Resonances and subharmonic bifurcations of large amplitude periodic orbits of planar polynomial vector fields

In this work are studied periodic perturbations, depending on two parameters, of planar polynomial vector fields having an annulus of large amplitude periodic orbits, which accumulate on a symmetric infinite heteroclinic cycle. Such periodic orbits and the heteroclinic trajectory can be seen only by the global consideration of the polynomial vector fields on the whole plane, and not by their restriction to any compact set. The global study involving infinity is performed via the Poincare Compactification. It is shown that, for certain types of periodic perturbations, one can seek, in a neighborhood of the origin in the parameter plane, curves C-(m) of subharmonic bifurcations, for which the periodically perturbed system has subharmonics of order m, for any integer m.

Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

EXPANSION OF THE DISTURBING FUNCTION FOR HIGH ECCENTRICITY AND LARGE-AMPLITUDE OF LIBRATION

Following some ideas, developed by Woltjer (1928), Message (1989), Yokoyama (1988, 1989) and Duriez (1990) an expansion of the disturbing function is given for high values of the eccentricity and large amplitude of libration. The classical expansion can be obtained as a particular case of the present model. Several asteroids with high eccentricity and large amplitude of libration are tested and the results are much better than those obtained from the classical theory.

Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

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.

Strong and fast phase modulation for quantitative analysis of photorefractive gratings

A new approach for studying photorefractive gratings in two-wave mixing experiments by a phase modulation technique is presented. The introduction of a large-amplitude, high-frequency sinusoidal phase modulation in one of the input beams blurs the interference pattern and provides powerful harmonic signals for accurate measurements of the grating diffraction efficiency eta and the output phase shift rho between the transmitted and diffracted waves. The blurring of the light fringes can be used to suppress the higher spatial harmonics of the grating, allowing a space-charge field with sinusoidal profile to be recorded. Although the presence of such a strong phase modulation affects the beam coupling in a rather complicated way, it is shown that for the special case of equal intensity input beams, the effect of the phase modulation on eta and rho is reduced to a weakening of the coupling strength. The potentialities of the technique are illustrated in a study of refractive-index waves excited by running interference patterns in a Bi12TiO20 crystal. Expressions for the diffraction efficiency and the output phase shift are derived and used to match numerically calculated curves to the experimental data. The theoretical model is supported by the very good data fitting and allows the computation of important material parameters.

Motional heterogeneities in siloxane/poly(ethylene glycol) ormolyte nanocomposites studied by C-13 solid-state exchange NMR

C-13 exchange solid-state NMR methods were used to study two families of siloxane/poly-(ethylene glycol) hybrid materials: Types I and II, where the polymer chains interact with the inorganic phase through physical (hydrogen bonds or van der Waals forces) or chemical (covalent bonds) interactions, respectively. These methods were employed to analyze the effects of the interactions between the organic and inorganic phases on the polymer dynamics in the milliseconds to seconds time scale, which occurs at temperatures below the motional narrowing of the NMR line width and around the polymer glass transition. Motional heterogeneities associated with these interactions and evidence of both small and large amplitude motions were directly observed for both types of hybrids. The results revealed that the hindrance to the slow molecular motions of the polymer chains due to the siloxane structures depends on the chain length and the nature of the interaction between the organic and inorganic phases.

Multiple active levels in Bi12TiO20 crystals

The existence of multiple active levels in a photorefractive Bi12TiO20 crystal is here investigated at 514.5nm wavelength. We carry out two-wave mixing experiments using symmetrically incident beams of equal intensities. A large amplitude fast phase modulation in one of the beams reduces the fringes visibility and improves the detection of the generated frequency modulated signals in both (R and S) output directions. Diffraction efficiencies of the phase (photorefractive) and the absorption (photochromic) gratings are quantitatively computed as functions of the grating period. Results show that the absorption grating has two distinct components: one associated to the photorefractive trap density modulation and another related to local light-induced effects between different levels. The photorefractive grating was also investigated at 633nm and 594nm (besides 514.5nm) and a significant quenching of the photorefractive effect was observed at these wavelengths.

On non-linear and non-ideal interactions in two vibrating problems

In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power, as that provided by a DC motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a non-ideal problem. In this work, we considerer two non-ideal problems analyzed by using numerical simulations. The existence of the Sommerfeld effect was verified, that is, the effect of getting stuck at resonance (energy imparted to the DC motor being used to excite large amplitude motions of the supporting structure). We considered two kinds of non-ideal problem: one related to the transverse vibrations of a shaft carrying two disks and another to a piezoceramic bar transducer powered by a vacuum tube generated by a non-ideal source Copyright © 2007 by ASME.

A structure excited by a DC motor of limited power supply and controlled by a pendulum like device

In this paper, a mathematical model is derived via Lagrange's Equation for a shear building structure that acts as a foundation of a non-ideal direct current electric motor, controlled by a mass loose inside a circular carving. Non-ideal sources of vibrations of structures are those whose characteristics are coupled to the motion of the structure, not being a function of time only as in the ideal case. Thus, in this case, an additional equation of motion is written, related to the motor rotation, coupled to the equation describing the horizontal motion of the shear building. This kind of problem can lead to the so-called Sommerfeld effect: steady state frequencies of the motor will usually increase as more power (voltage) is given to it in a step-by-step fashion. When a resonance condition with the structure is reached, the better part of this energy is consumed to generate large amplitude vibrations of the foundation without sensible change of the motor frequency as before. If additional increase steps in voltage are made, one may reach a situation where the rotor will jump to higher rotation regimes, no steady states being stable in between. As a device of passive control of both large amplitude vibrations and the Sommerfeld effect, a scheme is proposed using a point mass free to bounce back and forth inside a circular carving in the suspended mass of the structure. Numerical simulations of the model are also presented Copyright © 2007 by ASME.

An investigations on local and global behavior of a (SMA) oscillator of 3 - DOF driven by a limited power supply

SMART material systems offer great possibilities in terms of providing novel and economical solutions to engineering problems. The technological advantages of these materials over traditional ones are due to their unique microstructure and molecular properties. Smart materials such as shape memory alloys (SMA), has been used in such diverse areas of engineering science, nowadays. In this paper, we present a numerical investigation of the dynamics interaction of a nonideal structure (NIS). We analyze the phenomenon of the passage through resonance region in the steady state processes. We remarked that this kind of problem can lead to the so-called Sommerfeld effect: steady state frequencies of the DC motor will usually increase as more power (voltage) is given to it in a step-by-step fashion. When a resonance condition with the structure 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 as before. The results obtained by using numerical simulations are discussed in details. Copyright © 2009 by ASME.

A comparison of two nonlinear damping mechanisms in a vibration isolator

The vibration transmissibility characteristics of a single-degree-of- freedom (SDOF) passive vibration isolation system with different nonlinear dampers are investigated in this paper. In one configuration, the damper is assumed to be linear and viscous, and is connected to the mass so that it is perpendicular to the spring (horizontal damper). The vibration is in the direction of the spring. The second configuration is one in which the damper is in parallel with the spring but the damping force is proportional to the cube of the relative velocity across the damper (cubic damping). Both configurations are studied for small amplitudes of excitation, when some analysis can be conducted based on analytical expressions, and for large amplitudes of excitation, where the analysis is based on numerical simulations. It is found that the two nonlinear systems can outperform the linear system when force transmissibility is considered. However, for displacement transmissibility, the system with the horizontal damper exhibits some desirable properties, but the system with cubic damping does not. © 2012 Elsevier Ltd.

Dinâmica não linear de sistemas de levitação magnética

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Algumas contribuições da perspectiva filosófico-semiótica de Peirce para a análise de assunto

In the context of current scientific studies toward Information Science and Semiotics, this study highlights that Semiotics is relevant to the field, since that signs are interpreted in different ways by each person primarily when they arise from the interpretation of documental analysis, maintaining large amplitude and diversity. In this sense, Semiotics can furnish support for several areas since it focuses on elements which enable the understanding of the phenomena, in order to guide an adequate theory about the concerns pointed by research on information and knowledge organization. This study aims to present a theoretical reflection about the subject analysis from Peirce’s philosophical-semiotics approach. Thus, this study presents some relations and contributions of Semiotics on issues involving subject analysis as well as concepts of habit, experience, representation and types of signs generated in the process.