Publications

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Advanced friction models are often mathematically defined as nonlinear differential equations or complicated algebraic operations acting in single degree-of-freedom systems; however, such simplified conditions are not relevant to most design applications. As a result, current designers of practical structures typically simplify friction modeling to classical, Coulomb-like descriptions. In order to be viable for design purposes, friction models must be applicable to realistic structures and available in standard commercial codes. The goal of this work is to implement several different friction models into the commercial code, Abaqus, as user-defined contact models and to explore their properties in a dynamic simulation. A verification problem of interest to the joints community is utilized to evaluate efficacy. Several output quantities of the model will be presented and discussed, including frictional energy dissipation, amplitude, and frequency. The selected results are comparable to commonly observed experimental phenomena in mechanics of jointed structures.

Mechanical and aerospace structures often contain nonlinearities arising from frictional contact at joints. In order to calibrate response predicting models, these nonlinearities must be experimentally quantified to provide information about the type and strength of nonlinearity. For amplitude dependent nonlinearities, such as frictional contact, the nonlinear response is obtained by gathering ring down accelerometer data from impact testing with varying amplitudes. These accelerations are then spatially filtered to obtain a single degree-of-freedom response, which is used to identify a pseudo-modal model. This work examines a small test article with embedded frictional nonlinearities, in which accelerometers cannot be placed. Using a laser doppler vibrometer (LDV) to determine linear mode shapes and digital image correlation (DIC) to obtain response data during various amplitude hammer strikes, the nonlinearity in this small system is quantified.

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Complex mechanical structures are often subjected to random vibration environments. One strategy to analyze these nonlinear structures numerically is to use finite element analysis with an explicit solver to resolve interactions in the time domain. However, this approach is impractical because the solver is conditionally stable and requires thousands of iterations to resolve the contact algorithms. As a result, only short runs can be performed practically because of the extremely long runtime needed to obtain sufficient sampling for long-time statistics. The proposed approach uses a machine learning algorithm known as the Long Short-Term Memory (LSTM) network to model the response of the nonlinear system to random input. The LSTM extends the capability of the explicit solver approach by taking short samples and extending them to arbitrarily long signals. The efficient LSTM algorithm enables the capability to perform Monte Carlo simulations to quantify model-form and aleatoric uncertainty due to the random input.

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Component mode synthesis (CMS) is a widely employed model reduction technique used to reduce the computational cost associated with the dynamic analysis of complex engineering structures. To generate CMS models, specifically the formulation of Craig and Bampton, both normal fixed-interface modes and constraint modes of the component’s structure are calculated. These modes are used in conjunction with the component level mass and stiffness matrices to generate reduced mass and stiffness matrices used in the final analyses. For some component models, the most computationally expensive part of this procedure is calculating the component normal modes information. Several different approaches are utilized to investigate the sensitivity of system level responses to variations in several aspects of the CMS models. One approach evaluates changes due to modifications of the reduced mass and stiffness matrices assuming that the mode shapes do not change. The second approach assumes that the mode shapes change but the reduced mass and stiffness matrices do not change. An example is presented to show the influence of these two approaches.

Structural dynamics models with localized nonlinearities can be reduced using Hurty/Craig-Bampton component mode synthesis methods. The interior degrees-of-freedom of the linear subcomponents are reduced with a set of dynamic fixedinterface modes while the static constraint modes preserve the physical coordinates at which the nonlinear restoring forces are applied. For finite element models with a highly refined mesh at the boundary, a secondary modal analysis can be performed to reduce the interface down to a truncated set of local-level characteristic constraint modes. In this research, the cost savings and accuracy of the interface reduction technique are evaluated on a simple example problem involving two elastic blocks coming into contact.

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This work describes the energy dissipation arising from microslip for an elastic shell incorporating shear and longitudinal deformation resting on a rough-rigid foundation. This phenomenon is investigated using finite element (FE) analysis and nonlinear geometrically exact shell theory. Both approaches illustrate the effect of shear within the shell and observe a reduction in the energy dissipated from microslip as compared to a similar system neglecting shear deformation. In particular, it is found that the shear deformation allows for load to be transmitted beyond the region of slip so that the entire interface contributes to the load carrying capability of the shell. The energy dissipation resulting from the shell model is shown to agree well with that arising from the FE model, and this representation can be used as a basis for reduced order models that capture the microslip phenomenon.

We propose the use of the Primary Complex Mode Indicator Function (PCMIF), calculated from acceleration frequency response functions, as a response comparison metric to analyze unit-to-unit variability. The PCMIF has an advantage over the traditional dynamic representations of mode shapes, frequencies and damping in that it removes the user and algorithmic error that may be associated with those extractions. In addition, it is customizable according to the interest level. If consistent sets of acceleration measurements from chosen drive points can be acquired from multiple hardware units, the comparison of each unit's PCMIF metric can provide insight. In addition to measured PCMIF, finite element models of the system can predict variability in PCMIF response using known variability of hardware configurations, and this can be compared with experimental PCMIF data. This comparison allows meaningful unit-to-unit comparison even if components and/or system geometries differ from one system to the next.