Noise and vibration damping of Fe-Cr-x alloys

The aim of the present work is to study the noise and vibration damping capacity of ferromagnetic Fe-16%Cr base alloys (before and after heat treatment) with different Al and Mo contents. The noise damping was evaluated by the level of sound emission after an impact. The vibration damping was studied using a cantilever device. In addition to these tests, the magnetic structure of the materials was also investigated by Kerr effect. It was verified that the materials can decrease noise level in the frequency range of human earring. The vibration damping is influenced by heat treatment and chemical composition of the alloy. The improvement of vibration damping after heat treatment is ascribed to the decrease of internal stresses in materials and changes in magnetic domain structures.

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.

Simulation of Steady-State Nonlinear Heat Transfer Problems Through the Minimization of Quadratic Functionals

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.

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.

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.

Vibrations in Rotating Machinery Arising from Minor Imperfections in Component Geometries

Vibrations in machines can cause noise, decrease the performance, or even damage the machine. Vibrations appear if there is a source of vibration that excites the system. In the worst case scenario, the excitation frequency coincides with the natural frequency of the machine causing resonance. Rotating machines are a machine type, where the excitation arises from the machine itself. The excitation originates from the mass imbalance in the rotating shaft, which always exists in machines that are manufactured using conventional methods. The excitation has a frequency that is dependent on the rotational speed of the machine. The rotating machines in industrial use are usually designed to rotate at a constant rotational speed, the case where the resonances can be easily avoided. However, the machines that have a varying operational speed are more problematic due to a wider range of frequencies that have to be avoided. Vibrations, which frequencies equal to rotational speed frequency of the machine are widely studied and considered in the typical machine design process. This study concentrates on vibrations, which arise from the excitations having frequencies that are multiples of the rotational speed frequency. These vibrations take place when there are two or more excitation components in a revolution of a rotating shaft. The dissertation introduces four studies where three kinds of machines are experiencing vibrations caused by different excitations. The first studied case is a directly driven permanent magnet generator used in a wind power plant. The electromagnetic properties of the generator cause harmonic excitations in the system. The dynamic responses of the generator are studied using the multibody dynamics formulation. In another study, the finite element method is used to study the vibrations of a magnetic gear due to excitations, which frequencies equal to the rotational speed frequency. The objective is to study the effects of manufacturing and assembling inaccuracies. Particularly, the eccentricity of the rotating part with respect to non-rotating part is studied since the eccentric operation causes a force component in the direction of the shortest air gap. The third machine type is a tube roll of a paper machine, which is studied while the tube roll is supported using two different structures. These cases are studied using different formulations. In the first case, the tube roll is supported by spherical roller bearings, which have some wavinesses on the rolling surfaces. Wavinesses cause excitations to the tube roll, which starts to resonate at the frequency that is a half of the first natural frequency. The frequency is in the range where the machine normally operates. The tube roll is modeled using the finite element method and the bearings are modeled as nonlinear forces between the tube roll and the pedestals. In the second case studied, the tube roll is supported by freely rotating discs, which wavinesses are also measured. The above described phenomenon is captured as well in this case, but the simulation methodology is based on the flexible multibody dynamics formulation. The simulation models that are used in both of the last two cases studied are verified by measuring the actual devices and comparing the simulated and measured results. The results show good agreement.

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.

Stiffness based trajectory planning and feedforward based vibration suppression control of parallel robot machines

The dissertation proposes two control strategies, which include the trajectory planning and vibration suppression, for a kinematic redundant serial-parallel robot machine, with the aim of attaining the satisfactory machining performance. For a given prescribed trajectory of the robot's end-effector in the Cartesian space, a set of trajectories in the robot's joint space are generated based on the best stiffness performance of the robot along the prescribed trajectory. To construct the required system-wide analytical stiffness model for the serial-parallel robot machine, a variant of the virtual joint method (VJM) is proposed in the dissertation. The modified method is an evolution of Gosselin's lumped model that can account for the deformations of a flexible link in more directions. The effectiveness of this VJM variant is validated by comparing the computed stiffness results of a flexible link with the those of a matrix structural analysis (MSA) method. The comparison shows that the numerical results from both methods on an individual flexible beam are almost identical, which, in some sense, provides mutual validation. The most prominent advantage of the presented VJM variant compared with the MSA method is that it can be applied in a flexible structure system with complicated kinematics formed in terms of flexible serial links and joints. Moreover, by combining the VJM variant and the virtual work principle, a systemwide analytical stiffness model can be easily obtained for mechanisms with both serial kinematics and parallel kinematics. In the dissertation, a system-wide stiffness model of a kinematic redundant serial-parallel robot machine is constructed based on integration of the VJM variant and the virtual work principle. Numerical results of its stiffness performance are reported. For a kinematic redundant robot, to generate a set of feasible joints' trajectories for a prescribed trajectory of its end-effector, its system-wide stiffness performance is taken as the constraint in the joints trajectory planning in the dissertation. For a prescribed location of the end-effector, the robot permits an infinite number of inverse solutions, which consequently yields infinite kinds of stiffness performance. Therefore, a differential evolution (DE) algorithm in which the positions of redundant joints in the kinematics are taken as input variables was employed to search for the best stiffness performance of the robot. Numerical results of the generated joint trajectories are given for a kinematic redundant serial-parallel robot machine, IWR (Intersector Welding/Cutting Robot), when a particular trajectory of its end-effector has been prescribed. The numerical results show that the joint trajectories generated based on the stiffness optimization are feasible for realization in the control system since they are acceptably smooth. The results imply that the stiffness performance of the robot machine deviates smoothly with respect to the kinematic configuration in the adjacent domain of its best stiffness performance. To suppress the vibration of the robot machine due to varying cutting force during the machining process, this dissertation proposed a feedforward control strategy, which is constructed based on the derived inverse dynamics model of target system. The effectiveness of applying such a feedforward control in the vibration suppression has been validated in a parallel manipulator in the software environment. The experimental study of such a feedforward control has also been included in the dissertation. The difficulties of modelling the actual system due to the unknown components in its dynamics is noticed. As a solution, a back propagation (BP) neural network is proposed for identification of the unknown components of the dynamics model of the target system. To train such a BP neural network, a modified Levenberg-Marquardt algorithm that can utilize an experimental input-output data set of the entire dynamic system is introduced in the dissertation. Validation of the BP neural network and the modified Levenberg- Marquardt algorithm is done, respectively, by a sinusoidal output approximation, a second order system parameters estimation, and a friction model estimation of a parallel manipulator, which represent three different application aspects of this method.

Initialization of Continuous Nonlinear Models Using Extended Kalman Filter

The two main objectives of Bayesian inference are to estimate parameters and states. In this thesis, we are interested in how this can be done in the framework of state-space models when there is a complete or partial lack of knowledge of the initial state of a continuous nonlinear dynamical system. In literature, similar problems have been referred to as diffuse initialization problems. This is achieved first by extending the previously developed diffuse initialization Kalman filtering techniques for discrete systems to continuous systems. The second objective is to estimate parameters using MCMC methods with a likelihood function obtained from the diffuse filtering. These methods are tried on the data collected from the 1995 Ebola outbreak in Kikwit, DRC in order to estimate the parameters of the system.

Do whole-body vibration exercise and resistance exercise modify concentrations of salivary cortisol and immunoglobulin A?

A single bout of resistance exercise (RE) induces hormonal and immune responses, playing an important role in a long-term adaptive process. Whole-body vibration (WBV) has also been shown to affect hormonal responses. Evidence suggests that combining WBV with RE may amplify hormonal and immune responses due to the increased neuromuscular load. Therefore, the aim of this study was to evaluate salivary cortisol (Scortisol) and salivary IgA (SIgA) concentrations following a RE session combined or not with WBV. Nine university students (22.9 ± 5.1 years, 175.8 ± 5.2 cm, and 69.2 ± 7.3 kg) performed five sets of squat exercise (70% one-repetition-maximum) combined (R+V30) or not (R) with WBV at 30 Hz. Saliva samples were obtained before and after exercise. Subjects also rated their effort according to the Borg CR-10 scale (RPE). Data were analyzed by a mixed model. RPE was higher after R+V30 (8.3 ± 0.7) compared to R (6.2 ± 0.7). However, Scortisol (pre: 10.6 ± 7.6 and 11.7 ± 7.6, post: 8.3 ± 6.3 and 10.2 ± 7.2 ng/mL for R and R+V30, respectively) and SIgA concentrations (pre: 98.3 ± 22.6 and 116.1 ± 51.2, post: 116.6 ± 64.7 and 143.6 ± 80.5 µg/mL for R and R+V30, respectively) were unaffected. No significant correlations were observed between Scortisol and RPE (r = 0.45, P = 0.22; r = 0.30, P = 0.42, for R and R+V30, respectively). On the basis of these data, neither protocol modified salivary cortisol or IgA, although RPE was higher after R+V30 than R.

Linear and nonlinear analysis of heart rate variability in healthy subjects and after acute myocardial infarction in patients

The objectives of this study were to evaluate and compare the use of linear and nonlinear methods for analysis of heart rate variability (HRV) in healthy subjects and in patients after acute myocardial infarction (AMI). Heart rate (HR) was recorded for 15 min in the supine position in 10 patients with AMI taking β-blockers (aged 57 ± 9 years) and in 11 healthy subjects (aged 53 ± 4 years). HRV was analyzed in the time domain (RMSSD and RMSM), the frequency domain using low- and high-frequency bands in normalized units (nu; LFnu and HFnu) and the LF/HF ratio and approximate entropy (ApEn) were determined. There was a correlation (P < 0.05) of RMSSD, RMSM, LFnu, HFnu, and the LF/HF ratio index with the ApEn of the AMI group on the 2nd (r = 0.87, 0.65, 0.72, 0.72, and 0.64) and 7th day (r = 0.88, 0.70, 0.69, 0.69, and 0.87) and of the healthy group (r = 0.63, 0.71, 0.63, 0.63, and 0.74), respectively. The median HRV indexes of the AMI group on the 2nd and 7th day differed from the healthy group (P < 0.05): RMSSD = 10.37, 19.95, 24.81; RMSM = 23.47, 31.96, 43.79; LFnu = 0.79, 0.79, 0.62; HFnu = 0.20, 0.20, 0.37; LF/HF ratio = 3.87, 3.94, 1.65; ApEn = 1.01, 1.24, 1.31, respectively. There was agreement between the methods, suggesting that these have the same power to evaluate autonomic modulation of HR in both AMI patients and healthy subjects. AMI contributed to a reduction in cardiac signal irregularity, higher sympathetic modulation and lower vagal modulation.

Whole-body vibration decreases the proliferativeb response of TCD4+ cells in elderly individuals with knee osteoarthritis

The aim of this study was to investigate the effect of adding whole-body vibration (WBV; frequency = 35 to 40 Hz; amplitude = 4 mm) to squat training on the T-cell proliferative response of elderly patients with osteoarthritis (OA) of the knee. This study was a randomized controlled trial in which the selected variables were assessed before and after 12 weeks of training. Twenty-six subjects (72 ± 5 years of age) were divided into three groups: 1) squat training with WBV (WBV, N = 8); 2) squat training without WBV (N = 10), and 3) a control group (N = 8). Women who were ≥60 years of age and had been diagnosed with OA in at least one knee were eligible. The intervention consisted of 12 uninterrupted weeks of squatting exercise training performed 3 times/week. Peripheral blood mononuclear cells were obtained from peripheral blood collected before and after training. The proliferation of TCD4+ and TCD8+ cells was evaluated by flow cytometry measuring the carboxyfluorescein succinimidyl ester fluorescence decay before and after the intervention (∆). The proliferative response of TCD4+ cells (P = 0.02, effect size = 1.0) showed a significant decrease (23%) in the WBV group compared to the control group, while there was no difference between groups regarding the proliferative response of TCD8+ cells (P = 0.12, effect size = 2.23). The data suggest that the addition of WBV to squat exercise training might modulate T-cell-mediated immunity, minimizing or slowing disease progression in elderly patients with OA of the knee.

Vibration analysis of a power take-off line

Gear rattle is a phenomenon that occurs when idling or lightly loaded gears collide due to engine’s torque fluctuations. This behaviour is related to vibration behaviour of the transmission system. Aim of this master’s thesis is to evaluate Adams and Adams/Machinery as a simulation tools for modelling the rattle e ect in a transmission system. A case study of tractor’s power take-o driveline, suspected to be prone to rattle, is performed in this work. Modelling methods used by Adams in this type of study are presented in the theory section while simulation model build with the software during this work is presented in the results. The Machinery toolbox is used to create gears and bearings while other model components are created with standard Adams tool set. Geometries and excitations are exported from other softwares. Results were obtained from multiple variations of a base model. These result sets and literature review suggest that Adams/Machinery may not be the most suitable tool for rattle analysis. While the system behaviour was partially captured, for accurate modelling user-written routines must be used which may be more easily performed with other tools. Further research about this topic is required.

The effects of an acute bout of whole-body vibration on pulse wave velocity in individuals with SCI

Cardiovascular disease is a leading cause of mortality in the spinal cord injured (SCI) population. Reduced arterial compliance is a cardiovascular risk factor and whole body vibration (WBV) has be en shown to improve arterial compliance in able-bodied individuals. The study investigated the effect of an acute session ofWBV on arterial compliance as measured by pulse wave velocity (PWV). On separate days, arm, leg and aortic PWV were measured pre- and post- a 45 minute session of passive stance (PS) and WBV. The WBV was intermittent with a set frequency of 45Hz and amplitude of O.6mm. There was no condition by time effect when comparing PWV after WBV and PS. Following WBV, aortic (928.6±127.7 vs. 901.1±96.6cm/sec), leg (1035.2±113.8 vs.l099.8±114.2cm/sec) and arm PWV (1118.9±119.8 vs. 1181.1±124.4cm/s) did not change. As such, WBV did not reduce arterial compliance, however future research with protocol modifications is recommended.