An overview on a nonideal system with three and a half degrees of freedom

The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor. Copyright © 2005 by ASME.

Experimental Comparison of Two Degrees-of-Freedom Vortex-Induced Vibration on High and Low Aspect Ratio Cylinders with Small Mass Ratio

Vortex-induced motion (VIM) is a specific way for naming the vortex-induced vibration (VIV) acting on floating units. The VIM phenomenon can occur in monocolumn production, storage and offloading system (MPSO) and spar platforms, structures presenting aspect ratio lower than 4 and unity mass ratio, i.e., structural mass equal to the displaced fluid mass. These platforms can experience motion amplitudes of approximately their characteristic diameters, and therefore, the fatigue life of mooring lines and risers can be greatly affected. Two degrees-of-freedom VIV model tests based on cylinders with low aspect ratio and small mass ratio have been carried out at the recirculating water channel facility available at NDF-EPUSP in order to better understand this hydro-elastic phenomenon. The tests have considered three circular cylinders of mass ratio equal to one and different aspect ratios, respectively L/D = 1.0, 1.7, and 2.0, as well as a fourth cylinder of mass ratio equal to 2.62 and aspect ratio of 2.0. The Reynolds number covered the range from 10 000 to 50 000, corresponding to reduced velocities from 1 to approximately 12. The results of amplitude and frequency in the transverse and in-line directions were analyzed by means of the Hilbert-Huang transform method (HHT) and then compared to those obtained from works found in the literature. The comparisons have shown similar maxima amplitudes for all aspect ratios and small mass ratio, featuring a decrease as the aspect ratio decreases. Moreover, some changes in the Strouhal number have been indirectly observed as a consequence of the decrease in the aspect ratio. In conclusion, it is shown that comparing results of small-scale platforms with those from bare cylinders, all of them presenting low aspect ratio and small mass ratio, the laboratory experiments may well be used in practical investigation, including those concerning the VIM phenomenon acting on platforms. [DOI: 10.1115/1.4006755]

Which-path problem for one and two particles with two degrees of freedom and a relation between transverse spatial structure and group velocity of light

Quantum mechanics, optics and indeed any wave theory exhibits the phenomenon of interference. In this thesis we present two problems investigating interference due to indistinguishable alternatives and a mostly unrelated investigation into the free space propagation speed of light pulses in particular spatial modes. In chapter 1 we introduce the basic properties of the electromagnetic field needed for the subsequent chapters. In chapter 2 we review the properties of interference using the beam splitter and the Mach-Zehnder interferometer. In particular we review what happens when one of the paths of the interferometer is marked in some way so that the particle having traversed it contains information as to which path it went down (to be followed up in chapter 3) and we review Hong-Ou-Mandel interference at a beam splitter (to be followed up in chapter 5). In chapter 3 we present the first of the interference problems. This consists of a nested Mach-Zehnder interferometer in which each of the free space propagation segments are weakly marked by mirrors vibrating at different frequencies [1]. The original experiment drew the conclusions that the photons followed disconnected paths. We partition the description of the light in the interferometer according to the number of paths it contains which-way information about and reinterpret the results reported in [1] in terms of the interference of paths spatially connected from source to detector. In chapter 4 we briefly review optical angular momentum, entanglement and spontaneous parametric down conversion. These concepts feed into chapter 5 in which we present the second of the interference problems namely Hong-Ou-Mandel interference with particles possessing two degrees of freedom. We analyse the problem in terms of exchange symmetry for both boson and fermion pairs and show that the particle statistics at a beam splitter can be controlled for suitably chosen states. We propose an experimental test of these ideas using orbital angular momentum entangled photons. In chapter 6 we look at the effect that the transverse spatial structure of the mode that a pulse of light is excited in has on its group velocity. We show that the resulting group velocity is slower than the speed of light in vacuum for plane waves and that this reduction in the group velocity is related to the spread in the wave vectors required to create the transverse spatial structure. We present experimental results of the measurement of this slowing down using Hong-Ou-Mandel interference.

Self-calibration of wireless cameras with restricted degrees of freedom

This paper presents an approach for the automatic calibration of low-cost cameras which are assumed to be restricted in their freedom of movement to either pan or tilt movements. Camera parameters, including focal length, principal point, lens distortion parameter and the angle and axis of rotation, can be recovered from a minimum set of two images of the camera, provided that the axis of rotation between the two images goes through the camera’s optical center and is parallel to either the vertical (panning) or horizontal (tilting) axis of the image. Previous methods for auto-calibration of cameras based on pure rotations fail to work in these two degenerate cases. In addition, our approach includes a modified RANdom SAmple Consensus (RANSAC) algorithm, as well as improved integration of the radial distortion coefficient in the computation of inter-image homographies. We show that these modifications are able to increase the overall efficiency, reliability and accuracy of the homography computation and calibration procedure using both synthetic and real image sequences

Analysis of two degrees of freedom systems through weighted mean square linearization approach

In this paper a study of the free, forced and self-excited vibrations of non-linear, two degrees of freedom systems is reported. The responses are obtained by linearizing the nonlinear equations using the weighted mean square linearization approach. The scope of this approach, in terms of the type of non-linearities the method can tackle, is also discussed.

Analysis of two degrees of freedom systems through weighted mean square linearization approach

In this paper a study of the free, forced and self-excited vibrations of non-linear, two degrees of freedom systems is reported. The responses are obtained by linearizing the nonlinear equations using the weighted mean square linearization approach. The scope of this approach, in terms of the type of non-linearities the method can tackle, is also discussed.

Decoupling in non-linear systems with two degrees of freedom

The problem of decoupling a class of non-linear two degrees of freedom systems is studied. The coupled non-linear differential equations of motion of the system are shown to be equivalent to a pair of uncoupled equations. This equivalence is established through transformation techniques involving the transformation of both the dependent and independent variables. The sufficient conditions on the form of the non-linearity, for the case wherein the transformed equations are linear, are presented. Several particular cases of interest are also illustrated.

Diversity and degrees of freedom of cooperative wireless networks

Two key parameters in the outage characterization of a wireless fading network are the diversity and the degrees of freedom (DOF). These two quantities represent the two endpoints of the diversity multiplexing gain tradeoff, In this paper, we present max-flow min-cut type theorems for computing both the diversity and the DOF of arbitrary single-source single-sink networks with nodes possessing multiple antennas. We also show that an amplify-and-forward protocol is sufficient to achieve the same. The DOF characterization is obtained using a conversion to a deterministic wireless network for which the capacity was recently found. This conversion is operational in the sense that a capacity-achieving scheme for the deterministic network can be converted into a DOF-achieving scheme for the fading network. We also show that the diversity result easily extends to multisource multi-sink networks whereas the DOF result extends to a single-source multi-cast network. Along the way, we prove that the zero error capacity of the deterministic network is the same as its c-error capacity.

Neutron diffraction study of the coupling between spin, lattice, and structural degrees of freedom in 0.8BiFeO(3)-0.2PbTiO(3)

A powder neutron diffraction study was carried out on 0.8BiFeO(3)-0.2PbTiO(3) in the temperature range 27-1000 degrees C. The system exhibits magnetic transition at similar to 300 degrees C and a rhombohedral (R3c)-cubic (Pm3m) ferroelectric phase transition at similar to 650 degrees C. Anomalous variation in the lattice parameters and the octahedral tilt angle is observed across the magnetic transition temperature. In the magnetic phase, the c parameter is contracted and the octahedral tilt angle is slightly increased. The results suggest coupling between the spin, lattice and structural degrees of freedom. (C) 2011 American Institute of Physics. doi:10.1063/1.3555093]

Interplay of spin and lattice degrees of freedom in the frustrated antiferromagnet CdCr2O4: High-field and temperature-induced anomalies of the elastic constants

Temperature and magnetic field studies of the elastic constants of the chromium spinel CdCr2O4 show pronounced anomalies related to strong spin-phonon coupling in this frustrated antiferromagnet. A detailed comparison of the longitudinal acoustic mode propagating along the 111] direction with a theory based on an exchange-striction mechanism leads to an estimate of the strength of the magnetoelastic interaction. The derived spin-phonon coupling constant is in good agreement with previous determinations based on infrared absorption. Further insight is gained from intermediate and high magnetic field experiments in the field regime of the magnetization plateau. The role of the antisymmetric Dzyaloshinskii-Moriya interaction is discussed.

Degrees of freedom of relay aided MIMO X network with orthogonal components

We consider the one-way relay aided MIMO X fading Channel where there are two transmitters and two receivers along with a relay with M antennas at every node. Every transmitter wants to transmit messages to every other receiver. The relay broadcasts to the receivers along a noisy link which is independent of the transmitters channel. In literature, this is referred to as a relay with orthogonal components. We derive an upper bound on the degrees of freedom of such a network. Next we show that the upper bound is tight by proposing an achievability scheme based on signal space alignment for the same for M = 2 antennas at every node.

On the generalized degrees of freedom of the K-user symmetric MIMO Gaussian interference channel

This work derives inner and outer bounds on the generalized degrees of freedom (GDOF) of the K-user symmetric MIMO Gaussian interference channel. For the inner bound, an achievable GDOF is derived by employing a combination of treating interference as noise, zero-forcing at the receivers, interference alignment (IA), and extending the Han-Kobayashi (HK) scheme to K users, depending on the number of antennas and the INR/SNR level. An outer bound on the GDOF is derived, using a combination of the notion of cooperation and providing side information to the receivers. Several interesting conclusions are drawn from the bounds. For example, in terms of the achievable GDOF in the weak interference regime, when the number of transmit antennas (M) is equal to the number of receive antennas (N), treating interference as noise performs the same as the HK scheme and is GDOF optimal. For K >; N/M+1, a combination of the HK and IA schemes performs the best among the schemes considered. However, for N/M <; K ≤ N/M+1, the HK scheme is found to be GDOF optimal.

Analysis of the degrees-of-freedom of spatial parallel manipulators in regular and singular configurations

This paper presents a study of the nature of the degrees-of-freedom of spatial manipulators based on the concept of partition of degrees-of-freedom. In particular, the partitioning of degrees-of-freedom is studied in five lower-mobility spatial parallel manipulators possessing different combinations of degrees-of-freedom. An extension of the existing theory is introduced so as to analyse the nature of the gained degree(s)-of-freedom at a gain-type singularity. The gain of one- and two-degrees-of-freedom is analysed in several well-studied, as well as newly developed manipulators. The formulations also present a basis for the analysis of the velocity kinematics of manipulators of any architecture. (C) 2013 Elsevier Ltd. All rights reserved.

Flow-Induced Vibrations Of A Cylinder With Two Degrees Of Freedom Near Rigid Plane Boundary

Based on similarity analyses, the flow-induced vibrations of a near-wall cylinder with 2 degrees of freedom are investigated experimentally by employing a hydroelastic apparatus in conjunction with a flume. The cylinder's vibration amplitude, vibration frequency and vortex shedding frequency were measured and analyzed. The effects of gap-to-diameter ratio (e,ID) upon the vibration responses are further investigated. The experimental results indicate that, when the reduced velocity (Vr) is small (e.g. Vr = 1.2 similar to 2.6), only streamwise vibration occurs, and its frequency is quite close to its natural frequency in still water. When increasing Vr (e.g. Vr > 3.4), both streamwise and transverse vibrations of the near-wall cylinder may occur. In the examined range of gap-to-diameter ratio (0.42 < e(0)/D < 2.68), 2 vibration stages (in terms of Vr) of streamwise vibrations usually exist: First Streamwise Vibration (FSV) and Second Streamwise Vibration (SSV). In the SSV stage, the vortex shedding frequency may either undergo a jump to that of the streamwise vibration, or stay consistent with that of the transverse vibration. The amplitudes of transverse vibration are usually much larger than those of streamwise vibration for the same value of e(0)/D. The maximum amplitudes of both streamwise and transverse vibration get larger with the increase of e(0)/D (0.42 < e(0)/D < 2.68).

Experimental Study on Flow Induced Vibration of a Cylinder with Two Degrees of Freedom Near a Rigid Wall

The flow-induced vibration of a cylinder with two degrees of freedom near a rigid wall under the action of steady flow is investigated experimentally. The vibration amplitude and frequency of the cylinder and the vortex shedding frequency at the wake flow region of the cylinder are measured. The influence of gap-to-diameter ratio upon the amplitude response is analyzed. The experimental results indicate that when the reduced velocity (Vr) is in the range of 1.2 < Vr < 2.6, only streamwise vibration with small amplitude occurs, whose frequency is quite close to its natural frequency in the still water. When the reduced velocity Vr > 3.4, both the streamwise and transverse vibrations of the cylinder occur. In this range, the amplitudes of transverse vibration are much larger than those of streamwise vibrations, and the amplitudes of the streamwise vibration also get larger than those at the range of 1.2 < Vr < 2.6. At the range of Vr > 3.4, the frequency of streamwise vibration undergoes a jump at certain values of Vr, at which the streamwise vibrating frequency is twice as much as the transverse one. However, when the streamwise vibration does not experience a jump, its frequency is the same as that of the transverse vibration. The maximum values of second streamwise and transverse vibration amplitudes increase with increasing gap-to-diameter ratios.