortunately, due to lack of symmetry in the experimental data, only the RFS and ZCA could have been used, leading to the finding that the MEMS device may be modelled using quadratic stiffness.

Overhead collisions of trucks with low-clearance railway bridges cause more than half of the railway traffic interruptions over bridges in the United States. Railroad owners are required to characterize the damage caused by such events and assess the safety of subsequent train crossings. However, damage characterization is currently visual (subjective) and becomes difficult in remote locations where collisions are not reported and inspections are not performed following the impact. To mitigate these shortcomings, this paper presents a new impact definition and rating strategy for automatically and remotely quantify damage. This research proposes an impact rating strategy based on the information that best describes the consequences of vehicle-railway bridge collisions. A series of representative impacts were simulated using numerical finite element models of a steel railway bridge. Railway owners provided information about the bridge and impact characterization based on railway industry experience. The resulting nonlinear dynamic responses were evaluated with the proposed rating strategy to assess the effect of these impacts. In addition, a neural network methodology was implemented on a simplified numerical model to identify spatial characteristics of the impact damage.

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). Finally, 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.

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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.

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The Fourth International Workshop on Jointe d 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 ne w roadmap for the evoluti on of joints research from academic to industrial appli cations over the next five to te n years. The workshop itself was organized around four themes: applications that ca n benefit from joints research (applicability), repeatability and variability issues in experi ments (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 deve lop a validated method for the de sign and analysis of dynamically loaded structures with frictional joints. Acknowledgement The authors thank all of the participants of the workshop for their contributions to the discussion and goals laid out herein. Additio nally, we would like to thank Sandia National Laboratories, the National Scie nce Foundation, and the Atomic Weapons Establishment for their support of this workshop.

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 st ructural models that interact with each other at localized interfaces. ROMULIS is meant to provide a us er-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 sc ripts. The theory behind th e 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 in teract 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 di rections 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.

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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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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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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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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 and can be applied with a variety of boundary conditions. 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 frequency and damping ratio from either measured or simulated transient ring-down data. By combining the discrete Fourier transform with an expanding or contracting window function that moves along the time axis, the resulting spectrum is used to estimate the instantaneous frequencies, damping and complex Fourier coefficients. This method is demonstrated on a multi-degree-of-freedom beam with a cubic spring attachment, and investigates the amplitudefrequency dependence in connection to the undamped nonlinear normal modes. A second example shows the results from experiment ring-down response on a beam with a lap joint, and reveals how the system behaves as energy dissipates.

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Two of the central challenges in the mechanical design of components in nuclear systems are the dissipation of energy from external shocks and the localization of energy in energetic materials. This research seeks to address these problems by developing a patterned granular microstructure that can be optimized to direct or impede the transfer of energy carried by stress waves. Such structures require the development of a manufacturing technique that can yield perfectly ordered lattices. Two branches of research are detailed here: the development of a sphere-by-sphere additive manufacturing technique, and the development of a framework for modeling the technique in order to guide future improvements. Proof of concept of the method is demonstrated, and recommendations for future work are made.

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The use of parameterized reduced order models(PROMs) within the stochastic reduced order model (SROM) framework is a logical progression for both methods. In this report, five different parameterized reduced order models are selected and critiqued against the other models along with truth model for the example of the Brake-Reuss beam. The models are: a Taylor series using finite difference, a proper orthogonal decomposition of the the output, a Craig-Bampton representation of the model, a method that uses Hyper-Dual numbers to determine the sensitivities, and a Meta-Model method that uses the Hyper-Dual results and constructs a polynomial curve to better represent the output data. The methods are compared against a parameter sweep and a distribution propagation where the first four statistical moments are used as a comparison. Each method produces very accurate results with the Craig-Bampton reduction having the least accurate results. The models are also compared based on time requirements for the evaluation of each model where the Meta- Model requires the least amount of time for computation by a significant amount. Each of the five models provided accurate results in a reasonable time frame. The determination of which model to use is dependent on the availability of the high-fidelity model and how many evaluations can be performed. Analysis of the output distribution is examined by using a large Monte-Carlo simulation along with a reduced simulation using Latin Hypercube and the stochastic reduced order model sampling technique. Both techniques produced accurate results. The stochastic reduced order modeling technique produced less error when compared to an exhaustive sampling for the majority of methods.

This paper discusses the results of a study to determine the impact of culture on engineering. The study took place during the 2015 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 24 graduate students participating in seven different projects. Twenty-two of the participants and two of the mentors were interviewed to study the effects of cultural background on engineering processes and interactions. The results of this study indicate that cultural differences drive engineering practices.

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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 cause issues when generating a mesh of the model. This paper 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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A collaborative research institute was organized and held at Sandia Albuquerque for a period of six weeks. This research institute brought together researchers from around the world to work collaboratively on a set of research projects. These research projects included: developing experimental guidelines for studying variability and repeatability of nonlinear structures; decoupling aleatoric and epistemic uncertainty in measurements to improve dynamic predictions; a numerical round robin to assess the performance of five different numerical codes for modeling systems with strong nonlinearities; and an assessment of experimentally derived and numerically derived reduced order models. In addition to the technical collaborations, the institute also included a series of seminars given by both Sandians and external experts, as well as a series of tours and field trips to local places of scientific and engineering importance. This report details both the technical research and the programmatic organization of the 2014 Sandia Nonlinear Mechanics and Dynamics Summer Research Institute.

The following details the implementation of an analytical elastic plastic contact model with strain hardening for normal im pacts into the LAMMPS granular package. The model assumes that, upon impact, the co llision has a period of elastic loading followed by a period of mixed elastic plas tic loading, with contributions to each mechanism estimated by a hyperbolic seca nt weight function. This function is implemented in the LAMMPS source code as the pair style gran/ep/history. Preliminary tests, simulating the pouring of pure nickel spheres, showed the elastic/plastic model took 1.66x as long as similar runs using gran/hertz/history.

Impact between metallic surfaces is a phenomenon that is ubiquitous in the design and analysis of mechanical systems. We found that to model this phenomenon, a new formulation for frictional elastic–plastic contact between two surfaces is developed. The formulation is developed to consider both frictional, oblique contact (of which normal, frictionless contact is a limiting case) and strain hardening effects. The constitutive model for normal contact is developed as two contiguous loading domains: the elastic regime and a transitionary region in which the plastic response of the materials develops and the elastic response abates. For unloading, the constitutive model is based on an elastic process. Moreover, the normal contact model is assumed to only couple one-way with the frictional/tangential contact model, which results in the normal contact model being independent of the frictional effects. Frictional, tangential contact is modeled using a microslip model that is developed to consider the pressure distribution that develops from the elastic–plastic normal contact. This model is validated through comparisons with experimental results reported in the literature, and is demonstrated to be significantly more accurate than 10 other normal contact models and three other tangential contact models found in the literature.

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Quantifying uncertainty in model parameters is a challenging task for analysts. Soize has derived a method that is able to characterize both model and parameter uncertainty independently. This method is explained with the assumption that some experimental data is available, and is divided into seven steps. Monte Carlo analyses are performed to select the optimal dispersion variable to match the experimental data. Along with the nominal approach, an alternative distribution can be used along with corrections that can be utilized to expand the scope of this method. This method is one of a very few methods that can quantify uncertainty in the model form independently of the input parameters. Two examples are provided to illustrate the methodology, and example code is provided in the Appendix.

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In 2012, a Matlab GUI for the prediction of the coefficient of restitution was developed in order to enable the formulation of more accurate Finite Element Analysis (FEA) models of components. This report details the development of a new Rebound Dynamics GUI, and how it differs from the previously developed program. The new GUI includes several new features, such as source and citation documentation for the material database, as well as a multiple materials impact modeler for use with LMS Virtual.Lab Motion (LMS VLM), and a rigid body dynamics modeling software. The Rebound Dynamics GUI has been designed to work with LMS VLM to enable straightforward incorporation of velocity-dependent coefficients of restitution in rigid body dynamics simulations.

In the process of model validation, models are often declared valid when the differences between model predictions and experimental data sets are satisfactorily small. However, little consideration is given to the effectiveness of a model using parameters that deviate slightly from those that were fitted to data, such as a higher load level. Furthermore, few means exist to compare and choose between two or more models that reproduce data equally well. These issues can be addressed by analyzing model form error, which is the error associated with the differences between the physical phenomena captured by models and that of the real system. This report presents a new quantitative method for model form error analysis and applies it to data taken from experiments on tape joint bending vibrations. Two models for the tape joint system are compared, and suggestions for future improvements to the method are given. As the available data set is too small to draw any statistical conclusions, the focus of this paper is the development of a methodology that can be applied to general problems.

It is often prohibitively expensive to integrate the response of a high order nonlinear system, such as a finite element model of a nonlinear structure, so a set of linear eigenvectors is often used as a basis in order to create a reduced order model (ROM). By augmenting the linear basis with a small set of discontinuous basis functions, ROMs of systems with local nonlinearities have been shown to compare well with the corresponding full order models.When evaluating the quality of a ROM, it is common to compare the time response of the model to that of the full order system, but the time response is a complicated function that depends on a predetermined set of initial conditions or external force. This is difficult to use as a metric to measure convergence of a ROM, particularly for systems with strong, non-smooth nonlinearities, for two reasons: (1) the accuracy of the response depends directly on the amplitude of the load/initial conditions, and (2) small differences between two signals can become large over time. Here, a validation metric is proposed that is based solely on the ROM’s equations of motion. The nonlinear normalmodes (NNMs) of the ROMs are computed and tracked as modes are added to the basis set. The NNMs are expected to converge to the true NNMs of the full order system with a sufficient set of basis vectors. This comparison captures the effect of the nonlinearity through a range of amplitudes of the system, and is akin to comparing natural frequencies and mode shapes for a linear structure. In this research, the convergencemetric is evaluated on a simply supported beam with a contacting nonlinearity modeled as a unilateral piecewise-linear function. Various time responses are compared to show that the NNMs provide a good measure of the accuracy of the ROM. The results suggest the feasibility of using NNMs as a convergencemetric for reduced order modeling of systems with various types of nonlinearities.

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The goal of most computational simulations is to accurately predict the behavior of a real, physical system. Accurate predictions often require very computationally expensive analyses and so reduced order models (ROMs) are commonly used. ROMs aim to reduce the computational cost of the simulations while still providing accurate results by including all of the salient physics of the real system in the ROM. However, real, physical systems often deviate from the idealized models used in simulations due to variations in manufacturing or other factors. One approach to this issue is to create a parameterized model in order to characterize the effect of perturbations from the nominal model on the behavior of the system. This report presents a methodology for developing parameterized ROMs, which is based on Craig-Bampton component mode synthesis and the use of hyper-dual numbers to calculate the derivatives necessary for the parameterization.

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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.

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This report presents an efficient and accurate method for integrating a system of ordinary differential equations, particularly those arising from a spatial discretization of partially differential equations. The algorithm developed, termed the IMEX a algorithm, belongs to a class of algorithms known as implicit-explicit (IMEX) methods. The explicit step is based on a fifth order Runge-Kutta explicit step known as the Dormand-Prince algorithm, which adaptively modifies the time step by calculating the error relative to a fourth order estimation. The implicit step, which follows the explicit step, is based on a backward Euler method, a special case of the generalized trapezoidal method. Reasons for choosing both of these methods, along with the algorithm development are presented. In applications that have less stringent accuracy requirements, several other methods are available through the IMEX a toolbox, each of which simplify the fifth order Dormand-Prince explicit step: the third order Bogacki-Shampine method, the second order Midpoint method, and the first order Euler method. The performance of the algorithm is evaluated on to examples. First, a two pawl system with contact is modeled. Results predicted by the IMEX a algorithm are compared to those predicted by six widely used integration schemes. The IMEX a algorithm is demonstrated to be significantly faster (by up to an order of magnitude) and at least as accurate as all of the other methods considered. A second example, an acoustic standing wave, is presented in order to assess the accuracy of the IMEX a algorithm. Finally, sample code is given in order to demonstrate the implementation of the proposed algorithm.

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Although interdisciplinary research attracts more and more interest and effort, the benefits of this type of research are not always realized. To understand when expertise diversity will have positive or negative effects on research efforts, we examine how expertise diversity and diversity salience affect task conflict and idea sharing in interdisciplinary research groups. Using data from 148 researchers in 29 academic research labs, we provide evidence on the importance of social categorization states (i.e., expertise diversity salience) in understanding both the information processes (i.e., task conflict) and the creativity processes (i.e., idea sharing) in groups with expertise diversity. We show that expertise diversity can either increase or decrease task conflict depending on the salience of group members' expertise in a curvilinear way: at a medium level of expertise diversity the moderating effect of diversity salience is strongest. Furthermore, enriched group work design can strengthen the benefits of task conflict for creative idea sharing only when expertise diversity salience is low. Finally, we show that idea sharing predicts group performance in interdisciplinary academic research labs over and above task conflict.

The analysis of continuous systems with nonlinearities in their domain have previously been limited to either numerical approaches, or analytical methods that are constrained in the parameter space, boundary conditions, or order of the system. The present analysis develops a robust method for studying continuous systems with arbitrary boundary conditions and nonlinearities using the assumption that the nonlinear constraint can be modeled with a piecewise-linear force-deflection constitutive relationship. Under this assumption, a superposition method is used to generate homogeneous boundary conditions, and modal analysis is used to find the displacement of the system in each state of the piecewise-linear nonlinearity. In order to map across each nonlinearity in the piecewise-linear force-deflection profile, a variational calculus approach is taken that minimizes the L2 energy norm between the previous and current states. To illustrate this method, a leaf spring coupled with a connector pin immersed in a viscous fluid is modeled as a beam with a piecewise-linear constraint. From the results of the convergence and parameter studies, a high correlation between the finite-time Lyapunov exponents and the contact time per period of the excitation is observed. The parameter studies also indicate that when the system's parameters are changed in order to reduce the magnitude of the velocity impact between the leaf spring and connector pin, the extent of the regions over which a chaotic response is observed increases.

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This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled 'Reduced Order Modeling of Fluid/Structure Interaction.' This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preserves numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convection-diffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.

This report summarizes design and modeling activities for the MEMS passive shock sensor. It provides a description of past design revisions, including the purposes and major differences between design revisions but with a focus on Revisions 4 through 7 and the work performed in fiscal year 2008 (FY08). This report is a reference for comparing different designs; it summarizes design parameters and analysis results, and identifies test structures. It also highlights some of the changes and or additions to models previously documented [Mitchell et al. 2006, Mitchell et al. 2008] such as the way uncertainty thresholds are analyzed and reported. It also includes dynamic simulation results used to investigate how positioning of hard stops may reduce vibration sensitivity.

This report summarizes the functional, model validation, and technology readiness testing of the Sandia MEMS Passive Shock Sensor in FY08. Functional testing of a large number of revision 4 parts showed robust and consistent performance. Model validation testing helped tune the models to match data well and identified several areas for future investigation related to high frequency sensitivity and thermal effects. Finally, technology readiness testing demonstrated the integrated elements of the sensor under realistic environments.

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