On the appearance of a Hopf bifurcation in a non-ideal mechanical problem

In this paper we studied a non-ideal system with two degrees of freedom consisting of a dumped nonlinear oscillator coupled to a rotatory part. We investigated the stability of the equilibrium point of the system and we obtain, in the critical case, sufficient conditions in order to obtain an appropriate Normal Form. From this, we get conditions for the appearance of Hopf Bifurcation when the difference between the driving torque and the resisting torque is small. It was necessary to use the Bezout Theorem, a classical result of Algebraic Geometry, in the obtaining of the foregoing results. (C) 2003 Elsevier Ltd. All rights reserved.

On local analysis of oscillations of a non-ideal and non-linear mechanical model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.

Thermal and mechanical properties of PVDF/PANI blends

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.

The role of chain scission and chain branching in high density polyethylene during thermo-mechanical degradation

The mechanical and thermo-oxidative degradation of high density polyethylene (HDPE) was measured in a twin-screw extruder using various processing conditions. Two types of HDPE, Phillips and Ziegler-Natta, having different levels of terminal vinyl unsaturation were analysed. Mild screw profiles, having mainly conveying elements, have short mean residence times then profiles with kneading discs and left hand elements. Carbonyl and traps-vinylene group concentrations increased, whereas vinyl group concentration decreased with number of extrusions. Higher temperature profiles intensified these effects. The thermo-mechanical degradation mechanism begins with chain scission in the longer chains due to their higher probability of entanglements. These macroradicals then react with the vinyl terminal unsaturations of other chains producing chain branching. Shorter chains are more mobile, not suffering scission but instead are used for grafting the macroradicals, increasing the molecular weight. Increase in the levels of extrusion temperature, shear and vinyl end groups content facilitates the thermo-mechanical degradation reducing the amount of both, longer chains via chain scission and shorter chains via chain branching, narrowing the polydispersity. Phillips HDPE produces a higher level of chain branching than does the Ziegler-Natta type. (C) 2004 Elsevier Ltd. 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.

Application of compression test in analysis of mechanical and color changes in grapefruit juice powder as related to glass transition and water activity

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event

This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.

Behavioural Analysis of a Nonlinear Mechanical System Using Transient Trajectories

This work aims at a better comprehension of the features of the solution surface of a dynamical system presenting a numerical procedure based on transient trajectories. For a given set of initial conditions an analysis is made, similar to that of a return map, looking for the new configuration of this set in the first Poincaré sections. The mentioned set of I.C. will result in a curve that can be fitted by a polynomial, i.e. an analytical expression that will be called initial function in the undamped case and transient function in the damped situation. Thus, it is possible to identify using analytical methods the main stable regions of the phase portrait without a long computational time, making easier a global comprehension of the nonlinear dynamics and the corresponding stability analysis of its solutions. This strategy allows foreseeing the dynamic behavior of the system close to the region of fundamental resonance, providing a better visualization of the structure of its phase portrait. The application chosen to present this methodology is a mechanical pendulum driven through a crankshaft that moves horizontally its suspension point.

The role of the oblique ligament in the mechanical behavior of the medial collateral ligament of the mongrel dog elbow joint - Some biomechanical aspects

This study investigated the oblique ligament mechanical contribution to the medial collateral ligament of the canine elbow joint. Fifteen dogs were used for the study of the failure load, displacement, and energy absorption of the medial collateral and oblique ligaments of the canine elbow joint, associate and separately in the joint. Medial collateral ligament failure load and energy absorption were significantly higher in relation to the isolated oblique ligament. When the ligaments were associated in the joint, they presented an increment in failure load, displacement and energy absorption in relation to the ligaments analyzed separately. It was concluded, therefore, that the oblique ligament could have an important paper in the stability of the canine elbow joint, as it favors the medial collateral ligament resistance to the tensile load, one of the main stabilizer of the elbow joint.

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.

Effects of thermocycling on mechanical properties of soft lining materials.

Soft linings are materials used to reduce the tension and forces of mastication, forming all or part of the fitting surface of a denture. This study evaluated the effect of thermocycling on water absorption, solubility, Shore A hardness and color stability of permanent soft liner materials. MATERIAL AND METHODS: Two chemically activated soft liner materials (Sofreliner S; GC Reline Ultrasoft) were tested. Twenty cylindrical specimens (30.0 x 1.0 mm) were prepared for measuring water absorption and solubility and another twenty (30.0 x 3 mm) for analyzing Shore A hardness and color stability. Color was measured by a spectrophotometer before and after 2000 thermocycles. A one-way ANOVA test and Tukey test at a 5% confidence level (p<0.05) were performed. RESULTS: The results did not show statistical differences for water absorption, solubility or color stability. The post-thermocycling Shore A hardness values were significantly higher than those before the treatment. CONCLUSION: Thermocycling of soft liner materials increased Shore A hardness.

A mechanical analogous model for the power system with Automatic Voltage Regulator

This paper deals with the subject-matter of teaching immaterial issues like power system dynamics where the phenomena and events are not sense-perceptible. The dynamics of the power system are recognized as analogous to the dynamics of a simple mechanical pendulum taken into account the well-known classical model for the synchronous machine. It is shown that even for more sophisticated models including flux decay and Automatic Voltage Regulator the mechanical device can be taken as an analogous, since provided some considerations about variation and control of the pendulum length using certain control laws. The resulting mathematical model represents a mechanical system that can be built for use in laboratory teaching of power system dynamics. © 2010 Praise Worthy Prize S.r.l. - All rights reserved.

Quenching in a non-ideal mechanical system and the Averaging Method

In this paper, for the first time, a quenching result in a non-ideal system is rigorously obtained. In order to do this a new mechanical hypothesis is assumed, it means that the moment of inertia of the rotating parts of the energy source is big. From this is possible to use the Averaging Method. © 2012 American Institute of Physics.

A simple procedure for the preparation of laponite and thermoplastic starch nanocomposites: Structural, mechanical, and thermal characterizations

The aim of this article is to propose advances for the preparation of hybrid nanocomposites prepared by the combination of intercalation from solution and melt-processing methods. This research investigates the effect of the laponite RDS content on the thermal, structural, and mechanical properties of thermoplastic starch (TPS). X-ray diffraction was performed to investigate the dispersion of the laponite RDS layers into the TPS matrix. The results show good nanodispersion, intercalation, and exfoliation of the clay platelets, indicating that these composites are true nanocomposites. The presence of laponite RDS also improves the thermal stability and mechanical properties of the TPSmatrix due to its reinforcement effect which was optimized by the high degree of exfoliation of the clay. Thus, these results indicate that the exfoliated TPS-laponite nanocomposites have great potential for industrial applications and, more specifically, in the packaging field. © The Author(s) 2011 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.