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.

Short comments on self-synchronization of two non-ideal sources supported by a flexible portal frame structure

A practical problem of synchronization of a non-ideal (i.e. when the excitation is influenced by the response of the system) and non-linear vibrating system was posed and investigated by means of numerical simulations. Two rotating unbalanced motors compose the mathematical model considered here with limited power supply mounted on the horizontal beam of a simple portal frame. As a starting point, the problem is reduced to a four-degrees-of-freedom model and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. The numerical results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, by using the variation of torque constants, the control of the self-synchronization and synchronization (in the system) are observed at certain levels of excitations.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

On an Non-Ideal Global and Local Energy Transfer, Using an Electro-Magneto and Magneto-Rheological Dampers

In this paper, we investigated the nonlinear vibrations of a Non-ideal (NIS) electromechanical absorber (NEVA), taking into account a modified mathematical model of (MR) Damper. We observed the presence of the Sornmerfeld effect (it is the steady state frequencies of the DC motor, which it will usually increasing as more power (Voltage) is given to it, in a step-by-step fashion. When a resonance condition it is reached, the better part of this energy it is consumed to generate large amplitude vibrations of the foundation, without sensible change of the motor frequency). The obtained results, by using numerical and analytical simulations, were discussed, in details.

Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

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

A note on the attenuation of the sommerfeld effect of a non-ideal system taking into account a MR damper and the complete model of a DC motor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Introduction to Focus Issue: Statistical mechanics and billiard-type dynamical systems

Dynamical systems of the billiard type are of fundamental importance for the description of numerous phenomena observed in many different fields of research, including statistical mechanics, Hamiltonian dynamics, nonlinear physics, and many others. This Focus Issue presents the recent progress in this area with contributions from the mathematical as well as physical stand point. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4730155]

On a nonlinear and chaotic non-ideal vibrating system with shape memory alloy (SMA)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On non-ideal simple portal frame structural model: Experimental results under a non-ideal excitation

We present measurements of the non-linear oscillations of a portal frame foundation for a non-ideal motor. We consider a three-time redundant structure with two columns, clamped in their bases and a horizontal beam. An electrical unbalanced motor is mounted at mid span of the beam. Two non-linear phenomena are studied: a) mode saturation and energy transfer between modes; b) interaction between high amplitude motions of the structure and the rotation regime of a real limited power motor. The dynamic characteristics of the structure were chosen to have one-to-two internal resonance between the anti-symmetrical mode (sway motions) and the first symmetrical mode natural frequencies. As the excitation frequency reaches near resonance conditions with the 2nd natural frequency, the amplitude of this mode grows up to a certain level and then it saturates. The surplus energy pumped into the system is transferred to the sway mode, which experiences a sudden increase in its amplitude. Energy is transformed from low amplitude high frequency motion into high amplitude low frequency motion. Such a transformation is potentially dangerous.We consider the fact that real motors, such as the one used in this study, have limited power output. In this case, this energy source is said to be non-ideal, in contrast to the ideal source whose amplitude and frequency are independent of the motion of the structure. Our experimental research detected the Sommerfeld Effect: as the motor accelerates to reach near resonant conditions, a considerable part of its output energy is consumed to generate large amplitude motions of the structure and not to increase its own angular speed. For certain parameters of the system, the motor can get stuck at resonance not having enough power to reach higher rotation regimes. If some more power is available, jump phenomena may occur from near resonance to considerably higher motor speed regimes, no stable motions being possible between these two.

Comparison of simulated periodontal bone defect depth measured in digital radiographs in dedicated and non-dedicated software systems

Objectives: To compare simulated periodontal bone defect depth measured in digital radiographs with dedicated and non-dedicated software systems and to compare the depth measurements from each program with the measurements in dry mandibles.Methods: Forty periodontal bone defects were created at the proximal area of the first premolar in dry pig mandibles. Measurements of the defects were performed with a periodontal probe in the dry mandible. Periapical digital radiographs of the defects were recorded using the Schick sensor in a standardized exposure setting. All images were read using a Schick dedicated software system (CDR DICOM for Windows v.3.5), and three commonly available non-dedicated software systems (Vix Win 2000 v.1.2; Adobe Photoshop 7.0 and Image Tool 3.0). The defects were measured three times in each image and a consensus was reached among three examiners using the four software systems. The difference between the radiographic measurements was analysed using analysis of variance (ANOVA) and by comparing the measurements from each software system with the dry mandibles measurements using Student's t-test.Results: the mean values of the bone defects measured in the radiographs were 5.07 rum, 5.06 rum, 5.01 mm and 5.11 mm for CDR Digital Image and Communication in Medicine (DICOM) for Windows, Vix Win, Adobe Photoshop, and Image Tool, respectively, and 6.67 mm for the dry mandible. The means of the measurements performed in the four software systems were not significantly different, ANOVA (P = 0.958). A significant underestimation of defect depth was obtained when we compared the mean depths from each software system with the dry mandible measurements (t-test; P congruent to 0.000).Conclusions: the periodontal bone defect measurements in dedicated and in three non-dedicated software systems were not significantly different, but they all underestimated the measurements when compared with the measurements obtained in the dry mandibles.