A frequency-domain pseudo-force method for dynamic structural analysis nonlinear systems and nonproportional damping

A frequency-domain method for nonlinear analysis of structural systems with viscous, hysteretic, nonproportional and frequency-dependent damping is presented. The nonlinear effects and nonproportional damping are considered through pseudo-force terms. The modal coordinates uncoupled equations are iteratively solved. The treatment of initial conditions in the frequency domain which is necessary for the treatment of the uncoupled equations is initially adressed.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Covalidation of Integral Transforms and Method of Lines in Nonlinear Convection-Diffusion with Mathematica

The Mathematica system (version 4.0) is employed in the solution of nonlinear difusion and convection-difusion problems, formulated as transient one-dimensional partial diferential equations with potential dependent equation coefficients. The Generalized Integral Transform Technique (GITT) is first implemented for the hybrid numerical-analytical solution of such classes of problems, through the symbolic integral transformation and elimination of the space variable, followed by the utilization of the built-in Mathematica function NDSolve for handling the resulting transformed ODE system. This approach ofers an error-controlled final numerical solution, through the simultaneous control of local errors in this reliable ODE's solver and of the proposed eigenfunction expansion truncation order. For covalidation purposes, the same built-in function NDSolve is employed in the direct solution of these partial diferential equations, as made possible by the algorithms implemented in Mathematica (versions 3.0 and up), based on application of the method of lines. Various numerical experiments are performed and relative merits of each approach are critically pointed out.

Estimating Attractor Dimension on the Nonlinear Pendulum Time Series

Chaotic dynamical systems exhibit trajectories in their phase space that converges to a strange attractor. The strangeness of the chaotic attractor is associated with its dimension in which instance it is described by a noninteger dimension. This contribution presents an overview of the main definitions of dimension discussing their evaluation from time series employing the correlation and the generalized dimension. The investigation is applied to the nonlinear pendulum where signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the time series. State space reconstruction and the determination of attractor dimensions are carried out regarding periodic and chaotic signals. Results obtained from time series analyses are compared with a reference value obtained from the analysis of mathematical model, estimating noise sensitivity. This procedure allows one to identify the best techniques to be applied in the analysis of experimental data.

An Investigation into Mechanisms of Loss of Safe Basins in a 2 D.O.F. Nonlinear Oscillator

In this work we consider the transient stability of coupled motions of a 2 D.O.F. nonlinear oscillator that can represent, for example, the motions of a sea vessel under the action of trains of regular lateral waves. Instability is studied as the escape of the system from a safe potential well. The set of initial conditions in phase space that lead to acceptable motions constitutes its safe basin. We investigate the evolution of these safe basins under variation of parameters such as frequency and amplitude of waves, and an internal tuning parameter. Complex nonlinear phenomena are known to play an important role in determining the loss of safe basins as, say, wave amplitude is increased. We therefore investigate those processes, and attempt to classify them in terms of their speed relative to changes in parameter values. "Mechanism basins" are produced depicting regions of parameter space in which rapid or slow losses of safe basin are observed. We propose that a comprehensive understanding of mechanisms of loss of safe basins can be a valuable tool in assessing stability properties of these systems, and we give a conceptual view of how such information could be used.

Experimental Vibration Characteristics of a Beam with Nonlinear Support Using Receptance Coupling Analysis

This paper applies the Multi-Harmonic Nonlinear Receptance Coupling Approach (MUHANORCA) (Ferreira 1998) to evaluate the frequency response characteristics of a beam which is clamped at one end and supported at the other end by a nonlinear cubic stiffness joint. In order to apply the substructure coupling technique, the problem was characterised by coupling a clamped linear beam with a nonlinear cubic stiffness joint. The experimental results were obtained by a sinusoidal excitation with a special force control algorithm where the level of the fundamental force is kept constant and the level of the harmonics is kept zero for all the frequencies measured.

Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study

In this paper is Analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. The dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. In this critical point, a Hopf bifurcation occurs. In this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). This local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.

Signaled two-way avoidance learning using electrical stimulation of the inferior colliculus as negative reinforcement: effects of visual and auditory cues as warning stimuli

The inferior colliculus is a primary relay for the processing of auditory information in the brainstem. The inferior colliculus is also part of the so-called brain aversion system as animals learn to switch off the electrical stimulation of this structure. The purpose of the present study was to determine whether associative learning occurs between aversion induced by electrical stimulation of the inferior colliculus and visual and auditory warning stimuli. Rats implanted with electrodes into the central nucleus of the inferior colliculus were placed inside an open-field and thresholds for the escape response to electrical stimulation of the inferior colliculus were determined. The rats were then placed inside a shuttle-box and submitted to a two-way avoidance paradigm. Electrical stimulation of the inferior colliculus at the escape threshold (98.12 ± 6.15 (A, peak-to-peak) was used as negative reinforcement and light or tone as the warning stimulus. Each session consisted of 50 trials and was divided into two segments of 25 trials in order to determine the learning rate of the animals during the sessions. The rats learned to avoid the inferior colliculus stimulation when light was used as the warning stimulus (13.25 ± 0.60 s and 8.63 ± 0.93 s for latencies and 12.5 ± 2.04 and 19.62 ± 1.65 for frequencies in the first and second halves of the sessions, respectively, P<0.01 in both cases). No significant changes in latencies (14.75 ± 1.63 and 12.75 ± 1.44 s) or frequencies of responses (8.75 ± 1.20 and 11.25 ± 1.13) were seen when tone was used as the warning stimulus (P>0.05 in both cases). Taken together, the present results suggest that rats learn to avoid the inferior colliculus stimulation when light is used as the warning stimulus. However, this learning process does not occur when the neutral stimulus used is an acoustic one. Electrical stimulation of the inferior colliculus may disturb the signal transmission of the stimulus to be conditioned from the inferior colliculus to higher brain structures such as amygdala

Kalm's account of his visit to England on his way to America in 1748

With two maps and several illustrations

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.

Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Kinetics of TNF-alpha and IFN-gamma mRNA expression in islets and spleen of NOD mice

Insulin-dependent diabetes mellitus is caused by autoimmune destruction of pancreatic ß cells. Non-obese diabetic (NOD) mice spontaneously develop diabetes similar to the human disease. Cytokines produced by islet-infiltrating mononuclear cells may be directly cytotoxic and can be involved in islet destruction coordinated by CD4+ and CD8+ cells. We utilized a semiquantitative RT-PCR assay to analyze in vitro the mRNA expression of TNF-alpha and IFN-gamma cytokine genes in isolated islets (N = 100) and spleen cells (5 x 10(5) cells) from female NOD mice during the development of diabetes and from female CBA-j mice as a related control strain that does not develop diabetes. Cytokine mRNAs were measured at 2, 4, 8, 14 and 28 weeks of age from the onset of insulitis to the development of overt diabetes. An increase in IFN-gamma expression in islets was observed for females aged 28 weeks (149 ± 29 arbitrary units (AU), P<0.05, Student t-test) with advanced destructive insulitis when compared with CBA-j mice, while TNF-alpha was expressed in both NOD and CBA-j female islets at the same level at all ages studied. In contrast, TNF-alpha in spleen was expressed at higher levels in NOD females at 14 weeks (99 ± 8 AU, P<0.05) and 28 weeks (144 ± 17 AU, P<0.05) of age when compared to CBA-j mice. The data suggest that IFN-gamma and TNF-alpha expression in pancreatic islets of female NOD mice is associated with ß cell destruction and overt diabetes.

Pressure-assisted cold denaturation of hen egg white lysozyme: the influence of co-solvents probed by hydrogen exchange nuclear magnetic resonance

COSY proton nuclear magnetic resonance was used to measure the exchange rates of amide protons of hen egg white lysozyme (HEWL) in the pressure-assisted cold-denatured state and in the heat-denatured state. After dissolving lysozyme in deuterium oxide buffer, labile protons exchange for deuterons in such a way that exposed protons are substituted rapidly, whereas "protected" protons within structured parts of the protein are substituted slowly. The exchange rates k obs were determined for HEWL under heat treatment (80ºC) and under high pressure conditions at low temperature (3.75 kbar, -13ºC). Moreover, the influence of co-solvents (sorbitol, urea) on the exchange rate was examined under pressure-assisted cold denaturation conditions, and the corresponding protection factors, P, were determined. The exchange kinetics upon heat treatment was found to be a two-step process with initial slow exchange followed by a fast one, showing residual protection in the slow-exchange state and P-factors in the random-coil-like range for the final temperature-denatured state. Addition of sorbitol (500 mM) led to an increase of P-factors for the pressure-assisted cold denatured state, but not for the heat-denatured state. The presence of 2 M urea resulted in a drastic decrease of the P-factors of the pressure-assisted cold denatured state. For both types of co-solvents, the effect they exert appears to be cooperative, i.e., no particular regions within the protein can be identified with significantly diverse changes of P-factors.