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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Relaxation-chaos phenomena in celestial mechanics. I. On wisdom's model for the 3/1 kirkwood gap

Sudden eccentricity increases of asteroidal motion in 3/1 resonance with Jupiter were discovered and explained by J. Wisdom through the occurrence of jumps in the action corresponding to the critical angle (resonant combination of the mean motions). We pursue some aspects of this mechanism, which could be termed relaxation-chaos: that is, an unconventional form of homoclinic behavior arising in perturbed integrable Hamiltonian systems for which the KAM theorem hypothesis do not hold. © 1987.

A contribution for nonlinear structural dynamics characterization of cantilever beams

Successful experiments in nonlinear vibrations have been carried out with cantilever beams under harmonic base excitation. A flexible slender cantilever has been chosen as a convenient structure to exhibit modal interactions, subharmonic, superharmonic and chaotic motions, and others interesting nonlinear phenomena. The tools employed to analyze the dynamics of the beam generally include frequency- and force-response curves. To produce force-response curves, one keeps the excitation frequency constant and slowly varies the excitation amplitude, on the other hand, to produce frequency-response curves, one keeps the excitation amplitude fixed and slowly varies the excitation frequency. However, keeping the excitation amplitude constant while varying the excitation frequency is a difficult task with an open-loop measurement system. In this paper, it is proposed a closed-loop monitor vibration system available with the electromagnetic shaker in order to keep the harmonic base excitation amplitude constant. This experimental setup constitutes a significant improvement to produce frequency-response curves and the advantages of this setup are evaluated in a case study. The beam is excited with a periodic base motion transverse to the axis of the beam near the third natural frequency. Modal interactions and two-period quasi-periodic motion are observed involving the first and the third modes. Frequency-response curves, phase space and Poincaré map are used to characterize the dynamics of the beam.

Application of Volterra series in nonlinear mechanical system identification and in structural health monitoring problems

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

Time-periodic perturbation of a Lienard equation with an unbounded homoclinic loop

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Global dynamics of the Rikitake system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Continuously deformable topological structure

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Using a one-dimensional lattice applied to the thermodynamic study of DNA

In this work it is analyzed a one-dimensional lattice which is composed by mass-spring systems with one additional Rosen-Morse potential on site. This kind of lattice is used to study thermodynamic properties of DNA, especially its thermal denaturation. on the context of this work, the Rosen-Morse potential simulates hydrogen bonds between double strands of the molecule. From the graphic of the average stretching of base pairs versus temperature it is possible to observe the thermal denaturation of the system. This result shows that it is possible to obtain phase transition with an asymmetric potential without an infinite barrier.

Stability of breathers in simple mechanical models for DNA

This work studies through the Floquet theory the stability of breathers generated by the anti-continuous limit. We used the Peyrard-Bishop model for DNA and two kinds of nonlinear potential: the Morse potential and a potential with a hump. The comparison of their stability was done in function of the coupling parameter. We also investigate the dynamic behaviour of the system in stable and unstable regions. Qualitatively, the dynamic of mobile breathers resembles DNA.

Regularization and singular perturbation techniques for non-smooth systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Theory of small aspect ratio waves in deep water

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water) without potential flow assumption. The resulting equation is shown to sustain periodic waves which on the one side tend to the proper linear limit at small amplitudes, on the other side possess a threshold amplitude where wave crest peaking is achieved. An explicit expression of the crest angle at wave breaking is found in terms of the wave velocity. By numerical simulations, stable soliton-like solutions (experiencing elastic interactions) propagate in a given velocities range on the edge of which they tend to the peakon solution. (c) 2005 Elsevier B.V. All rights reserved.

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves. Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns. (c) 2007 Elsevier B.V. All rights reserved.

Evolution equation for short surface waves on water of finite depth

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

Gap solitons in a model of a superfluid fermion gas in optical lattices

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

Escape and transport for an open bouncer: Stretched exponential decays

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)