Nonlinear dynamics and control of multibody systems

The dynamics of flexible systems, such as robot manipulators , mechanical chains or multibody systems in general, is becoming increasingly important in engineering. This article deals with some nonlinearities that arise in the study of dynamics and control of multibody systems in connection to large rotations. Specifically, a numerical scheme that adresses the conservation of fundamental constants is presented in order to analyse the control-structure interaction problems.

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.

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.

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.

Escape in a nonideal electro-mechanical system

In this work a particular system is investigated consisting of a pendulum whose point of support is vibrated along a horizontal guide by a two bar linkage driven from a DC motor, considered as a limited power source. This system is nonideal since the oscillatory motion of the pendulum influences the speed of the motor and vice-versa, reflecting in a more complicated dynamical process. This work comprises the investigation of the phenomena that appear when the frequency of the pendulum draws near a secondary resonance region, due to the existing nonlinear interactions in the system. Also in this domain due to the power limitation of the motor, the frequency of the pendulum can be captured at resonance modifying completely the final response of the system. This behavior is known as Sommerfeld effect and it will be studied here for a nonlinear system.

Use of single photon emission computed tomography and magnetic resonance to evaluate central nervous system involvement in patients with juvenile systemic lupus erythematosus

The objective of the present study was to identify the single photon emission computed tomography (SPECT) and magnetic resonance (MR) findings in juvenile systemic lupus erythematosus (JSLE) patients with CNS involvement and to try to correlate them with neurological clinical history data and neurological clinical examination. Nineteen patients with JSLE (16 girls and 3 boys, mean age at onset 9.2 years) were submitted to neurological examination, electroencephalography, cerebrospinal fluid analysis, SPECT and MR. All the evaluations were made separately within a period of 15 days. SPECT and MR findings were analyzed independently by two radiologists. Electroencephalography and cerebrospinal fluid analysis revealed no relevant alterations. Ten of 19 patients (53%) presented neurological abnormalities including present or past neurological clinical history (8/19, 42%), abnormal neurological clinical examination (5/19, 26%), and abnormal SPECT or MR (8/19, 42% and 3/19, 16%, respectively). The most common changes in SPECT were cerebral hypoperfusion and heterogeneous distribution of blood flow. The most common abnormalities in MR were leukomalacia and diffuse alterations of white matter. There was a correlation between SPECT and MR (P<0.05). We conclude that SPECT and MR are complementary and useful exams in the evaluation of neurological involvement of lupus.

Decreased left temporal lobe volume of panic patients measured by magnetic resonance imaging

Reported neuroimaging studies have shown functional and morphological changes of temporal lobe structures in panic patients, but only one used a volumetric method. The aim of the present study was to determine the volume of temporal lobe structures in patients with panic disorder, measured by magnetic resonance imaging. Eleven panic patients and eleven controls matched for age, sex, handedness, socioeconomic status and years of education participated in the study. The mean volume of the left temporal lobe of panic patients was 9% smaller than that of controls (t21 = 2.37, P = 0.028). In addition, there was a trend (P values between 0.05 and 0.10) to smaller volumes of the right temporal lobe (7%, t21 = 1.99, P = 0.06), right amygdala (8%, t21 = 1.83, P = 0.08), left amygdala (5%, t21 = 1.78, P = 0.09) and left hippocampus (9%, t21 = 1.93, P = 0.07) in panic patients compared to controls. There was a positive correlation between left hippocampal volume and duration of panic disorder (r = 0.67, P = 0.025), with recent cases showing more reduction than older cases. The present results show that panic patients have a decreased volume of the left temporal lobe and indicate the presence of volumetric abnormalities of temporal lobe structures.

Radiography, computed tomography and magnetic resonance imaging at 0.5 Tesla of mechanically inducedosteoarthritis in rabbit knees

In the present experimental study we assessed induced osteoarthritis data in rabbits, compared three diagnostic methods, i.e., radiography (XR), computed tomography (CT) and magnetic resonance imaging (MRI), and correlated the imaging findings with those obtained by macroscopic evaluation. Ten young female rabbits of the Norfolk breed were used. Seven rabbits had the right knee immobilized in extension for a period of 12 weeks (immobilized group), and three others did not have a limb immobilized and were maintained under the same conditions (control group). Alterations observed by XR, CT and MRI after the period of immobilization were osteophytes, osteochondral lesions, increase and decrease of joint space, all of them present both in the immobilized and non-immobilized contralateral limbs. However, a significantly higher score was obtained for the immobilized limbs (XT: P = 0.016, CT: P = 0.031, MRI: P = 0.0156). All imaging methods were able to detect osteoarthritis changes after the 12 weeks of immobilization. Macroscopic evaluation identified increased thickening of joint capsule, proliferative and connective tissue in the femoropatellar joint, and irregularities of articular cartilage, especially in immobilized knees. The differences among XR, CT and MRI were not statistically significant for the immobilized knees. However, MRI using a 0.5 Tesla scanner was statistically different from CT and XR for the non-immobilized contralateral knees. We conclude that the three methods detected osteoarthritis lesions in rabbit knees, but MRI was less sensitive than XR and CT in detecting lesions compatible with initial osteoarthritis. Since none of the techniques revealed all the lesions, it is important to use all methods to establish an accurate diagnosis.

Late-life depression, heart failure and frontal white matter hyperintensity: a structural magnetic resonance imaging study

The relevance of the relationship between cardiac disease and depressive symptoms is well established. White matter hyperintensity, a bright signal area in the brain on T2-weighted magnetic resonance imaging scans, has been separately associated with cardiovascular risk factors, cardiac disease and late-life depression. However, no study has directly investigated the association between heart failure, major depressive symptoms and the presence of hyperintensities. Using a visual assessment scale, we have investigated the frequency and severity of white matter hyperintensities identified by magnetic resonance imaging in eight patients with late-life depression and heart failure, ten patients with heart failure without depression, and fourteen healthy elderly volunteers. Since the frontal lobe has been the proposed site for the preferential location of white matter hyperintensities in patients with late-life depression, we focused our investigation specifically on this brain region. Although there were no significant group differences in white matter hyperintensities in the frontal region, a significant direct correlation emerged between the severity of frontal periventricular white matter hyperintensity and scores on the Hamilton scale for depression in the group with heart failure and depression (P = 0.016, controlled for the confounding influence of age). There were no significant findings in any other areas of the brain. This pattern of results adds support to a relationship between cardiovascular risk factors and depressive symptoms, and provides preliminary evidence that the presence of white matter hyperintensities specifically in frontal regions may contribute to the severity of depressive symptoms in cardiac disease.

Compensatory enlargement of human coronary arteries identified by magnetic resonance imaging

The aim of the present study was to evaluate the role of magnetic resonance imaging (MRI) for the non-invasive detection of coronary abnormalities and specifically the remodeling process in patients with coronary artery disease (CAD). MRI was performed in 10 control healthy subjects and 26 patients with angiographically proven CAD of the right coronary (RCA) or left anterior descending (LAD) artery; 23 patients were within two months of acute coronary syndromes, and 3 had stable angina with a positive test for ischemia. Wall thickness (WT), vessel wall area (VWA), total vessel area (TVA), and luminal area (LA) were measured. There were significant increases in WT (mean ± SEM, RCA: 2.62 ± 0.75 vs 0.53 ± 0.15 mm; LAD: 2.21 ± 0.69 vs 0.62 ± 0.24 mm) and in VWA (RCA: 30.96 ± 17.57 vs 2.1 ± 1.2 mm²; LAD: 19.53 ± 7.25 vs 3.6 ± 2.0 mm²) patients compared to controls (P < 0.001 for each variable). TVA values were also greater in patients compared to controls (RCA: 44.56 ± 21.87 vs 12.3 ± 4.2 mm²; LAD: 31.89 ± 11.31 vs 17.0 ± 6.2 mm²; P < 0.001). In contrast, the LA did not differ between patients and controls for RCA or LAD. When the LA was adjusted for vessel size using the LA/TVA ratio, a significant difference was found: 0.33 ± 0.16 in patients vs 0.82 ± 0.09 in controls (RCA) and 0.38 ± 0.13 vs 0.78 ± 0.06 (LAD) (P < 0.001). As opposed to normal controls, positive remodeling was present in all patients with CAD, as indicated by larger VWA. We conclude that MRI detected vessel wall abnormalities and was an effective tool for the noninvasive evaluation of the atherosclerotic process and coronary vessel wall modifications, including positive remodeling that frequently occurs in patients with acute coronary syndromes.