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.

Rapid diagnosis of resistance to imidazolinone herbicides in barnyardgrass (Echinochloa crus-galli) and control of resistant biotypes with alternative herbicides

The resistance of barnyardgrass (Echinochloa crus-galli) to imidazolinone herbicides is a worldwide problem in paddy fields. A rapid diagnosis is required for the selection of adequate prevention and control practices. The objectives of this study were to develop expedite bioassays to identify the resistance to imidazolinone herbicides in barnyardgrass and to evaluate the efficacy of alternative herbicides for the post-emergence control of resistant biotypes. Three experiments were conducted to develop methods for diagnosis of resistance to imazethapyr and imazapyr + imazapic in barnyardgrass at the seed, seedling and tiller stages, and to carry out a pot experiment to determine the efficacy of six herbicides applied at post-emergence in 13 biotypes of barnyardgrass resistant to imidazolinones. The seed soaking bioassay was not able to differentiate the resistant and susceptible biotypes. The resistance of barnyardgrass to imidazolinones was effectively discriminated in the seedlings and tiller bioassays seven days after incubation at the concentrations of 0.001 and 0.0001 mM, respectively, for both imazethapyr and imazapyr + imazapic. The biotypes identified as resistant to imidazolinones showed different patterns of susceptibility to penoxsulam, bispyribac-sodium and pyrazosulfuron-ethyl, and were all controlled with profoxydim and cyhalofop-butyl. The seedling and tiller bioassays are effective in the diagnosis of barnyardgrass resistance to imidazolinone herbicides, providing an on-season opportunity to identify the need to use alternative herbicides to be applied at post-emergence for the control of the resistant biotypes.

Dose-response curves of Lolium multiflorum biotypes resistant and susceptible to clethodim

Chemical control with herbicides, especially glyphosate, is the main method used to control ryegrass. However, the repeated use of glyphosate has selected resistant ryegrass biotypes. Thus, the ACCase inhibitor herbicides have become the main alternative to control glyphosate-resistant biotypes, being widely used by farmers in Rio Grande do Sul. Repeated use of ACCase inhibitors, in turn, have selected ryegrass biotypes resistant to this herbicide mechanism. Thus, the objective of this study was to evaluate the response of ryegrass biotypes to different clethodim rates by dose-response curves. Increasing doses (0, 12, 24, 48, 72, 96, 144 and 192 g a.i. ha-1) of the herbicide clethodim were applied at the 3-4 ryegrass leaf stage. The variables control at 14 and 28 days after treatment (DAT) and shoot dry weight were evaluated. The data were fitted by nonlinear regression log-logistic and C50 and GR50 were calculated based on the equation. The resistance factor was obtained by the ratio of C50 or GR50 of the resistant biotype by matching the susceptible biotype. Based on the equation parameters, the doses of GR50 64.7 and 234.5 g a.i. ha-1 clethodim and C50 11.2 and 172.1 g a.i. ha-1 clethodim were obtained, at 28 DAT for the susceptible and resistant biotypes, respectively. The ryegrass biotype denominated Cotril is resistant to clethodim, being controlled with a dose 15.3 times greater than that of the susceptible biotype, and a 50% reduction of this biotype occurs with a dose 3.62 times higher than that of the susceptible one.

An Alternative American Approach to Repositories

Presentation at Open Repositories 2014, Helsinki, Finland, June 9-13, 2014

Resistence of Radish Biotypes to Iodosulfuron and Alternative Control

The repetitive use of iodosulfuron for the control of weeds in winter cereals in the south of Brazil has favored the emergence of resistant Raphanus sativus biotypes. The objective of this study was to evaluate: the response of Raphanus sativus biotypes susceptible and resistant to different dosages of iodosulfuron; the control of biotypes with alternative registered herbicides for the control of the species in crops of wheat, corn and soybean; and the existence of cross-resistance of the biotypes. Thus, four experiments were done in a greenhouse, with a completely randomized design and four replicates. The experimental units were composed of vases with a volumetric capacity of 0.75 L filled with substrate, containing a plant each. For the dose-response curve, three biotypes (factor A) and nine doses of the iodosulfuron herbicide (factor B) were used. For the alternative control, the recommendation was herbicides in pre or postemergence of the crops, and the crossed-resistance was evaluated by using herbicides that inhibit the ALS enzyme of different chemical groups. The analyzed variables were control and shoot dry matter. GR50 of the susceptible biotype (B1) was 0.11 g a.i. ha-1, whereas GR50 of resistant biotypes (B4 and B13) was 102.9 and 86.8 g a.i. ha-1 of the iodosulfuron herbicide, respectively. The resistant biotypes presented crossed resistance to herbicides that inhibit the ALS enzyme, where the control can be efficient with the use of herbicides with different action mechanisms.