Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

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

Classical and quantal aspects of resonant normal forms

The Birkhoff-Gustavson normal form is employed to study separately chaos and resonances in a system with two degrees of freedom. In the integrable regime, tunnelling effects are appreciable when the nearest level spacings show oscillations. Tunnelling among states in the libration and rotation tori regions is also observed. The regularity of avoided crossings due to tunnelling indicates a collective effect and is associated with an isolated resonance. The spectral fluctuations also show a strong level correlation. The Husimi distribution, on the other hand, is insensitive to avoided crossings. An integrable approximation to the overlap of resonances is obtained and a theoretical description is given for an isolated cubic resonance plus a complex orbit. In the non-integrable regime chaos is stronger after overlapping and preferentially at low energies.

On Nonlinear Dynamics and Control of A Particular Portal Frame Foundation Model, Excited by a Non-Ideal Motor

The nonlinear dynamic response and a nonlinear control method of a particular portal frame foundation for an unbalanced rotating machine with limited power (non-ideal motor) are examined. Numerical simulations are performed for a set of control parameters (depending on the voltage of the motor) related to the static and dynamic characteristics of the motor. The interaction of the structure with the excitation source may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the systems. A mathematical model having two degrees of freedom simplifies the non-ideal system. The study of controlling steady-state vibrations of the non-ideal system is based on the saturation phenomenon due to internal resonance.

On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.

Nonlinear dynamical analysis of an aeroelastic system with multi-segmented moment in the pitch degree-of-freedom

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

Experimental comparative study on vortex-induced motion (VIM) of a monocolumn platform

An analysis methodology is presented as well as a comparison of results obtained from vortex-induced motion (VIM) model tests of the MonoGoM platform, a monocolumn floating unit designed for the Gulf of Mexico. The choice of scale between the model and the platform in which the tests took place was a very important issue that took into account the basin dimensions and mooring design. The tests were performed in three different basins: the IPT Towing Tank in Brazil (Sept. 2005), the NMRI Model Ship Experimental Towing Tank in Japan (Mar. 2007), and the NMRI Experimental Tank in Japan (Jun. 2008). The purpose is to discuss the most relevant issues regarding the concept, execution, and procedures to comparatively analyze the results obtained from VIM model tests, such as characteristic motion amplitudes, motion periods, and forces. The results pointed out the importance of considering the 2DOF in the model tests, i.e., the coexistence of the motions in both in-line and transverse directions. The approach employed in the tests was designed to build a reliable data set for comparison with theoretical and numerical models for VIM prediction, especially that of monocolumn platforms. [DOI: 10.1115/1.4003494]

A new enrichment space for the treatment of discontinuous pressures in multi-fluid flows

In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 10191031, 2010) in several problems involving jumps in the viscosity and/or the presence of singular forces at interfaces not conforming with the element edges. The combination of this enrichment space with another enrichment that accommodates discontinuities in the pressure gradient has also been explored, exhibiting excellent results in problems involving jumps in the density or the volume forces. Copyright (c) 2011 John Wiley & Sons, Ltd.

Low-dimensional modeling of streaks in a wedge flow boundary layer

This paper is concerned with the low dimensional structure of optimal streaks in a wedge flow boundary layer, which have been recently shown to consist of a unique (up to a constant factor) three-dimensional streamwise evolving mode, known as the most unstable streaky mode. Optimal streaks exhibit a still unexplored/unexploited approximate self-similarity (not associated with the boundary layer self-similarity), namely the streamwise velocity re-scaled with their maximum remains almost independent of both the spanwise wavenumber and the streamwise coordinate; the remaining two velocity components instead do not satisfy this property. The approximate self-similar behavior is analyzed here and exploited to further simplify the description of optimal streaks. In particular, it is shown that streaks can be approximately described in terms of the streamwise evolution of the scalar amplitudes of just three one-dimensional modes, providing the wall normal profiles of the streamwise velocity and two combinations of the cross flow velocity components; the scalar amplitudes obey a singular system of three ordinary differential equations (involving only two degrees of freedom), which approximates well the streamwise evolution of the general streaks.

Design and analysis of a 2-DoF split-stator induction motor

A two degrees of freedom (2-DOF) actuator capable of producing linear translation, rotary motion, or helical motion would be a desirable asset to the fields of machine tools, robotics, and various apparatuses. In this paper, a novel 2-DOF split-stator induction motor was proposed and electromagnetic structure pa- rameters of the motor were designed and optimized. The feature of the direct-drive 2-DOF induction motor lies in its solid mover ar- rangement. In order to study the complex distribution of the eddy current field on the ferromagnetic cylinder mover and the motor’s operating characteristics, the mathematical model of the proposed motor was established, and characteristics of the motor were ana- lyzed by adopting the permeation depth method (PDM) and finite element method (FEM). The analytical and numerical results from motor simulation clearly show a correlation between the PDM and FEM models. This may be considered as a fair justification for the proposed machine and design tools.

[N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized [N]pT ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the [N]pT ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.

An Ergonomic Evaluation of a Wrist Brace for Canadian Tree Planters

Tree planting is one of the most physically demanding occupations in Canada and as a result, tree planters are at an elevated risk of injury, specifically at the wrist. Wrist injuries develop on account of the highly repetitive nature of the job, as well as other musculoskeletal risk factors including non-neutral wrist postures and high impact forces sustained at the wrist during shovel-ground impact. As a result, wrist brace use has become common among planters, in an effort to limit deviated wrist postures while also providing enhanced stability at the wrist. The external stability provided by a wrist brace is thought to reduce the muscular effort required to provide stiffness at the wrist during shovel-ground impact. Since these prospective benefits have not been formally investigated, the purpose of this study was to determine the effect of a wrist brace on wrist posture, muscle activity, and joint rotational stiffness about the wrist joint (for two degrees of freedom: flexion/extension and ulnar/radial deviation). We hypothesized that the brace would promote more neutrally aligned wrist angles, and that muscle activity and joint rotational stiffness would also decrease when participants wore the brace. Fourteen tree planters with at least one season of experience were recruited to complete two planting conditions in a laboratory setting: one condition while wearing the brace (with brace, WB) and one condition without the brace (no brace, NB). The results from this study showed that at shovel-ground impact muscle activity trended towards increasing in three muscles when participants wore the brace. Additionally, wrist angles improved about the flexion/extension axis of rotation while increasing in deviation about the ulnar/radial axis of rotation when participants wore the brace. Joint rotational stiffness increased when participants wore the wrist brace. Participants from this study indicated difficulty gripping the shovel due to the bulk of the wrist brace, and this feature is discussed with possible suggestions for future iterations of design. In addition to grip diameter this analysis also prompts the suggestion that hand length and experience should also be considered in the design of tree planting tools, specifically an ergonomic aid such as a wrist brace.

Controle inteligente aplicado a uma mesa de coordenadas de dois graus de liberdade

This work presents the design and construction of an X-Y table of two degrees of freedom, as well as the development of a fuzzy system for its position and trajectory control. The table is composed of two bases that move perpendicularly to each other in the horizontal plane, and are driven by two DC motors. Base position is detected by position sensors attached to the motor axes. A data acquisition board performs the interface between a laptop and the plant. The fuzzy system algorithm was implemented in LabVIEW® programming environment that processes the sensors signals and determines the control variables values that drive the motors. Experimental results using position reference signals (step type signal) and straight and circular paths reference signals are presented to demonstrate the dynamic behavior of fuzzy system

Construção e controle inteligente de um manipulador robótico com dois graus de liberdade

The present work shows the development and construction of a robot manipulator with two rotary joints and two degrees of freedom, driven by three-phase induction motors. The positions of the arm and base are made, for comparison, by a fuzzy controller and a PID controller implemented in LabVIEW® programming environment. The robot manipulator moves in an area equivalent to a quarter of a sphere. Experimental results have shown that the fuzzy controller has superior performance to PID controller when tracking single and multiple step trajectories, for the cases of load and no load

On homoclinic chaos and a control chaos strategy applied to a free-joint nonholonomic manipulator

In this work, the occurrence of chaos (homoclinic scene) is verified in a robotic system with two degrees of freedom by using Poincare-Mel'nikov method. The studied problem was based on experimental results of a two-joint planar manipulator-first joint actuated and the second joint free-that resides in a horizontal plane. This is the simplest model of nonholonomic free-joint manipulators. The purpose of the present study is to verify analytically those results and to suggest a control strategy.

A nonlinear and non-ideal wind generator supporting structure

We present a simple mathematical model of a wind turbine supporting tower. Here, the wind excitation is considered to be a non-ideal power source. In such a consideration, there is interaction between the energy supply and the motion of the supporting structure. If power is not enough, the rotation of the generator may get stuck at a resonance frequency of the structure. This is a manifestation of the so-called Sommerfeld Effect. In this model, at first, only two degrees of freedom are considered, the horizontal motion of the upper tip of the tower, in the transverse direction to the wind, and the generator rotation. Next, we add another degree of freedom, the motion of a free rolling mass inside a chamber. Its impact with the walls of the chamber provides control of both the amplitude of the tower vibration and the width of the band of frequencies in which the Sommerfeld effect occur. Some numerical simulations are performed using the equations of motion of the models obtained via a Lagrangian approach.