Vibration analysis of cracked aluminium plates

This research is concerned with analytical modelling of the effects of cracks in structural plates and panels within aerospace systems such as aeroplane fuselage, wing, and tail-plane structures, and, as such, is part of a larger body of research into damage detection methodologies in such systems. This study is based on generating a so-called reduced order analytical model of the behaviour of the plate panel, within which a crack with some arbitrary characteristics is present, and which is subjected to a force that causes it to vibrate. In practice such a scenario is potentially extremely dangerous as it can lead to failure, with obvious consequences. The equation that is obtained is in the form of the classical Duffing equation, in this case, the coefficients within the equation contain information about the geometrical and mass properties of the plate, the loading and boundary conditions, and the geometry, location, and potentially the orientation of the crack. This equation has been known for just over a century and has in the last few decades received very considerable attention from both the analytical dynamics community and also from the dynamical systems researchers, in particular the work of Ueda, Thompson, in the 1970s and 1980s, and Thomsen in the 1990s and beyond. An approximate analytical solution is obtained by means of the perturbation method of multiple scales. This powerful method was popularized in the 1970s by Ali H.Nayfeh, and discussed in his famous books, ‘Perturbation Methods’ (1974) and ‘Nonlinear Oscillations’ (1979, with D.T.Mook), and also by J.Murdock (1990), and M.P.Cartmell et al. (2003) and has been shown to be immensely useful for a wide range of nonlinear vibration problems. In this work it is shown that different boundary conditions can be admitted for the plate and that the modal natural frequencies are sensitive to the crack geometry. Bifurcatory behaviour of the cracked plate has then been examined numerically, for a range of parameters. The model has been tested against experimental work and against a Finite Element model, with good corroboration from both. In all events, this is a significant new result in the field and one that if implemented within a larger damage detection strategy, could be of considerable practical use

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Anticipating Critical Transitions with Nonlinearity, Periodicity and Heterogeneity

Many natural and engineering systems may switch abruptly from one stable state to another due to a small perturbation to the system's state or a small change in the underlining conditions. In ecosystems, for example, extinctions of species or desertification can occur rapidly. Therefore, critical transitions can be dangerous to a number of systems, and it could be very beneficial if monitoring or early warning methods were available while the system is still in the healthy regime. The approach of critical transitions in many natural and engineering systems is accompanied by a phenomenon called critical slowing down. Theoretical and experimental studies have suggested that responses to small perturbations become increasingly slow when these systems are near critical transitions. Statistics such as variance, autocorrelation calculated from time series data have been proposed as early warning signals to anticipate the system's approach to a transition point. The problem of anticipating critical transitions becomes more complicated when other factors come into play. Factors such as nonlinearity, periodicity and heterogeneity can alter the behavior of the system, and thus affect the applicability of generic early warning signals. This thesis examines the effect of these factors on the critical transition of a system, and develops new data-driven approaches accordingly. To deal with and exploit the existence of nonlinearity in the system, recoveries from large instead of small perturbations are used to calculate the recovery rates of the system versus amplitudes. Under the circumstances of periodicity, recovery rates are calculated discretely via the Poincare section. Using experimental and computational data, we show that a combination of using recoveries from large perturbations and calculating recovery rates using the Poincare section can be highly effective in terms of anticipating critical transitions for systems with parametric resonance. Moreover, this thesis develops new early warning signals for spatially extended systems based on the eigenvalues of the covariance matrix. We mathematically show that the dominance of the largest eigenvalue of the covariance matrix can be used as an early warning signal by establishing the relationship between the eigenvalues of the covariance matrix and the eigenvalues of the force matrix. This new set of early warning signals are especially useful when the system has strong spatial heterogeneity. Lastly, this thesis investigates the influence of the choice of hyper-parameters, such as moving window size, sample rate, detrending methods, on the robustness of several early warning signals. General rules regarding data preparation and hypothesis testing are proposed.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145907/1/shychen_1.pd

Experimental investigation of oscillatory heat release mechanisms and stability margin analysis in lean -premixed combustion

Lean-premixed combustion has become an acceptable means of achieving ultra-low NOx emissions from land-based gas turbines. Further reduction may be possible through the use of hydrogen augmented or syngas fuels. However, advanced combustor designs developed to utilize these technologies often encounter thermoacoustic instabilities that may significantly hamper engine performance and shorten component life-cycles. These dynamics, although not fully understood, occur through a complex interaction between variations in heat release rate and acoustic properties of the system, and can be exacerbated by variable fuel properties in natural gas and syngas applications.;Theoretical models of thermoacoustic instabilities have attempted to describe the coupling process through reduced-order models that represent mechanisms suspected of contributing to variations in the heat release rate such as variations in fuel/air mixing, fluctuations of heat release through vortex shedding and periodic changes in the flame structure. These reduced-order models have demonstrated only a modest ability at predicting instabilities even in relatively simple systems. This may be due to the inherent complexity from interacting processes, the use of over-simplifying assumptions and the lack of experimental verification.;In this study a simple conical flame, used to reduce the number of contributing mechanisms, is utilized to experimentally evaluate the relationship between the heat release rate and variations in the flame surface area. Results indicated that while area perturbations can adequately describe the magnitude of heat release fluctuations, the area perturbations are not a direct indicator of the phase of heat release needed for closed-loop stability analysis.;Time-resolved particle image velocimetry was used to quantify the near-field acoustics and the dilatation rate field in the pre- and post-flame regions of the flow. Measurements indicated that multi-dimensional acoustics dominate the pre-combustion flow field with radial and axial acoustic velocities of similar magnitudes. Variations in the flame structure potentially due to alternating regions of positive and negative flame stretch were also observed and may result in variations in the flame speed. As it is common to assume constant flame speed and one-dimensional acoustics, the experimental identification of these altered mechanisms may help to resolve discrepancies compared to a number of published reduced-order models

A Comparative Analysis of Signal Decomposition Techniques for Structural Health Monitoring on an Experimental Benchmark

Signal Processing is, arguably, the fundamental enabling technology for vibration-based Structural Health Monitoring (SHM), which includes damage detection and more advanced tasks. However, the investigation of real-life vibration measurements is quite compelling. For a better understanding of its dynamic behaviour, a multi-degree-of-freedom system should be efficiently decomposed into its independent components. However, the target structure may be affected by (damage-related or not) nonlinearities, which appear as noise-like distortions in its vibrational response. This response can be nonstationary as well and thus requires a time-frequency analysis. Adaptive mode decomposition methods are the most apt strategy under these circumstances. Here, a shortlist of three well-established algorithms has been selected for an in-depth analysis. These signal decomposition approaches—namely, the Empirical Mode Decomposition (EMD), the Hilbert Vibration Decomposition (HVD), and the Variational Mode Decomposition (VMD)—are deemed to be the most representative ones because of their extensive use and favourable reception from the research community. The main aspects and properties of these data-adaptive methods, as well as their advantages, limitations, and drawbacks, are discussed and compared. Then, the potentialities of the three algorithms are assessed firstly on a numerical case study and then on a well-known experimental benchmark, including nonlinear cases and nonstationary signals

Task-adaptive physical reservoir computing

Reservoir computing is a neuromorphic architecture that potentially offers viable solutions to the growing energy costs of machine learning. In software-based machine learning, neural network properties and performance can be readily reconfigured to suit different computational tasks by changing hyperparameters. This critical functionality is missing in ``physical" reservoir computing schemes that exploit nonlinear and history-dependent memory responses of physical systems for data processing. Here, we experimentally present a `task-adaptive' approach to physical reservoir computing, capable of reconfiguring key reservoir properties (nonlinearity, memory-capacity and complexity) to optimise computational performance across a broad range of tasks. As a model case of this, we use the temperature and magnetic-field controlled spin-wave response of Cu$_2$OSeO$_3$ that hosts skyrmion, conical and helical magnetic phases, providing on-demand access to a host of different physical reservoir responses. We quantify phase-tunable reservoir performance, characterise their properties and discuss the correlation between these in physical reservoirs. This task-adaptive approach overcomes key prior limitations of physical reservoirs, opening opportunities to apply thermodynamically stable and metastable phase control across a wide variety of physical reservoir systems, as we show its transferable nature using above(near)-room-temperature demonstration with Co$_{8.5}$Zn$_{8.5}$Mn$_{3}$ (FeGe).Comment: Main manuscript: 14 pages, 5 figures. Supplementary materials: 13 pages, 10 figure