Development of a three-dimensional nonlinear viscoelastic constitutive model of solid propellant

A three dimensional nonlinear viscoelastic constitutive model for the solid propellant is developed. In their earlier work, the authors have developed an isotropic constitutive model and verified it for one dimensional case. In the present work, the validity of the model is extended to three-dimensional cases. Large deformation, dewetting and cyclic loading effects are treated as the main sources of nonlinear behavior of the solid propellant. Viscoelastic dewetting criteria is used and the softening of the solid propellant due to dewetting is treated by the modulus decrease. The nonlinearities during cyclic loading are accounted for by the functions of the octahedral shear strain measure. The constitutive equation is implemented into a finite element code for the analysis of propellant grains. A commercial finite element package ‘ABAQUS’ is used for the analysis and the model is introduced into the code through a user subroutine. The model is evaluated with different loading conditions and the predicted values are in good agreement with the measured ones. The resulting model applied to analyze a solid propellant grain for the thermal cycling load.

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.

Bioelectrical impedance spectroscopy for the assessment of body fluid volumes of term neonates

The assessment of fluid volume in neonates by a noninvasive, inexpensive, and fast method can contribute significantly to increase the quality of neonatal care. The objective of the present study was to calibrate an acquisition system and software to estimate the bioelectrical impedance parameters obtained by a method of bioelectrical impedance spectroscopy based on step response and to develop specific equations for the neonatal population to determine body fluid compartments. Bioelectric impedance measurements were performed by a laboratory homemade instrument. The volumes were estimated in a clinical study on 30 full-term neonates at four different times during the first month of life. During the first 24 hours of life the total body water, extracellular water and intracellular water were 2.09 ± 0.25, 1.20 ± 0.19, and 0.90 ± 0.25 liters, respectively. By the 48th hour they were 1.87 ± 0.27, 1.08 ± 0.17, and 0.79 ± 0.21 liters, respectively. On the 10th day they were 2.02 ± 0.25, 1.29 ± 0.21, and 0.72 ± 0.14 liters, respectively, and after 1 month they were 2.34 ± 0.27, 1.62 ± 0.20, and 0.72 ± 0.13 liters, respectively. The behavior of the estimated volume was correlated with neonatal body weight changes, leading to a better interpretation of such changes. In conclusion, this study indicates the feasibility of bioelectrical impedance spectroscopy as a method to help fluid administration in intensive care neonatal units, and also contribute to the development of new equations to estimate neonatal body fluid contents.

Proton magnetic resonance spectroscopy of the frontal, cingulate and perirolandic cortices and its relationship to skin conductance in patients with schizophrenia

The aim of the present study was to determine whether specific subgroups of schizophrenic patients, grouped according to electrodermal characteristics, show differences in the N-acetylaspartate/creatine plus choline (NAA / (Cr + Cho)) ratios in the frontal, cingulate and perirolandic cortices. Skin conductance levels (SCL) and skin conductance responses to auditory stimulation were measured in 38 patients with schizophrenia and in the same number of matched healthy volunteers (control). All subjects were submitted to multivoxel proton magnetic resonance spectroscopic imaging. When compared to the control group, patients presented significantly lower NAA / (Cr + Cho) ratios in the right dorsolateral prefrontal cortex (schizophrenia = 0.95 ± 0.03; control = 1.12 ± 0.04) and in the right (schizophrenia = 0.88 ± 0.02; control = 0.94 ± 0.03) and left (schizophrenia = 0.84 ± 0.03; control = 0.94 ± 0.03) cingulates. These ratios did not differ between electrodermally responsive and non-responsive patients. When patients were divided into two groups: lower SCL (less than the mean SCL of the control group minus two standard deviations) and normal SCL (similar to the control group), the subgroup with a lower level of SCL showed a lower NAA / (Cr + Cho) ratio in the left cingulate (0.78 ± 0.05) than the controls (0.95 ± 0.02, P < 0.05) and the subgroup with normal SCL (0.88 ± 0.03, P < 0.05). There was a negative correlation between the NAA / (Cr + Cho) ratio in the left cingulate of patients with schizophrenia and the duration of the disease and years under medication. These data suggest the existence of a schizophrenic subgroup characterized by low SCL that could be a consequence of the lower neuronal viability observed in the left cingulate of these patients.

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.

Thalamic metabolic abnormalities in patients with Huntington's disease measured by magnetic resonance spectroscopy

Huntington's disease (HD) is a neurologic disorder that is not completely understood; its fundamental physiological mechanisms and chemical effects remain somewhat unclear. Among these uncertainties, we can highlight information about the concentrations of brain metabolites, which have been widely discussed. Concentration differences in affected, compared to healthy, individuals could lead to the development of useful tools for evaluating the progression of disease, or to the advance of investigations of different/alternative treatments. The aim of this study was to compare the thalamic concentration of metabolites in HD patients and healthy individuals using magnetic resonance spectroscopy. We used a 2.0-Tesla magnetic field, repetition time of 1500 ms, and echo time of 135 ms. Spectra from 40 adult HD patients and 26 control subjects were compared. Quantitative analysis was performed using the LCModel method. There were statistically significant differences between HD patients and controls in the concentrations ofN-acetylaspartate+N-acetylaspartylglutamate (NAA+NAAG; t-test, P<0.001), and glycerophosphocholine+phosphocholine (GPC+PCh;t-test, P=0.001) relative to creatine+phosphocreatine (Cr+PCr). The NAA+NAAG/Cr+PCr ratio was decreased by 9% and GPC+PCh/Cr+PCr increased by 17% in patients compared with controls. There were no correlations between the concentration ratios and clinical features. Although these results could be caused by T1 and T2 changes, rather than variations in metabolite concentrations given the short repetition time and long echo time values used, our findings point to thalamic dysfunction, corroborating prior evidence.