Browsing by Author "Balaji, Nidish Narayanaa"
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Item A quantitative assessment of the model form error of friction models across different interface representations for jointed structures(Elsevier, 2022) Porter, Justin H.; Balaji, Nidish Narayanaa; Little, Clayton R.; Brake, Matthew R.W.Hysteretic models are widely used to model frictional interactions in joints to recreate experimental behavior. However, it is unclear which models are best suited for fitting or predicting the responses of structures. The present study evaluates 26 friction model/interface representation combinations to quantify the model form error. A Quasi-Static Modal Analysis approach (termed Rayleigh Quotient Nonlinear Modal Analysis) is adopted to calculate the nonlinear system response, and a Multi-Objective Optimization is solved to fit experimental data of the first mode of the Brake-Reuß Beam. Optimized parameters from the first mode are applied to the second and third bending modes to quantify the predictive ability of the models. Formulations for both tracing full hysteresis loops and recreating hysteresis loops from a single loading curve (Masing assumptions) are considered. Smoothly varying models applied to a five patch representation showed the highest flexibility (for fitting mode 1) and good predictive potential (for modes 2 and 3). For a second formulation, which uses 152 frictional elements to represent the interface, the physically motivated spring in series with a Coulomb slip model (elastic dry friction) has high error for fitting mode 1 and performs near the middle for predicting higher modes. For both interface representation, the best fit models are not the most physical, but rather the ones with the most parameters (as expected); however, the more physical models perform somewhat better for predicting the higher modes.Item Multi-Scale Modeling in Bolted Interfaces(2019-08-06) Balaji, Nidish Narayanaa; Brake, Matthew R. W.The thesis develops a framework for modeling the dynamics of bolted structures in a multi-scale manner. Understanding that most of the challenges faced by the joints community is around the reconciliation of contact response with physical parameters of the system, the current work is an attempt for this reconciliation using properties identified from interfacial scans of the structure. The basic idea of statistical averaging as conducted in rough contact studies is used here for achieving this in a segment-by-segment fashion. Thus, the response characterization may be done in a manner that represents the micro-level asperity distributions while also preserving a meso-level understanding of possible local variations. Since all of these are used, through the framework, for macro-level simulations of the dynamics, the approach links the micro-, meso-, and the macro-length scales (in that order). For the dynamical simulations, a modified modal quasi-static approach is proposed, which is capable of representing amplitude-dependent nonlinear modal characteristics of nonlinear dynamical systems with linear limit cases. Since the fully stuck and the fully slipped cases may be taken as the limit cases, this is well applicable for the cases with frictional contacts. The results for the modified approach are compared with the responses characterized from other time- and frequency-domain approaches for a simple example in order to validate its efficacy. Finally, the approach is applied for a three bolt lap-joint benchmark (the so-called ``Brake-Reu{\ss}-Beam''). Since the characterization of the interface is conducted in a full-field manner on top of a finite element mesh, the framework is also demonstrated to be applicable for conducting full-field micro-scale interface evolution studies. Validating this would enable models with backward-evolutionary dependence (macro- influencing meso- influencing micro-scale attributes). To this end, preliminary statistical studies are conducted to establish and/or understand correlations of local changes in relevant roughness parameters with predicted local tractions and dissipation fluxes.Item Reduced order modeling for the dynamics of jointed structures through hyper-reduced interface representation(Elsevier, 2021) Balaji, Nidish Narayanaa; Dreher, Tobias; Krack, Malte; Brake, Matthew R.W.One strategy to develop both accurate and computationally tractable models of jointed structures is reduced order modeling through hyper-reduced representations of the interfaces in contact. Hyper reduction refers to reduction techniques that result in a Reduced Order Model (ROM) that is complete by itself, i.e., all displacements and forces are fully described in the ROM coordinates directly. Focusing primarily on applications involving small relative displacement contacts, two fundamentally different approaches are formulated and compared for merits and limitations in applicability. The first is an adaptation of the stiffness-preserving RBE3 constraint elements, and the second is an interpolation approach based on remeshing the interface. Although RBE3 is extensively used in the literature, the current formulation derives stiffness preserving elements that are specifically useful for contact dynamics applications. Transformations are developed to express force–displacement relationships in the ROM coordinates that are congruent (in the sense of using the same contact models) as well as consistent (in the sense of being faithful to the quantities involved) with a high-fidelity model of the same structure. These approaches are applied to study a three-bolted lap-joint structure (the Brake-Reuß Beam (BRB) benchmark) that has been observed to demonstrate characteristic contact non-linearities. Multiple strategies for the hyper reduction are evaluated, including graph partitioning, finite element coarsening, and homogenization of field objectives, some of which involve an extra step of remeshing/choosing patches based on a field objective (e.g., contact pressure). The performances of the ROMs are assessed by conducting nonlinear modal analysis and computing a posteriori error metrics.Item The surrogate system hypothesis for joint mechanics(Elsevier, 2019) Balaji, Nidish Narayanaa; Brake, Mathew R.W.The main challenges in the design and analysis of jointed structures deal with the prediction of dissipation across bolted interfaces. Since friction is thought to be one of the main mechanisms for this, the current study investigates the utility of frictional parameter identification applied across different structures. Based on recent discoveries, a Surrogate System Hypothesis has been formulated to systematize this: the hypothesis states in brief, that the physical properties of a joint are independent of its structural context. The current work seeks to obtain a better understanding of the underlying systems by evaluating a confidence metric for the hypothesis for a relatively simple set of systems—physically perturbed configurations of the Brake-Reuß Beam. Interfacial friction is modeled using whole jointed patches with distributed hysteretic (Iwan) elements and simulations are conducted using the Quasi-Static Modal Analysis (QSMA) approach to estimate the modal characteristics of the system response (amplitude dependence of natural frequency and dissipation). Posing the estimation as a Multi-Objective Optimization Problem (MOOP) is shown to reveal important features of both the employed constitutive model as well as the structure that is modeled. Consequently, the approach is used to evaluate the epistemic uncertainty inherent in three different friction models. The studies reveal that a confidence metric for the hypothesis can be formulated in such a way that it is nearly independent of the friction constitutive model that is employed.Item Wave-based analysis of jointed elastic bars: nonlinear periodic response(Springer Nature, 2022) Balaji, Nidish Narayanaa; Brake, Matthew R.W.; Leamy, Michael J.In this paper, we develop two wave-based approaches for predicting the nonlinear periodic response of jointed elastic bars. First, we present a nonlinear wave-based vibration approach (WBVA) for studying jointed systems informed by re-usable, perturbation-derived scattering functions. This analytical approach can be used to predict the steady-state, forced response of jointed elastic bar structures incorporating any number and variety of nonlinear joints. As a second method, we present a nonlinear Plane-Wave Expansion (PWE) approach for analyzing periodic response in the same jointed bar structures. Both wave-based approaches have advantages and disadvantages when compared side-by-side. The WBVA results in a minimal set of equations and is re-usable following determination of the reflection and transmission functions, while the PWE formulation can be easily applied to new joint models and maintains solution accuracy to higher levels of nonlinearity. For example cases of two and three bars connected by linearly damped joints with linear and cubic stiffness, the two wave-based approaches accurately predict the expected Duffing-like behavior in which multiple periodic responses occur in the near-resonant regime, in close agreement with reference finite element simulations. Lastly, we discuss extensions of the work to jointed structures composed of beam-like members, and propose follow-on studies addressing opportunities identified in the application of the methods presented.Item Wave-based analysis of jointed elastic bars: stability of nonlinear solutions(Springer Nature, 2022) Balaji, Nidish Narayanaa; Brake, Matthew R.W.; Leamy, Michael J.In this paper we develop two new approaches for directly assessing stability of nonlinear wave-based solutions, with application to jointed elastic bars. In the first stability approach, we strain a stiffness parameter and construct analytical stability boundaries using a wave-based method. Not only does this accurately determine stability of the periodic solutions found in the example case of two bars connected by a nonlinear joint, but it directly governs the response and stability of parametrically forced continuous systems without resorting to discretization, a new development in of itself. In the second stability approach, we pose a perturbation eigenproblem residue (PER) and show that changes in the sign of the PER locate critical points where stability changes from stable to unstable, and vice-versa. Lastly, we discuss follow-on research using the developed stability approaches. In particular, we identify an opportunity to study stability around internal resonance, and then identify a need to further develop and interpret the PER approach to directly predict stability.