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.

Neutron tomography using projection data obtained by Monte Carlo simulation for nondestructive evaluation

This work present the application of a computer package for generating of projection data for neutron computerized tomography, and in second part, discusses an application of neutron tomography, using the projection data obtained by Monte Carlo technique, for the detection and localization of light materials such as those containing hydrogen, concealed by heavy materials such as iron and lead. For tomographic reconstructions of the samples simulated use was made of only six equal projection angles distributed between 0º and 180º, with reconstruction making use of an algorithm (ARIEM), based on the principle of maximum entropy. With the neutron tomography it was possible to detect and locate polyethylene and water hidden by lead and iron (with 1cm-thick). Thus, it is demonstrated that thermal neutrons tomography is a viable test method which can provide important interior information about test components, so, extremely useful in routine industrial applications.

Estimativa do grau de infestação numa pastagem de Panicum maximum Jacq

Um piquete de capim-colonião (Panicum maximum Jacq) submetido a pastoreio contínuo e a roçadas periódicas revelou, seis anos após o plantio, elevado grau de infestação por outras plantas, destacando-se entre elas a grama-batatais (Paspalum notatum Flügge) que apresentou 85% de frequência e 20,9% de biomassa epígea seca relativa. As dicotiledóneas, em conjunto, apresentaram frequência de 95% e biomassa relativa de 38,7% mas a sua contribuição específica foi muito reduzida. O capim-colonião, por sua vez, apesar da frequência de 95%, apresentou apenas 32,2% de biomassa relativa (diminuição de 67,8%). Estas profundas alterações da flora e da vegetação podem ser atribuidas, em grande parte, a dois fatores: a) ação seletiva da roçadeira; b) preferências alimentares e disseminação endozoócora da gramabatatais pelos bovinos.

Efeito de adjuvantes na calda e do estádio de desenvolvimento das plantas, no controle do capim-colonião (Panicum maximum) com glyphosate

O objetivo do presente trabalho foi estudar a possibilidade da redução de dosagens de glyphosate (N-(fosfonometil)-glicina) em função de aumentos na quantidade de óleo vegetal e uréia adicionados como adjuvantes à calda. Além disso, avaliou-se o efeito desse herbicida aplicado isolado ou combinado com os adjuvantes, em três estádios de crescimento do capim-colonião. Os experimentos foram instalados nas entrelinhas de pomares de citros, variedade Pera Rio, do município de Barretos/SP, com altas infestações de capim-colonião, no ano de 1990. Testou-se o glyphosate isolado, na dosagem de 1,8 kg/ha de equivalente ácido (e.a.) e nas dosagens de 1,44, 1,08 e 0,72 kg/ha, adicionadas de 1,0, 2,0 e 3,0 l/ha de óleo vegetal e utilizou-se uma testemunha, tratada apenas com água. As plantas de capim-colonião mediam 1,5 m de altura. Em outro experimento, o herbicida foi testado isoladamente na dosagem de 1,08 kg e.a./ha, e combinado com 2 l/ha de óleo vegetal ou 0,3% de uréia, sob os três estádios de crescimento do capim-colonião: a) 0,6m de altura e início do florescimento e frutificação; b) 1,5m de altura, florescimento e frutificação plenos; c) 0,5m de altura, na forma de rebrota da “touceira” após roçada da planta adulta, início de florescimento e frutificação. A adição de 2 l/ha de óleo vegetal na calda de pulverização, permitiu redução de 0,72 kg/ha do e.a. do glyphosate, sem prejuízos para o controle em relação a aplicação isolada na dosagem de 1,80 kg/ha. Nas mesmas condições, a adição de 0,2% de uréia proporcionou redução de 0,36 kg/ha do e.a. do herbicida. O controle sempre foi menor quando as plantas estavam mais velhas, o que pode ser resolvido com a aplicação dos produtos sobre a rebrota de tais plantas, após a roçada. A aplicação do herbicida, isolado ou com aditivos, no início do florescimento e frutificação das plantas, quer seja no seu desenvolvimento inicial ou após a brotação da soqueira, promoveu a inviabilização das sementes produzidas, diminuindo sensivelmente o número de dissemínulos viáveis no banco de sementes dessa espécie, presentes no solo.

Efeito de concentrações de espalhante adesionante e doses de glyphosate no controle de Brachiaria decumbens e Panicum maximum

Foram avaliadas as interações entre o glyphosate e o espalhante adesionante correspondente ao condensado de alcoolfenóis com óxido de eteno e sulfonados orgânicos quanto à redução de tensão superficial e ao controle de Panicum maximum e Brachiaria decumbens. Os produtos comerciais apresentavam 360 g e.a./l e 466 g i.a./l, respectivamente. O herbicida reduziu o efeito do espalhante sobre a tensão superficial. Na concentração de 0,1% de p.c., o espalhante maximizou o controle das duas espécies pelo glyphosate. P. maximum mostrou-se menos sensível ao glyphosate que B. decumbens, exigindo doses 24,05% superiores.

Estimativa da área foliar de Panicum maximum usando dimensões lineares do limbo foliar

Com o objetivo de obter uma equação que, por meio de parâmetros lineares dimensionais das folhas, permitisse a estimativa da área foliar de Panicum maximum, estudaram-se relações entre a área foliar real (Sf) e os parâmetros dimensionais do limbo foliar, como o comprimento ao longo da nervura principal (C) e a largura máxima (L), perpendicular à nervura principal. As equações lineares simples, exponenciais e geométricas obtidas podem ser usadas para estimação da área foliar. Do ponto de vista prático, sugere-se optar pela equação envolvendo apenas o produto C x L. Desse modo, a estimativa da área foliar de P. maximum pode ser feita pela fórmula Sf = 0,6058 x (C x L), que equivale a tomar 60,58% do produto entre o comprimento ao longo da nervura principal e a largura máxima, com coeficiente de determinação de 0,8586.

Períodos de interferência das plantas daninhas na cultura da cana-de-açúcar: III - capim-braquiária (Brachiaria decumbens) e capim-colonião (Panicum maximum)

Um experimento foi conduzido em São João da Boa Vista-SP, com o objetivo de determinar o período anterior à interferência (PAI) e o período total de prevenção à interferência (PTPI) das plantas daninhas na cultura da cana-de-açúcar. A cana foi plantada em abril de 1995, na época de plantio caracterizada por maior deficiência hídrica. A comunidade infestante presente foi variada, sendo Brachiaria decumbens e Panicum maximum as espécies mais importantes. Essa comunidade tendeu a apresentar acúmulo crescente de matéria seca durante todo o período de avaliação e reduziu em até 40% a produtividade de colmos da cana-de-açúcar. A cultura conviveu com a comunidade infestante até 74 dias após o plantio, sem sofrer redução significativa na produtividade (PAI). O período mínimo de controle para garantir a produtividade foi de 127 DAP (PTPI). Dessa forma, o controle das plantas daninhas foi crítico no período compreendido entre 74 e 127 dias após o plantio.