1,283 research outputs found

    Eliminating flutter for clamped von Karman plates immersed in subsonic flows

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    We address the long-time behavior of a non-rotational von Karman plate in an inviscid potential flow. The model arises in aeroelasticity and models the interaction between a thin, nonlinear panel and a flow of gas in which it is immersed [6, 21, 23]. Recent results in [16, 18] show that the plate component of the dynamics (in the presence of a physical plate nonlinearity) converge to a global compact attracting set of finite dimension; these results were obtained in the absence of mechanical damping of any type. Here we show that, by incorporating mechanical damping the full flow-plate system, full trajectories---both plate and flow---converge strongly to (the set of) stationary states. Weak convergence results require "minimal" interior damping, and strong convergence of the dynamics are shown with sufficiently large damping. We require the existence of a "good" energy balance equation, which is only available when the flows are subsonic. Our proof is based on first showing the convergence properties for regular solutions, which in turn requires propagation of initial regularity on the infinite horizon. Then, we utilize the exponential decay of the difference of two plate trajectories to show that full flow-plate trajectories are uniform-in-time Hadamard continuous. This allows us to pass convergence properties of smooth initial data to finite energy type initial data. Physically, our results imply that flutter (a non-static end behavior) does not occur in subsonic dynamics. While such results were known for rotational (compact/regular) plate dynamics [14] (and references therein), the result presented herein is the first such result obtained for non-regularized---the most physically relevant---models

    Utilization of Decomposition Techniques for Analyzing and Characterizing Flows

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    This thesis presents the utilization of two different decomposition techniques, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), for enhanced understanding of flow structures and their stability. The advantages of these techniques are shown for a range of flow situations, most of which are turbulent. It is shown that by these methods additional insight into complex flow situations can be gained. Such insight has been found to be needed for the flow in straight and 90 degree curved pipes. The so-called swirl switching phenomenon is investigated, which is a large scale oscillation of the flow after the bend. This phenomenon is classified into a low frequency and a high frequency switching, each with its own mechanism of formation. It is shown that while the low frequency switching stems from very-large-scale motions created in the upstream pipe, the high frequency switching results from the bend itself, making it an inherent property of the system. The second set of studies consider swirling flow in combustor-related geometries, using both high and low swirl levels. These investigations show highly energetic unsteady structures in the strongly vortical regions. The spatial symmetry of these flow modes reflect the level of confinement. While the vortices that are weakly confined show unsteady modes reflecting their displacement, the strongly confined vortices show low-order multipole deformations. For the low swirl burner, which is the only reacting flow considered, the flame is stabilized without the presence of vortex breakdown. To be able to investigate how the flame is anchored above the burner, an extended version of DMD (EDMD) is introduced, which helps to couple the flow with the flame. Using this method, a mechanism contributing to the flame stabilization is isolated. The third and final set of studies involve flow around cylinders and beams. These objects are flexible and respond to the forces that the flow exerts on them. For the flow around cylinders, which are connected to a spring system, the natural frequency of the spring-cylinder system and the frequency from the von Karman vortex shedding are the two a priori known frequencies of the system. Three different flow regimes are considered, one where the two frequencies are similar, giving resonance, and two cases where one frequency is far above/below the other. For flow around a single cylinder, an unexpected high energy low frequency mode is found off-resonance, which is argued to contribute greatly to the chaotic behaviour for the case with the loose spring. For a multiple cylinder array, while the strong low frequency mode found for the single cylinder case has been suppressed, an unexpected synchronization is seen. Considering the flow around a stiff and a flexible beam, a strong beat frequency is found for the lift force. While the beating is seen to be regular for the flexible beam, it appears intermittently for the stiff beam. The flow behaviour giving rise to this forcing is elucidated using the POD and DMD analyses

    Von Karman Evolution Equations

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    The role of dissipation in flexural wave turbulence: from experimental spectrum to Kolmogorov-Zakharov spectrum

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    The Weak Turbulence Theory has been applied to waves in thin elastic plates obeying the F\"oppl-Von K\'arm\'an dynamical equations. Subsequent experiments have shown a strong discrepancy between the theoretical predictions and the measurements. Both the dynamical equations and the Weak Turbulence Theory treatment require some restrictive hypotheses. Here a direct numerical simulation of the F\"oppl-Von K\'arm\'an equations is performed and reproduces qualitatively and quantitatively the experimental results when the experimentally measured damping rate of waves Îłk=a+bk2\gamma_\mathbf{k}= a + bk^2 is used. This confirms that the F\"oppl-Von K\'arm\'an equations are a valid theoretical framework to describe our experiments. When we progressively tune the dissipation so that to localize it at the smallest scales, we observe a gradual transition between the experimental spectrum and the Kolmogorov-Zakharov prediction. Thus it is shown dissipation has a major influence on the scaling properties stationary solutions of weakly non linear wave turbulence.Comment: 10 pages, 11 figure

    Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping

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    Presented here is a study of a viscoelastic wave equation with supercritical source and damping terms. We employ the theory of monotone operators and nonlinear semigroups, combined with energy methods to establish the existence of a unique local weak solution. In addition, it is shown that the solution depends continuously on the initial data and is global provided the damping dominates the source in an appropriate sense.Comment: The 2nd version includes a new proof of the energy identit

    Moore-Gibson-Thompson equation with memory, part II: general decay of energy

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    We study a temporally third order (Moore-Gibson-Thompson) equation with a memory term. Previously it is known that, in non-critical regime, the global solutions exist and the energy functionals decay to zero. More precisely, it is known that the energy has exponential decay if the memory kernel decays exponentially. The current work is a generalization of the previous one (Part I) in that it allows the memory kernel to be more general and shows that the energy decays the same way as the memory kernel does, exponentially or not.Comment: 22 page

    Efficient synthesis of tension modulation in strings and membranes based on energy estimation

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    String and membrane vibrations cannot be considered as linear above a certain amplitude due to the variation in string or membrane tension. A relevant special case is when the tension is spatially constant and varies in time only in dependence of the overall string length or membrane surface. The most apparent perceptual effect of this tension modulation phenomenon is the exponential decay of pitch in time. Pitch glides due to tension modulation are an important timbral characteristic of several musical instruments, including the electric guitar and tom-tom drum, and many ethnic instruments. This paper presents a unified formulation to the tension modulation problem for onedimensional (1-D) (string) and two-dimensional (2-D) (membrane) cases. In addition, it shows that the short-time average of the tension variation, which is responsible for pitch glides, is approximately proportional to the system energy. This proportionality allows the efficient physics-based sound synthesis of pitch glides. The proposed models require only slightly more computational resources than linear models as opposed to earlier tension-modulated models of higher complexity

    Studies on Dynamics of Financial Markets and Reacting Flows

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    One of the central problems in financial markets analysis is to understand the nature of the underlying stochastic dynamics. Several intraday behaviors are analyzed to study trading day ensemble averages of both high frequency foreign exchange and stock markets data. These empirical results indicate that the underlying stochastic processes have nonstationary increments. The three most liquid foreign exchange markets and five most actively traded stocks each contains several time intervals during the day where the mean square fluctuation and variance of increments can be fit by power law scaling in time. The fluctuations in return within these intervals follow asymptotic bi-exponential distributions. Based on these empirical results, an intraday stochastic model with linear variable diffusion coefficient is proposed to approximate the real dynamics of financial markets to the lowest order, and to test the effects of time averaging techniques typically used for financial time series analysis. The proposed model replicates major statistical characteristics of empirical financial time series and only ensemble averaging techniques deduce the underlying dynamics correctly. The proposed model also provides new insight into the modeling of financial markets' dynamics in microscopic time scales. Also discussed are analytical and computational studies of reacting flows. Many dynamical features of the flows can be inferred from modal decompositions and coupling between modes. Both proper orthogonal (POD) and dynamic mode (DMD) decompositions are conducted on high-frequency, high-resolution empirical data and their results and strengths are compared and contrasted. In POD the contribution of each mode to the flow is quantified using the latency only, whereas each DMD mode can be associated a latency as well as a unique complex growth rate. By comparing DMD spectra from multiple nominally identical experiments, it is possible to identify "reproducible" modes in a flow. A similar differentiation cannot be made using POD. Time-dependent coefficients of DMD modes are complex. Even in noisy experimental data, it is found that the phase of these coefficients (but not their magnitude) exhibits repeatable dynamics. Hence it is suggested that dynamical characterizations of complex flows are best analyzed through the phase dynamics of reproducible DMD modes.Physics, Department o

    Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non-Fourier heat flux model

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    Nonlinear, steady-state, viscous flow and heat transfer between two stretchable rotating disks spinning at dissimilar velocities is studied with a non-Fourier heat flux model. A non-deformable porous medium is intercalated between the disks and the Darcy model is employed to simulate matrix impedance. The conservation equations are formulated in a cylindrical coordinate system and via the Von Karman transformations are rendered into a system of coupled, nonlinear ordinary differential equations. The emerging boundary value problem is controlled by number of dimensionless dimensionless parameters i.e. Prandtl number, upper disk stretching, lower disk stretching, permeability, non-Fourier thermal relaxation and relative rotation rate parameters. A perturbation solution is developed and the impact of selected parameters on radial and tangential velocity components, temperature, pressure, lower disk radial and tangential skin friction components and surface heat transfer rate are visualized graphically. Validation of solutions with the homotopy analysis method is included. Extensive interpretation of the results is presented which are relevant to to rotating disk bioreactors in chemical engineering
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