On chaotic behavior of a fixed offshore structure

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

Chaotic vibrations of a nonideal electro-mechanical system

Nonideal systems are those in which one takes account of the influence of the oscillatory system on the energy supply with a limited power (Kononenko, 1969). In this paper, a particular nonideal system is investigated, consisting of a pendulum whose support point is vibrated along a horizontal guide by a two bar linkage driven by a DC motor, considered to be a limited power supply. Under these conditions, the oscillations of the pendulum are analyzed through the variation of a control parameter. The voltage supply of the motor is considered to be a reliable control parameter. Each simulation starts from zero speed and reaches a steady-state condition when the motor oscillates around a medium speed. Near the fundamental resonance region, the system presents some interesting nonlinear phenomena, including multi-periodic, quasiperiodic, and chaotic motion. The loss of stability of the system occurs through a saddle-node bifurcation, where there is a collision of a stable orbit with an unstable one, which is approximately located close to the value of the pendulum's angular displacement given by alpha (C)= pi /2. The aims of this study are to better understand nonideal systems using numerical simulation, to identify the bifurcations that occur in the system, and to report the existence of a chaotic attractor near the fundamental resonance. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Oxygen mobility and structural phase transformation in Bi2Sr2CaCu2O8+delta measured by anelastic spectroscopy

One of the most studied ceramic superconductors for application has been, undoubtedly, Bi2Sr2CaCu2O8+delta. Although being a multiphasic material, it has proved to have great advantages compared to other ceramic systems. Measurements of the elastic energy loss and modulus (anelastic spectroscopy) as a function of temperature call distinguish among different atomic jumps that occur inside the various phases or at different local ordering. In this paper, mechanical loss spectra of Bi2Sr2CaCu2O8+delta bar shaped samples, made by a conventional method, have been measured between 80 and 600 K, using a torsion pendulum operating in frequencies below 50 Hz, for samples annealed in vacuum up to 600 K. Possible relaxation mechanisms are proposed to explain the origin of the mechanical-loss peaks observed 300 and 500 K. (C) 2004 Elsevier B.V. All rights reserved.

Stress induced ordering due interstitials in Nb-4.7 at.%Ta

The presence of interstitial elements in metals cause strong changes in their physical, chemical or mechanical properties. These interstitial impurities interact with the metallic matrix atoms by a relaxation process known as stress induced ordering. Relaxation processes give rise to a peak in the internal friction spectrum, known as Snock effect. The presence of substitutional solutes has a strong influence on Snoek effect, particularly if the substitutional solute element is the one, which interacts with the interstitial element. Anelastic spectroscopy measurements provide information of the behavior of these impurities in the metallic matrix. In this paper, polycrystalline samples of Nb-4.7 at.%Ta alloy have been analyzed in the as-received condition. Measurements of anelastic spectroscopy were carried out using an inverted torsion pendulum, operating with frequency of 2.0-30.0 Hz and in a temperature range between 300 and 700 K. It was observed the presence of a relaxation structure that have been attributed to stress induced ordering due to interstitial atoms around atoms of the metallic matrix. The relaxation structure have been decomposed in its constituent peaks, what it allowed to identify the following relaxation processes: Ta-O, Nb-O and Nb-N. (c) 2005 Elsevier B.V. All rights reserved.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Effect of interstitial impurities on internal friction measurements in niobium

Measurements of internal friction as a function of temperature were carried out in samples of mobium containing different amounts of interstitial solutes (oxygen and nitrogen) and one sample of mobium containing initially only nitrogen as interstitial solute. The experimental spectra of internal friction as a function of temperature were obtained with a torsion pendulum of the inverted Ke-type and resolved, using the method of successive subtraction, into a series of constituent Debye peaks corresponding to different interactions. For each relaxation process it was possible to obtain the height (Q(max)(-1)) and temperature (T-p) of the peak, the activation energy (E) and the relaxation time (t(o)). The height, shape and temperature of these peaks depend on the concentration of interstitial elements. The observed peaks were associated with matrix-interstitial (Nb-O, Nb-N) and interstitial-interstitial (O-N) interaction processes. (C) 2003 Elsevier B.V. All rights reserved.

Internal friction measurements in Nb-0.3wt.%Ti containing oxygen

Internal friction measurements were made in the Nb-Ti alloy containing 0.3 wt. % of Ti, doped with various quantities of oxygen (0.04 to 0.08 wt. %) utilizing a torsion pendulum. These measurements were performed in the temperature range of 300 K to 700 K with the oscillation frequency about 1.0 Hz. The experimental results showed relaxation peaks due the stress induced ordering of oxygen atom and pairs of oxygen atom around the niobium atoms (metallic matrix) and around titanium atoms (substitutional solute).

Possible structural phase transitions on Bi2Sr2CaCu2Oy measured by anelastic spectroscopy

Anelastic spectroscopy measurements (internal friction) are sensitive tools for the study of defects in solids, in particular the mobility of interstitial oxygen. Samples of Bi2Sr2CaCu2Oy were analyzed after being submitted to two thermal treatments in vacuum, one at 973 K and another at 673 K. Anelastic spectroscopy measurements were performed using a torsion pendulum operating at around 38 Hz and at a temperature range of 88 and 700 K with heating rate of 1 K/min and vacuum better than 10(-5) Torr. Complex relaxation structures reversible with new thermal treatments were observed. These relaxation structures were attributed to O-M structural phase transitions. (c) 2005 Elsevier B.V. All rights reserved.

On a control of a non-ideal mono-rail system with periodics coefficients

In this work, the problem in the loads transport (in platforms or suspended by cables) it is considered. The system in subject is composed for mono-rail system and was modeled through the system: inverted pendulum, car and motor and the movement equations were obtained through the Lagrange equations. In the model, was considered the interaction among of the motor and system dynamics for several potencies motor, that is, the case studied is denominated a non-ideal periodic problem. The non-ideal periodic problem dynamics was analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, one was made it analyzes quantitative of the problem through the analysis of the Floquet multipliers. Finally, the non-ideal problem was controlled. The method that was used for analysis and control of non-ideal periodic systems is based on the Chebyshev polynomial expansion, in the Picard iterative method and in the Lyapunov-Floquet transformation (L-F trans formation). This method was presented recently in [3-9].

Interstitial oxygen mobility in superconducting samples of Bi2Sr2CaCu2O8+y

Since high-temperature superconductors were discovered, several studies have been made on their physical properties, attempting to associate them to the origin of superconductivity. Obviously, the oxygen atoms interstitially dissolved in the matrix have an important role in superconductivity, since they move easily in the lattice. In addition, they contribute to hole creation in the CuO2 planes. Anelastic spectroscopy ( internal friction) measurements are sensitive tools for the study of defects in solids, in particular for oxygen mobility. In this paper, Bi2Sr2CaCu2O8+y samples with several different amounts of interstitial oxygen were analysed by means of anelastic spectroscopy measurements. The measurements were performed by using a torsion pendulum operating at a frequency of about 40 Hz. Complex relaxation structures were observed and attributed to the shift of the oxygen interstitial atoms in BiO chains.

Internal friction and frequency measurements in molybdenum containing oxygen and nitrogen

We have measured internal friction and frequency as a function of temperature in molybdenum containing oxygen and nitrogen in solid solution. These measurements were performed by a torsion pendulum operating in the temperature range of 300 K to 700 K with oscillation frequency about 1.0 Hz. The results showed the complex relaxation process identifying the stress induced ordering of oxygen and nitrogen atom around the molybdenum atoms of the metallic matrix.

Oxygen mobility in SmBa2Cu3O7-delta measured by anelastic spectroscopy

Anelastic spectroscopy has been performed on a sample of superconducting oxide SmBa2Cu3O7-delta (SBCO) using a torsion pendulum operating with frequency around 10 Hz. A thermally activated relaxation peak is observed near 500 K with the activation enthalpy of 1.55 +/- 0.03 eV and the pre-exponential factor of approximately 10(-15) s, which is attributed to the mobility of non-stoichiometric oxygen by jumps in positions O1 and O5 of the lattice. (c) 2006 Elsevier B.V. All rights reserved.

Using transient and steady state considerations to investigate the mechanism of loss of stability of a dynamical system

This work presents the complete set of features for solutions of a particular non-ideal mechanical system near the fundamental and near to a secondary resonance region. The system comprises a pendulum with a horizontally moving suspension point. Its motion is the result of a non-ideal rotating power source (limited power supply), acting oil the Suspension point through a crank mechanism. Main emphasis is given to the loss of stability, which occurs by a sequence of events, including intermittence and crisis, when the system reaches a chaotic attractor. The system also undergoes a boundary-crisis, which presents a different aspect in the bifurcation diagram due to the non-ideal supposition. (c) 2004 Published by Elsevier B.V.

Influence of interstitial elements on internal friction measurements in Nb and Nb-Zr alloys

Internal friction and frequency measurements as a function of temperature have been carried out in Nb and Nb-Zr policrystalline samples, using a torsion pendulum in the temperature range between 300K and 700K the heating rate was 1K/min and the pressure was kept better than 5x10(-3) mbar. Metals with bce lattice containing solute atoms dissolved interstitially often show anelastic behaviour due to a process know as stress-induced ordering responsible for the appearance of Snoek peaks. In the Nb sample it has been identified two constituent peaks corresponding to the interstitial-matrix interactions (Nb-O and Nb-N), but for the Nb-Zr samples with interstitial solute concentrations very close to those measured for the unalloyed Nb, it was not observed any mechanical relaxation peaks due to the presence of oxygen and nitrogen in solid solution.

Anelastic relaxation processes due oxygen in Nb-3.1 at.% Ti alloys

In the last 50 years several studies have been made to understand the relaxation mechanisms of the heavy interstitial atoms present in transition metals and their alloys. Internal friction measurements have been carried out in a Nb-Ti alloy containing 3.1 at.% of Ti produced by the Materials Department of Chemical Engineering Faculty of Lorena (Brazil), with several quantities of oxygen in solid solution using a torsion pendulum. These measurements have been performed by a torsion pendulum in the temperature range from 300 to 700 K with an oscillation frequency between 0.5 and 10 Hz. The experimental results show complex internal friction spectra that have been resolved, into a series of Debye peaks corresponding to different interactions. For each relaxation process it was possible to obtain the height and temperature of the peak, the activation energy and the relaxation time of the process. (C) 2003 Elsevier B.V. All rights reserved.