On Nonlinear Dynamics and Control of A Particular Portal Frame Foundation Model, Excited by a Non-Ideal Motor

The nonlinear dynamic response and a nonlinear control method of a particular portal frame foundation for an unbalanced rotating machine with limited power (non-ideal motor) are examined. Numerical simulations are performed for a set of control parameters (depending on the voltage of the motor) related to the static and dynamic characteristics of the motor. The interaction of the structure with the excitation source may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the systems. A mathematical model having two degrees of freedom simplifies the non-ideal system. The study of controlling steady-state vibrations of the non-ideal system is based on the saturation phenomenon due to internal resonance.

A nonlinear and non-ideal wind generator supporting structure

We present a simple mathematical model of a wind turbine supporting tower. Here, the wind excitation is considered to be a non-ideal power source. In such a consideration, there is interaction between the energy supply and the motion of the supporting structure. If power is not enough, the rotation of the generator may get stuck at a resonance frequency of the structure. This is a manifestation of the so-called Sommerfeld Effect. In this model, at first, only two degrees of freedom are considered, the horizontal motion of the upper tip of the tower, in the transverse direction to the wind, and the generator rotation. Next, we add another degree of freedom, the motion of a free rolling mass inside a chamber. Its impact with the walls of the chamber provides control of both the amplitude of the tower vibration and the width of the band of frequencies in which the Sommerfeld effect occur. Some numerical simulations are performed using the equations of motion of the models obtained via a Lagrangian approach.

Harmonic propagation analysis in electric energy distribution systems

An important alteration of the equivalent loads profile has been observed in the electrical energy distribution systems, for the last years. Such fact is due to the significant increment of the electronic processors of electric energy that, in general, behave as nonlinear loads, generating harmonic distortions in the currents and voltages along the electric network. The effects of these nonlinear loads, even if they are concentrated in specific sections of the network, are present along the branch circuits, affecting the behavior of the entire electric network. For the evaluation of this phenomenon it is necessary the analysis of the harmonic currents flow and the understanding of the causes and effects of the consequent voltage harmonic distortions. The usual tools for calculation the harmonic flow consider one-line equivalent networks, balanced and symmetrical systems. Therefore, they are not tools appropriate for analysis of the operation and the influence/interaction of mitigation elements. In this context, this work proposes the development of a computational tool for the analysis of the three-phase harmonic propagation using Norton modified models and considering the real nature of unbalanced electric systems operation. © 2011 IEEE.

On nonlinear dynamics in a free fluid surface of a tank excited by a non-ideal power source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor. Copyright © 2011 by ASME.

Comparative analysis for reactive energy measurement methodologies, under non-sinusoidal conditions in three-phase four-wire circuits

This paper presents some methodologies for reactive energy measurement, considering three modern power theories that are suitable for three-phase four-wire non-sinusoidal and unbalanced circuits. The theories were applied in some profiles collected in electrical distribution systems which have real characteristics for voltages and currents measured by commercial reactive energy meters. The experimental results are presented in order to analyze the accuracy of the methodologies, considering the standard IEEE 1459-2010 as a reference. Finally, for additional comparisons, the theories will be confronted with the modern Yokogawa WT3000 energy meter and three samples of a commercial energy meter through an experimental setup. © 2011 IEEE.

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

On Non-ideal and Chaotic Energy Harvester Behavior

In this paper, we deal with the research of a proposed mathematical model of energy harvesting, including nonlinearities in the piezoelectric coupling and a non-ideal force of excitation. We showed using numerical simulations to analysis of the dynamic responses that, the power harvested was influenced by the nonlinear vibrations of the structure, as well as by the influence of the non-linearities in the piezoelectric coupling. We concluded through of the numerical results that the limited energy source was interacting with the system. Thus, the increasing of the voltage in DC motor led the system produce a good power response, especially in high-energy orbits in the resonance region, but the Sommerfeld effect occurs in the system and a chaotic behavior was found in the post-resonance region. So the power harvested along the time decreases because occurs loses of energy due the interaction between energy source and structure. Keeping the energy harvested constant over time is essential to make possible the use of energy harvesting systems in real applications. To achieve this objective, we applied a control technique in order to stabilize the chaotic system in a periodic stable orbit. We announced that the results were satisfactory and the control maintained the system in a stable condition. © 2012 Foundation for Scientific Research and Technological Innovation.

Saddle points and rare collisions under scaling approach in a Fermi accelerator with two nonlinear terms

Rare collisions of a classical particle bouncing between two walls are studied. The dynamics is described by a two-dimensional, nonlinear and area-preserving mapping in the variables velocity and time at the instant that the particle collides with the moving wall. The phase space is of mixed type preventing diffusion of the particle to high energy. Successive and therefore rare collisions are shown to have a histogram of frequency which is scaling invariant with respect to the control parameters. The saddle fixed points are studied and shown to be scaling invariant with respect to the control parameters too. © 2012 Elsevier B.V. All rights reserved.

Nonlinear control in an electromechanical transducer with chaotic behaviour

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Information-entropic measure of energy-degenerate kinks in two-field models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Time-domain Harmonic Power-Flow Analysis in Electrical Energy Distribution Networks, Using Norton Models for Non-linear Loading

The purpose of this paper is to present the application of a three-phase harmonic propagation analysis time-domain tool, using the Norton model to approach the modeling of non-linear loads, making the harmonics currents flow more appropriate to the operation analysis and to the influence of mitigation elements analysis. This software makes it possible to obtain results closer to the real distribution network, considering voltages unbalances, currents imbalances and the application of mitigation elements for harmonic distortions. In this scenario, a real case study with network data and equipments connected to the network will be presented, as well as the modeling of non-linear loads based on real data obtained from some PCCs (Points of Common Coupling) of interests for a distribution company.

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrodinger equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An experimental nonlinear low dynamic stiffness device for shock isolation

The problem of shock generated vibration is very common in practice and difficult to isolate due to the high levels of excitation involved and its transient nature. If not properly isolated it could lead to large transmitted forces and displacements. Typically, classical shock isolation relies on the use of passive stiffness elements to absorb energy by deformation and some damping mechanism to dissipate residual vibration. The approach of using nonlinear stiffness elements is explored in this paper, focusing in providing an isolation system with low dynamic stiffness. The possibilities of using such a configuration for a shock mount are studied experimentally following previous theoretical models. The model studied considers electromagnets and permanent magnets in order to obtain nonlinear stiffness forces using different voltage configurations. It is found that the stiffness nonlinearities could be advantageous in improving shock isolation in terms of absolute displacement and acceleration response when compared with linear elastic elements. Copyright (C) 2015 Elsevier Ltd. All rights reserved

Accuracy of nonlinear feed formulation for broiler chickens: maximising broiler profit

The modeling technique is simple, useful and practical to calculate optimum nutrient density to maximize profit margins, using nonlinear programming by predictive broiler performance. To demonstrate the influence of the broiler price could interact with nutrient density, the experiment aimed to define the quadratic equations for consumption and weight gain, based on modeling, to be applied to nonlinear programming, according to sex (male and female) in the starter (1 to 21 days), grower (22 to 42 days) and finisher phases (43 to 56 days). The experimental design was a randomized, totaling 6 treatments [energy levels of 2800, 2900, 3000, 3100, 3200 and 3300kcal AME/kg with constant nutrient : AME (Apparent Metabolizable Energy)] with 4 replicates and 10 birds per plot, using the program free download PPFR Excel workbook for feed formulation (http://www.foa.unesp.br/downloads/file_detalhes.asp?CatCod=4&SubCatCod=138&FileCod=1677). Data from this trial confirmed that there was a significant relationship between feed intake and total energy consumption of the diet, in which feed intake was increased or decreased simply to keep the amount of energy, with a constant rate of nutrient : AME. Therefore, the data support that if the essential dietary nutrients are kept in proportion to the energy density of the diet, according to the appropriate requirements (male / female) of broilers, the weight and feed conversion are significantly (P<0.05) favored by increasing the energy density of the diet. Thus, it enables the application of models for maximum profit (nonlinear formulation), to estimate the proportion of weight gain most appropriate according to the price paid by the market.

Bio-energy conversion cost: a new index to evaluate the bioeconomic eficiency

This study evaluated a nonlinear programming excel workbook PPFR (http://www.fmva.unesp.br/ppfr) for determining the optimum nutrient density and maximize margins. Two experiments were conducted with 240 one-day-old female chicks and 240 one-day-old male chicks distributed in 48 pens (10 chicks per pen, 4 replicates) in a completely randomized design. The treatments include the average price history (2009s and 2010s) for broiler increased and decreased by 25% or 50% (5 treatments to nonlinear feed formulation) and 1 linear feed formulation. Body gain, feed intake, feed conversion were measured at 21, 42 and 56 d of age. Chicks had ad libitum access to feed and water in floor pens with wood shavings as litter. The bio-economic Energy Conversion [BEC= (Total energy intake*Feed weighted cost per kg)/ (Weight gain*kg live chicken cost)] was more sensitive for measuring the bio-economic performance for broilers, and especially with better magnitude. This allowed a better assessment of profitability, the rate of growth and not just energy consumption, the production of broilers, by incorporating energy consumption, allowing for more sensitivity to the new index (BEC). The BEC was demonstrated that the principle of nonlinear formulation minimizes losses significantly (P<0.05), especially under unfavorable conditions the price of chicken in the market. Thus, when considering that a diet of energy supply shows up as the most expensive item of a formulation, it should compose necessarily the formula proposed for a bio-economic index. Thus, there is need to evaluate more accurately, not only the ingredients of a ration, but the impact of nutrients on the stability of a solution, mainly due to the energy requirement. This strategy promotes better accuracy for decision making under conditions of uncertainty, to find alternative post-formulation. From the above, both weight gain and feed conversion, as traditional performance indicators, cannot finalize or predict a performance evaluation of an economic system creating increasingly intense and competitive. Thus, the energy concentration of the diet becomes more important definition to feed formulator, by directly impact profit activity by interactions with the density of nutrients. This allowed a better evaluation of profitability, the rate of energy performance for broilers, by incorporating the energy consumption formula, allowing more sensitivity to the new index (BEC). These data show that nonlinear feed formulation is a toll to offer new opportunities for poultry production to improved profitability.