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Topics in Modal Analysis & Testing, Volume 8: Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022, the eighth volume of nine from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Modal Analysis, including papers on: Operational Modal & Modal Analysis Applications Experimental Techniques Modal Analysis, Measurements & Parameter Estimation Modal Vectors & Modeling Basics of Modal Analysis Additive Manufacturing & Modal Testing of Printed Parts
Modal Analysis Topics Volume 3. Proceedings of the 29th IMAC, A Conference and Exposition on Structural Dynamics, 2011, the third volume of six from the Conference, brings together over 30 contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics.
Nonlinear dynamical systems are known to be sensitive to input parameters. In this thesis, we apply model order reduction to an important class of such systems -- one which exhibits limit cycle oscillations (LCOs) and Hopf-bifurcations. Highfidelity simulations for systems with LCOs are computationally intensive, precluding probabilistic analyses of these systems with uncertainties in the input parameters. In this thesis, we employ a projection-based model reduction approach, in which the proper orthogonal decomposition (POD) is used to derive the reduced basis while the discrete empirical interpolation method (DEIM) is employed to approximate the nonlinear term such that the repeated online evaluations of the reduced-order model (ROM) is independent of the full-order model (FOM) dimension. In problems where vastly different magnitudes exist in the unknowns variables, the original POD-DEIM approach results in large error in the smaller variables. In unsteady simulations, such error quickly accumulates over time, significantly reducing the accuracy of the ROM. The interpolatory nature of the DEIM also limits its accuracy in approximating highly oscillatory nonlinear terms. In this work, modifications to the existing methodology are proposed whereby scalar-valued POD modes are used in each variable of the state and the nonlinear term, and the pure interpolation of the DEIM approximation is also replaced by a regression via over-sampling of the nonlinear term. The modified methodology is applied to two nonlinear dynamical problems: a reacting flow model of a tubular reactor and an aeroelastic model of a cantilevered plate, both of which exhibit LCO and Hopf-bifurcation. Results indicate that in situations where the efficiency of the original POD-DEIM ROM is compromised by disparate magnitudes in unknown variables or by the need to include large sets of interpolation points, the modified POD-DEIM ROM accurately predicts the system responses in a small fraction of the FOM computational time.
Topics in Nonlinear Dynamics, Volume 3, Proceedings of the 30th IMAC, A Conference and Exposition on Structural Dynamics, 2012, the third volume of six from the Conference, brings together 26 contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Application of Nonlinearities: Aerospace Structures Nonlinear Dynamics Effects Under Shock Loading Application of Nonlinearities: Vibration Reduction Nonlinear Dynamics: Testing Nonlinear Dynamics: Simulation Nonlinear Dynamics: Identification Nonlinear Dynamics: Localization
The MIT mission - "to bring together Industry and Academia and to nurture the next generation in computational mechanics is of great importance to reach the new level of mathematical modeling and numerical solution and to provide an exciting research environment for the next generation in computational mechanics." Mathematical modeling and numerical solution is today firmly established in science and engineering. Research conducted in almost all branches of scientific investigations and the design of systems in practically all disciplines of engineering can not be pursued effectively without, frequently, intensive analysis based on numerical computations.The world we live in has been classified by the human mind, for descriptive and analysis purposes, to consist of fluids and solids, continua and molecules; and the analyses of fluids and solids at the continuum and molecular scales have traditionally been pursued separately. Fundamentally, however, there are only molecules and particles for any material that interact on the microscopic and macroscopic scales. Therefore, to unify the analysis of physical systems and to reach a deeper understanding of the behavior of nature in scientific investigations, and of the behavior of designs in engineering endeavors, a new level of analysis is necessary. This new level of mathematical modeling and numerical solution does not merely involve the analysis of a single medium but must encompass the solution of multi-physics problems involving fluids, solids, and their interactions, involving multi-scale phenomena from the molecular to the macroscopic scales, and must include uncertainties in the given data and the solution results. Nature does not distinguish between fluids and solids and does not ever repeat itself exactly.This new level of analysis must also include, in engineering, the effective optimization of systems, and the modeling and analysis of complete life spans of engineering products, from design to fabrication, to possibly multiple repairs, to end of service.
Spatiotemporal dynamical systems are ubiquitous across all areas of science and engineering. While some systems of interest can be studied through first-principles governing equations, often, the underlying dynamics are unknown. Furthermore, even for problems where equations are known, analytical solutions are rare. Computational solutions are then plagued by issues of nonlinearity, multiple relevant scales of time and space, chaos, and high-dimensionality. When parametric studies are needed, these simulations become prohibitively expensive, even under the most advance computational architectures. Often, even the most complex dynamical systems contain inherent low-dimensional coherent structure. Reduced-order models (ROMs) attempt to ease the computation burden of such simulations by uncovering this low-rank subspace, reducing the overall size of such models while retaining the critical dynamics. Many ROMs leverage the proper orthogonal decomposition (POD) to produce a linear dimensionality reduction, where a dominant set of correlated modes provide a subspace in which to project the dynamics. Dimensionality reduction techniques then enable downstream tasks such as prediction, estimation, and low-latency control. However, many dimensionality reduction techniques rely on separation of time and space variables. This assumption does not hold in systems with underlying symmetry, because the time and space variables are inherently coupled. Namely translation, or traveling waves, scaling, and rotation inhibit the effectiveness of dimensionality reduction techniques. The focus of this thesis is to develop an approach to make spatiotemporal systems with underlying symmetry amenable to traditional ROM architectures. Three objectives are addressed (1) developing a method to address translations in one spatial dimension, (2) demonstrating the effectiveness of such a method on complex dynamics in experimental data, and (3) expanding the method to approach higher-dimensional data with scaling symmetries. The Unsupervised Traveling Wave Identification with Shifting and Truncation (UnTWIST) method can be applied to pure data, yielding interpretable models for wave speeds. Several examples are explored, showing that even for systems with multiple waves, non-constant wave speeds, and nonlinear wave phenomenon, UnTWIST enables the use of traditional methods like POD for dimensionality reduction. Further, the method is demonstrated on experimental data from a rotating detonation engine, presenting complex nonlinear dynamics. UnTWIST enables the discovery of interpretable linear and nonlinear models for the traveling detonation speeds, and yields meaningful spatial modes to describe the wave shapes. Lastly, the method is augmented to accommodate higher-dimensional data and an arbitrary number of symmetries. Two-dimensional data with a scaling symmetry are investigated, and accurate models are found to improve the dimensionality reductions. Lastly, limitations to the method in the presence of interacting waves are explored, and improvements and expansions are discussed.
The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term Statistical and qualitative model validation methods that can be applied to any model class Generalised frequency response functions which provide significant insight into nonlinear behaviours A completely new class of filters that can move, split, spread, and focus energy The response spectrum map and the study of sub harmonic and severely nonlinear systems Algorithms that can track rapid time variation in both linear and nonlinear systems The important class of spatio-temporal systems that evolve over both space and time Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all included to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems NARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems. This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.
This edited monograph collects research contributions and addresses the advancement of efficient numerical procedures in the area of model order reduction (MOR) for simulation, optimization and control. The topical scope includes, but is not limited to, new out-of-the-box algorithmic solutions for scientific computing, e.g. reduced basis methods for industrial problems and MOR approaches for electrochemical processes. The target audience comprises research experts and practitioners in the field of simulation, optimization and control, but the book may also be beneficial for graduate students alike.