Publications

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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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