Translational Oscillations Research Articles

Bluff-body Flow Created By Combined RotaryAnd Translational Oscillation

Bluff-body Flow Created By Combined RotaryAnd Translational Oscillation

Tensor Properties of Added-mass and Damping Coefficients

It has been shown that in the context of a linear theory for a floating body with six degrees of freedom each of the 6× 6 added-mass and damping matrices contains three distinct Cartesian second-order tensors in regard to translational, rotational and interaction between translational and rotational oscillations. As a result of this, a new technique based on the transformation law of second-order tensors is introduced for motion analysis of offshore platforms which can be used as an alternative to the common methods in offshore engineering.

DETECTION AND STUDY OF THE TRANSLATIONAL OSCILLATIONS OF THE EARTH’S SOLID INNER CORE

The advances of the theoretical modeling and detection with the superconducting gravimeters (SGs), related to the Slichter triplet, are systematically introduced in this paper. The translational oscillations of the Earth’s solid inner core, which is usually called as the Slichter modes in honor of the scientist who firstly pointed out its theoretical existence, are a triplet of the principle normal modes of the Earth. The triplet is primarily driven by the gravitational forces and has eigenperiods of several hours. From the theoretical modeling, it is found that the eigenperiods of the Slichter modes are most sensitive to the density contrast across the inner core boundary (ICB), and are only slightly disturbed by the viscosity of the fluid near the ICB, the transitional zone between the outer and inner cores, Lorentz forces and some others effects. Therefore, study and detection of the Slichter modes may provide significant information about the structure of the Earth’s deep interior. Due to less knowledge to the Earth’s deep interior, there exists great uncertainty in the results of theoretical modeling based on the present Earth’s models. It is necessary to detect the signatures related to the Slichter modes by using the ground-based observations. Smylie (1992) claimed that the weak gravity resonance signatures, coming from the Slichter triplet, were found in the SG data from plural stations in the central Europe. Based on the results, the density and viscosity near the ICB have been evaluated. However, thses results were questioned by the other scientists. Recently, we have comprehensively analyzed and treated the continuous long-term SG data from!the worldwide network of the Global Geodynamics Projects. It is found that there is no evidence to support the existence of the resonance related to the Slichter triplet as what Smylie claimed. On the contrary, it is found that there are eight significant spectral peaks related to some globally geodynamical phenomena, and the Slichter triplet is one of their possible resources.

A tribological study of double-walled and triple-walled carbon nanotube oscillators

We reported in a previous study (Zhao et al 2003 Phys. Rev. Lett. 91 175504) that energytransfer from the orderly intertube translational oscillation to intratube vibrational modesfor an isolated system of two coaxial carbon nanotubes at low temperatures takes placeprimarily via two distinct types of collective motion of the carbon nanotubes, i.e., off-axialrocking motion of the inner tube and radial wavy motion of the outer tube, andthat these types of motion may or may not occur for such a system, dependingupon the amount of the initial extrusion of the inner tube out of the outer tube.Our present study, using micro-canonical molecular dynamics (MD), indicatesthe existence of an energy threshold, largely independent of system sizes andconfigurations, for a double-walled nano-oscillator to deviate from the intertubetranslational oscillation and thus to encounter significant intertube friction. Thefrictional forces associated with several distinct dissipative mechanisms are all foundto exhibit no proportional dependence upon the normal force between the twosurfaces in relative sliding, contrary to the conventional understanding resultingfrom tribological studies of macroscopic systems. Furthermore, simulation hasbeen performed at different initial temperatures, revealing a strong temperaturedependence of friction in the early phase of oscillation. Finally, our studies ofthree-walled nano-oscillators show that an initial extrusion of the middle tubecan cause inner-tube off-axial instabilities, leading to strong frictional effects.

Analytical calculation of far infrared spectra of ice in terms of a molecular model

Wideband far infrared (FIR) spectra of complex permittivity ε( ν) of ice are calculated in terms of a simple analytical theory based on the method of dipolar autocorrelation functions. The molecular model represents a revision of the model recently presented for liquid water in Adv. Chem. Phys. 127 (2003) 65. A composite two-fractional model is proposed. The model is characterised by three phenomenological potential wells corresponding to the three FIR bands observed in ice. The first fraction comprises dipoles reorienting in a rather narrow and deep hat-like well; these dipoles generate the librational band centred at the frequency ≈880 cm −1. The second fraction comprises elastically interacting particles; they generate two nearby bands placed around frequency 200 cm −1. For description of one of these bands the harmonic oscillator (HO) model is used, in which translational oscillations of two charged molecules along the H-bond are considered. The other band is produced by the H-bond stretch, which governs hindered rotation of a rigid dipole. Such a motion and its dielectric response are described in terms of a new cut parabolic (CP) model applicable for any vibration amplitude. The composite hat-HO–CP model results in a smooth ε( ν) ice spectrum, which does not resemble the noise-like spectra of ice met in the known literature. The proposed theory satisfactorily agrees with the experimental ice spectrum measured at −7 °C. The calculated longitudinal optic-transverse optic (LO–TO) splitting occurring at ≈250 cm −1 qualitatively agrees with the measured data.

Viscoelectromagnetic coupling in precession‐nutation theory

The estimates made by Mathews et al. [2002] for the strengths of magnetic fields at the core mantle boundary and the inner core boundary were based on the not unreasonable hypothesis that the torques generated by differential wobbles between the fluid core on the one hand and the mantle and the inner core on the other are due to the magnetic fields crossing the core mantle and inner core boundaries. In this paper, we investigate the possibility that viscous drag at these boundaries might contribute significantly to the torques. Our objectives are to find out, first, whether it would become possible, with part of the torques accounted for by viscosity, to reduce the estimates for the magnetic field strengths at the two boundaries from the values obtained by Mathews et al. to the considerably lower values that had been favored earlier and, second, whether any bounds can be placed on the fluid viscosity itself. For this purpose, we have generalized the theory of Buffett et al. [2002] to obtain new expressions for the coupling constants representing the torques at the two boundaries which include the effects due to both electromagnetism and viscosity. With the use of these we find that Mathews et al.'s estimates for the coupling constants (which are independent of the mechanism of the coupling) place upper bounds on the viscosities at the core mantle and inner core boundaries. These bounds rule out not only the very high viscosity called for in recent literature relating to the translational oscillation modes of the inner core but also other earlier estimates, with the exception of those derived from theoretical and experimental studies on liquid metals. We find also that the magnetic field strength at the inner core boundary cannot be brought down to anywhere near the levels deduced from geodynamo theories unless the inner core ellipticity and/or the density jump at the inner core boundary are assigned values that appear unrealistic. Our theoretical formulation takes the variations of the unperturbed magnetic field and the ambient flow in the fluid core to be on spatial scales that are large compared to the kilometer‐scale thickness of the boundary layers which dominate the coupling of the fluid core to the mantle and the inner core at the tidal frequencies relevant to nutations. Possible variations on scales of a few kilometers or less are not taken into account. Such fine‐scale maps of the fields are not obtainable, at least at present, and so definitive computations are not possible. Our assessment, however, is that the effects of such small‐scale variations on the torques over the boundaries of the fluid core are unlikely to be large and that their impact on our conclusions is likely to be not significant.

Regular and chaotic dynamics of a spherical bubble

The problem of the translational motion and oscillations of the radius of a spherical gas bubble in a spherical flask filled with a weakly compressible liquid is considered when there is forced radial perturbation of the flask wall. The translational motion is that of the bubble under the action of an acoustic field when there is viscous drag and the effect of added mass. A system of differential equations is proposed which describes the combined oscillations of the radius and the translational motion of the bubble. This system includes an ordinary differential equation of the Herring-Flinn-Gilmore type which describes the evolution of the radius of the bubble. Bifurcation diagrams are constructed for the radius of the bubble, which reveal a repeating structure of the bifurcation set within the limits of the harmonic resonances of the system. The dynamic characteristics of the bubble for different equilibrium radii are investigated numerically in connection with the analysis of the stability of its position in space.

Continuous Fuzzy Controller Design Subject to Minimizing Control Input Energy with Output Variance Constraints

This paper presents the stability synthesis subject to minimum control input energy and output variance constraints for a class of nonlinear systems, which is modeled by the Takagi–Sugeno (T–S) fuzzy model. For this T–S type fuzzy model, the proposed fuzzy controller design approach not only ensures the stability of the closed-loop system, but also minimizes the control input energy with output variance constraints. The proposed method uses linear matrix inequality technique to find the common positive definite covariance matrix and feedback gains for each rule of the T–S fuzzy models. Finally, the proposed model-based fuzzy control method is used to deal with the control problem of the translational oscillation with a rotational proof mass actuator (TORA) system.

The Vibration Response of a Cantilevered Rectangular Cylinder in Cross-Flow Oscillation

It is well known that a large-amplitude oscillation called galloping @1–3# is generated, in addition to Karman vortex excitation, for rectangular cylinders supported perpendicularly to a uniform flow when the slenderness b/d is in the range of 0.6 to 2.8 ~d5height, b5streamwise length of the rectangular cross-section!. The basic aerodynamic excitation mechanism of the cross-flow galloping of a rectangular cylinder is explained by the quasisteady nonlinear aerodynamic theory developed by Parkinson et al. @4#. In this theory, the relative attack angle plays an important role in the excitation mechanism of galloping. Also, as was shown by Deniz and Staubli @5#, the attack angle of a fixed rectangular cylinder strongly affects the vortex shedding frequency and lift. Although the mechanism of pure cross-flow oscillation for a circular and rectangular cylinder is becoming clear, as seen in the recent paper @6#, a slight difference in support conditions may affect strongly the oscillation behavior. The specific aim of this

Sliding-mode control design for a class of systems with non-matching nonlinearities and disturbances

A novel sliding-mode control design is proposed for the class of single-input nonlinear systems with non-matching nonlinearities and/or disturbances. This class of systems includes dual-spin spacecraft and rotational proof mass actuators that are used for suppressing translational oscillation. The sliding-mode control law is designed via an L 2 -norm bounding technique that ensures, under certain conditions, asymptotic stability of the system when the disturbances satisfy the matching condition or are zero; otherwise, it ensures system stability with an a priori bound on the transmission gain of the disturbances through the system for non-zero non-matching disturbances. Simulation results for a rotational proof mass actuator or dual-spin spacecraft example illustrate the excellent responses obtained by applying the control laws derived from this proposed design procedure.

Translational motion of a bubble undergoing shape oscillations

This paper studies the nonlinear coupling between the volume pulsation, translational motion and shape modes of an oscillating bubble, especially in the context of translational instability, known as ‘dancing motion’, that is demonstrated by bubbles in acoustic standing waves. A set of coupled equations is derived that describes volume pulsations of a bubble, its translational motion and shape oscillations evolving on the bubble surface. The amplitudes of the surface modes and the translational velocity of the bubble are assumed to be small and allowed for in the equations of motion up to only second-order terms. The amplitude of the volume oscillation is not limited. Unlike earlier work on this subject, where only two adjacent shape modes with given natural frequencies are taken into account, we allow for all shape modes and do not impose any limitations on their natural frequencies. As a result, the present analysis reveals additional features, which have not been noted previously, inherent in the mutual interactions of the shape modes as well as in the interaction between the shape modes and the translational motion.

Detection of the translational oscillations of the Earth?s solid inner core based on the international superconducting gravimeter observations

Based on the 21 series of the high precision tidal gravity observations recorded using superconducting gravimeters (SG) at 14 stations distributed globally (in totally about 86 years), the translational oscillations of the Earth’s solid inner core (ESIC) is detected in this paper. All observations are divided into two groups with G-I group (8 relatively longer observational series) and G-II group (13 relatively shorter observational series). The detailed corrections to minute original observations for each station are carried out, the error data due to the earthquakes, power supply impulses and some perturbations as change in atmospheric pressure and so on are carefully deleted for the first step, the gravity residuals are obtained after removing further synthetic tidal gravity signals. The Fast Fourier Transform analysis is carried out for each residual series, the estimations of the product spectral densities in the subtidal band are obtained by using a multi-station staking technique. The 8 common peaks are found after further removing the remaining frequency dependent pressure signals. The eigenperiods, quality factors and resonant strengths for these peaks are simulated. The numerical results show that the discrepancies of the eigenperiods for 3 of 8 peaks, compared to those of theoretical computation given by Smith, are only 0.4%, −0.4% and 1.0%. This coincidence signifies that the dynamical phenomenon of the Earth’s solid inner core can be detected by using high precision ground gravity observations. The reliability of the numerical computation is also checked, the spectral peak splitting phenomenon induced by Earth’s rotation and ellipticity is preliminary discussed in this paper.

The hydrodynamics of an oscillating porous sphere

We determine the hydrodynamics of a rigid, weakly permeable sphere undergoing translational oscillations in an incompressible Newtonian fluid. We check using homogenization and scaling arguments that the flow inside the sphere may be modeled by Darcy’s law and that the Beavers–Joseph–Saffman (BJS) boundary condition still applies for oscillatory flows, provided the frequency of oscillation is not too high. The BJS boundary condition introduces a slip velocity and to leading order in ε=k/a, where k is the particle permeability and a is the radius, the particle may be regarded as impermeable with a slip length independent of frequency. Under these circumstances we solve for the flow field, pressure distribution and drag explicitly and show their behavior for 0⩽ε⩽0.05 and frequencies relevant to electroacoustics (1–10 MHz). From the drag we find the leading order corrections due to particle permeability of the pseudo-steady drag, Basset force and added mass.

Tread Discontinuities as Source of Vibration/Noise — Transient Dynamics of Rolling Tire

Abstract Tire vibrations supply energy for noise generation. Tread band features, such as grooves and blade cuts, affect noise signatures since they impart vibrations to a rolling tire. Finite element transient dynamics simulations have been performed with ABAQUS/Explicit on a rolling passenger tire to examine the vibrations induced by the entrance of tread pattern discontinuities into the contact patch. The loaded tire rolls on a 3.05 m (10 ft) diameter drum at terminal speeds of 4.3 km/h (2.7 mph) and 34.4 km/h (21.4 mph). Three models with augmented discontinuities in the circumferential ribs have been examined: 1) continuous (control); 2) angled lateral grooves; and 3) transverse grooves. They are ordered in increasing severity of rib discontinuity. The induced rolling vibrations are evaluated by identifying the ‘perturbed’ dynamic responses of (2) and (3) from (1). The results indicate that any discontinuity or abruptness in tread patterns can induce vibrations, which are similar in nature, for the two speeds studied. The higher rolling speed changes only the amplitudes, but not the frequencies of the induced oscillations at the free spindle. The ‘perturbed’ vibrations for both speeds manifest at the spindle as translational (vertical) and rotational (axial) oscillations of 29 and 44 Hz, respectively, for the tire studied.

Ca−OH Bonding in the C−S−H Gel Phase of Tricalcium Silicate and White Portland Cement Pastes Measured by Inelastic Neutron Scattering

Inelastic neutron spectroscopy (INS) was used to determine the content of Ca−OH bonds in a series of mature tricalcium silicate (3CaO·SiO2) and white portland cement (WPC) pastes that were decalcified to calcium/silicon molar ratios (Ca/Si) as low as 1. These measurements indicate that the band in the INS data at 41 meV, which originates from lattice modes involving the translational oscillations of OH groups attached to Ca, has intensity contributions from both Ca(OH)2 and C−S−H gel, the main hydration product of cement paste. Quantitative analysis of the INS spectra show that ∼23% of the Ca in C−S−H gel with Ca/Si = 1.7 is charge-balanced by OH groups, with the remainder charge-balanced by silicate groups. This substantial concentration of Ca−OH bonds supports the hypothesis that C−S−H gel has a local structure resembling a disordered form of the mineral jennite. On decalcification, the concentration of Ca−OH bonds in C−S−H gel decreases and is eliminated at Ca/Si ratios slightly above 1. The observed trend is shown to be consistent with charge balance calculations and interpretations of recent phase equilibrium findings.

The Forced Oscillations of Submerged Bodies

The increasing use of very light structures in aerospace applications are given rise to the need of taking into account the effects of the surrounding media in the motion of a structure (as for instance, in modal testing of solar panels or antennae) as it is usually performed in the motion of bodies submerged in water in marine applications. New methods are in development aiming at to determine rigid-body properties (the center of mass position and inertia properties) from the results of oscillations tests (at low frequencies during modal testing, by exciting the rigid-body modes only) by using the equations of the rigid-body dynamics. As it is shown in this paper, the effect of the surrounding media significantly modifies the oscillation dynamics in the case of light structures and therefore this effect should be taken into account in the development of the above-mentioned methods. The aim of the paper is to show that, if a central point exists for the aerodynamic forces acting on the body, the motion equations for the small amplitude rotational and translational oscillations can be expressed in a form which is a generalization of the motion equations for a body in vacuum, thus allowing to obtain a physical idea of the motion and aerodynamic effects and also significantly simplifying the calculation of the solutions and the interpretation of the results. In the formulation developed here the translational oscillations and the rotational motion around the center of mass are decoupled, as is the case for the rigid-body motion in vacuum, whereas in the classical added mass formulation the six motion equations are coupled. Also in this paper the nonsteady motion of small amplitude of a rigid body submerged in an ideal, incompressible fluid is considered in order to define the conditions for the existence of the central point in the case of a three-dimensional body. The results here presented are also of interest in marine applications.

Aerodynamic Work Based on an Extended Theodorsen Function for an Airfoil with a Wake.

Extended lift and moment, based on an extended Theodorsen function for arbitrary and constant convection velocity of wake vortices, are converted to aerodynamic work. Pure pitching oscillations, pure translational oscillations and their combinations are considered. Decrease in convection velocity of wake vortices yields an increase in aerodynamic work, thus destabilizing airfoil oscillations. Some of the available wind-tunnel data support the present theoretical predictions.

An indirect boundary integral method for an oscillatory Stokesflow problem

The purpose of this paper is to present an indirect boundary integral method for the oscillatory Stokes flow provided by the translational oscillations of two rigid spheres in an incompressible Newtonian fluid of infinite expanse.

A continuous, hybrid field-gradient device for magnetic colloid-based separations

A fully continuous, hybrid field-gradient device is developed for colloidal magnetic affinity separation. The device consists of a 1.0 cm internal diameter 1.2 m long, axially rotating horizontal glass chamber, with four repeating magnetic units distributed axially along the tube. Each magnetic unit consists of a stationary alternating-current solenoid that surrounds the chamber, followed by a direct current flowing, computer-controlled electromagnet, placed at a distance of 4.0 cm from the end of the solenoid. The alternating-current-carrying solenoids impart translational and rotary oscillations to the magnetic particles, enhancing mixing. The computer-controlled electromagnets draw the magnetic particles to the chamber walls, and increase their residence time in the chamber. By manipulating the on–off cycle for these electromagnets, the exiting solution can be switched between one that contains a negligible concentration of target-bound magnetic particles and one that has a high concentration of the target, without interrupting the feed. The operation of this device is demonstrated for the removal of cadmium ions from a cadmium sulfate solution. 1–10 μm diameter anion-exchange-resin-coated magnetic particles at a concentration of 0.5 mg particles/ml were used as the mobile solid support. The feed consisted of a 10.0 mg/l cadmium sulfate solution, at a flow rate of 25 ml/min. The device was operated as a three-stage cross-current cascade. For this system, 45%, 58% and 63% of the entering cadmium ions are removed at each stage, respectively, with stage efficiencies that vary between 57% and 65%. Thus, more than 90% of the entering cadmium ions are removed. While this device has been demonstrated for metal ion removal from an aqueous feed, it can potentially be applied to several other affinity-based separations.

Chaos and flights in the atom-photon interaction in cavity QED.

We study dynamics of the atom-photon interaction in cavity quantum electrodynamics, considering a cold two-level atom in a single-mode high-finesse standing-wave cavity as a nonlinear Hamiltonian system with three coupled degrees of freedom: translational, internal atomic, and the field. The system proves to have different types of motion including Lévy flights and chaotic walkings of an atom in a cavity. The corresponding equations of motion for expectation values of the atom and field variables have two characteristic time scales: fast Rabi oscillations of the internal atomic and field quantities and slow translational oscillations of the center of the atom mass. It is shown that the translational motion, related to the atom recoils, is governed by an equation of a parametric nonlinear pendulum with a frequency modulated by the Rabi oscillations. This type of dynamics is chaotic with some width of the stochastic layer that is estimated analytically. The width is fairly small for realistic values of the control parameters, the normalized detuning delta and atomic recoil frequency alpha. We consider the Poincaré sections of the dynamics, compute the Lyapunov exponents, and find a range of the detuning, |delta| less, similar 3, where chaos is prominent. It is demonstrated how the atom-photon dynamics with a given value of alpha depends on the values of delta and initial conditions. Two types of Lévy flights, one corresponding to the ballistic motion of the atom and the other corresponding to small oscillations in a potential well, are found. These flights influence statistical properties of the atom-photon interaction such as distribution of Poincaré recurrences and moments of the atom position x. The simulation shows different regimes of motion, from slightly abnormal diffusion with <x(2)> approximately tau(1.13) at delta=1.2 to a superdiffusion with <x(2)> approximately tau(2.2) at delta=1.92 that corresponds to a superballistic motion of the atom with an acceleration. The obtained results can be used to find new ways to manipulate atoms, to cool and trap them by adjusting the detuning delta.