Translational Oscillations Research Articles

The steady streaming generated by a vibrating plate parallel to a fixed plate

A viscous fluid is sandwiched between two parallel plates. The top plate performs both normal and lateral small translatory oscillations. The unsteady Navier-Stokes equations are solved using perturbations. The nonlinear Reynolds stress causes a secondary steady streaming. It is found that the normal oscillations induce a steady lift while the interaction between normal and lateral oscillations causes a directional net flux. The system thus operates as a valveless pump with rigid walls.

The influence of an inhomogeneous sound field on the translational motion and nonlinear radial oscillation of a cavitation gas bubble in a compressible liquid

The influence of an inhomogeneous sound field on the translational motion and nonlinear radial oscillation of a cavitation gas bubble in a compressible liquid

Dynamics of wire boom oscillations on a spinning satellite Part II, normal modes in spin plane

Harmonic analysis of the normal modes in the spin plane of a satellite with four hinged wire booms each with a tip mass attached is presented. Analytical expressions of normal mode coordinates and frequencies are obtained by solving the matrix eigenvalue equations, using secular determinant and simultaneous diagonalization methods. Translational oscillation of the center body is present in configurations of lower symmetry. The analytical results are in good agreement with computer simulations.

Probability density functions for the translational itinerant oscillator

The translational itinerant oscillator model for molecular motion in fluids is developed in terms of two phenomenological parameters. These are : (a) the retarding frictional force acting on a rigid cage which undergoes translational Brownian motion, and (b) the angular frequency of oscillation of a particle hamonically bound within the cage. The equations of motion contain fewer parameters than those of Damle et al. [6] and may be solved using Laplace transforms. The underlying probability density functions in phase and configuration space may then be calculated.

The Unsteady Laminar Boundary Layer on Cylinders in Translational Oscillation : The Case in which the Influence of Wake Vortices is Disregarded

The Unsteady Laminar Boundary Layer on Cylinders in Translational Oscillation : The Case in which the Influence of Wake Vortices is Disregarded

Statistical mechanics of homogeneous nucleation in vapor

Statistical mechanics of homogeneous nucleation in vapor

Translational inner core oscillations of a rotating, slightly elliptical Earth

Application of a theory developed elsewhere enables us to generate good numerical normal mode eigensolutions for the translational oscillations of the solid inner core of a rotating, slightly elliptical earth model. Examination of the particle motions associated with these normal modes shows clearly the profound influence of the earth's steady rotation, particularly on motions in the fluid outer core. The variation of eigenfrequencies with core structure shows clearly how stable (or unstable) stratification in the outer core acts to increase (or decrease) the associated eigenfrequencies. A study of the energy partition during one cycle of motion shows that compressibility (as opposed to stratification) in the fluid outer core is of little significance but that inner core elasticity has a very significant effect. Normal mode excitation calculations show that the gravimeter signal available at the earth's surface as a result of the excitation of such a motion by some seismic event is intimately tied to the stability or instability of the stratification of the fluid outer core. We currently have little knowledge about this very important aspect of the earth's deep interior. We cannot currently preclude the possibility of observing this normal mode. We discuss how to estimate the damping of these modes by viscosity or anelasticity.

Secondary Flow Induced by an Unharmonically Oscillating Circular Cylinder

This paper deals theoretically with the two-dimensional flow driven by a circular cylinder which performs unharmonically translational oscillation in an unbounded viscous incompressible fluid otherwise at rest. Slow steady secondary flow occurs outside the oscillatory boundary layer around the cylinder, provided that the non-dimensional amplitude of the oscillation e and the boundary layer thickness are both extremely small. It is found that induced steady flow of O(e) is symmetric with respect to the direction of the oscillation and vanishes at infinity; however, in O(e 2 ) asymmetric steady streaming is induced in the main field and remains at infinity as a uniform flow in the direction of oscillation, due to the effect of the asymmetry in the motion of the circular cylinder.

Diffuse scattering from crystals of glycolic acid

Abstract From numerous experimental and theoretical studies of the thermal diffuse scattering of x-rays by molecular crystals, it follows that the loosely bound molecules in these crystals may undergo translational and librational oscillations as rigid units and as a result of this type of thermal motion a special kind of extended, continuous, diffuse scattering domains may appear in the diffraction pattern. A recent neutron crystal-structure analysis of glycolic acid suggests that the thermal motion in this crystal is of the type mentioned above. But the studies of the diffuse scattering pattern from the glycolic-acid crystal carried out in this work show that the extended, continuous, diffuse scattering domains that characterize this type of thermal motion are far too weak compared to their expected theoretical values as calculated on the basis of the thermal parameters evaluated by the method of crystal-structure analysis. A probable explanation is given for this disagreement between the experimental and theoretical results.

The excitation spectra of magnetic bubble lattices

The excitation spectra of a hexagonal lattice of magnetic bubbles are calculated using the methods of lattice dynamics. The bubbles are allowed one internal zero-mode radial degree of freedom and two translational degrees of freedom of the center of mass resulting in three branches of free oscillation. The equations of motion, whose Fourier transform yields a third order secular determinant corresponding to two acoustical and one optical branch, are obtained from a Lagrangian with a Rayleigh dissipative function. The inter-bubble potential is approximated by that of a dipole-dipole interaction and restricted to nearest neighbors. The dispersion curves are found for the symmetry directions k x and k y . For a dense lattice with no coupling between the radial and translational degrees of freedom the optical and acoustical branches cross. The inclusion of coupling has drastic effects on the dispersion relationships. The acoustical branches consist of admixtures of translational and radial oscillations. Because of damping a critical wavenumber exists below which no real part of the frequency exists. Changes in the acoustical branches can be brought about by changing the external magnetic field.

Excitation spectra of magnetic bubble lattices

The excitation spectra of a hexagonal lattice of magnetic bubbles is calculated using the methods of lattice dynamics. The bubbles are allowed one internal zero-mode radial degree of freedom and two translational degrees of freedom of the center of mass. This results in three branches of free oscillation, one optical and two acoustical. The equations of motion of the system are obtained from a Lagrangian with a Rayleigh dissipative function. The Fourier transform of these equations yields a secular determinant of order three corresponding to the three branches. The secular equation is a polynomial equation of sixth degree in the complex frequency. This is solved for the directions kx and ky. The interbubble potential is approximated by a dipole-dipole potential, and restricted to nearest neighbors. The magnetostatic bubble self-energy is replaced by the analytic approximation of Josephs and Callen. For a close-packed lattice with no coupling between the radial and translational degrees of freedom, the optical and acoustical branches cross. The inclusion of coupling has drastic effects on the dispersion relationships. The acoustical branches consist of admixtures of translational and radial oscillations. Because of damping, a critical wave number exists below which no real part of the frequency exists. Changes in the acoustical branches can be brought about by changing the external magnetic field.

Lattice Raman spectrum of pyridine‐N‐oxide

AbstractStokes and anti‐Stokes components in the lattice vibrational laser excited Raman spectrum of a polycrystalline sample of pyridine‐N‐oxide are reported. The six prominent peaks at 108, 80, 71, 49, 36 and 20 cm−1 have been tentatively assigned to librational and translational lattice oscillations of the molecule.

The Stokes-flow drag on prolate and oblate spheroids during axial translatory accelerations

Stokes's linearized equations of motion are used to calculate the flow field generated by a spheroid executing axial translatory oscillations in an infinite, otherwise still, incompressible, viscous fluid. The flow field, expressed in terms of spheroidal wave functions of order one, is used to develop general expressions for the drag on oscillating prolate and oblate spheroids. Formulae for the approximate drag, useful in making calculations, are obtained for small values of an oscillation parameter. These formulae reduce to the Stokes result in the limit when the spheroid becomes a sphere and the steady-state drag for a spheroid as the frequency of oscillation becomes zero. The fluid forces on spheroids of various shapes are compared graphically. The approximate formulae for the drag are integrated over all frequencies to obtain formulae for the drag on spheroids executing general axial translatory accelerations. The fluid resistance on the spheroid is expressed as the sum of an added mass effect, a steady-state drag and an effect due to the history of the motion. A table of added mass, viscous and history coefficients is given.

Cavitation microstreaming

The flow induced by an isolated spherical drop or bubble which performs translational harmonic oscillations relative to the liquid in which it is embedded is considered. Special attention is focused upon the steady or microstreaming which is induced. Except in very diffuse situations associated, for example, with liquids of high viscosity, the streaming is shown to be weaker than for a corresponding rigid body. Qualitative agreement is obtained between the theory and available experimental results.

Oscillations of a vessel containing a viscous fluid

The oscillations of a rigid body having a cavity partially filled with an ideal fluid have been studied in numerous reports, for example, [1–6]. Certain analogous problems in the case of a viscous fluid for particular shapes of the cavity were considered in [6, 7]. The general equations of motion of a rigid body having a cavity partially filled with a viscous liquid were derived in [8]. These equations were obtained for a cavity of arbitrary form under the following assumptions: 1) the body and the liquid perform small oscillations (linear approximation applicable); 2) the Reynolds number is large (viscosity is small). In the case of an ideal liquid the equations of [8] become the previously known equations of [2–6]. In the present paper, on the basis of the equations of [8], we study the free and the forced oscillations of a body with a cavity (vessel) which is partially filled with a viscous liquid. For simplicity we consider translational oscillations of a body with a liquid, since even in this case the characteristic mechanical properties of the system resulting from the viscosity of the liquid and the presence of a free surface manifest themselves.

An expression for the temperature factor of a librating atom

The temperature factor for an atom undergoing librational motion is usually expressed in the form of the Debye–Waller factor appropriate to a translational oscillation with an equivalent root-mean-square amplitude. As a result of this the atomic positions may depart significantly from their true positions, and in an X-ray structure analysis the effect on the final difference density hinders the study of bonding electron distributions. A new form of the temperature factor for thermal librations which obviates these difficulties is proposed.

Effects of Deviations from Isothermal and Quiescent Conditions on the He II Film Transfer Rates

We have studied the effects of temperature differences between and mechanical agitation of the source and sink bulk liquids on the volume rates of transfer of liquid He II through the film into and out of a glass capillary beaker over heights to 31 cm. Temperature differences were produced by electric heaters, and mechanical agitation was produced by using a magnetic field modulated at a low frequency to cause a 1-mm diameter superconducting sphere to undergo translational oscillation. Values of heat flux up to ${10}^{\ensuremath{-}4}$W/${\mathrm{cm}}^{2}$ produced only temperature differences which could be accounted for by distillation and thermomechanical effects. Such quantities of heat flux do not create sufficient turbulence to produce measurable effects on the transfer rates. Mechanical agitation of the source liquid increased the transfer rates, and agitation of the sink liquid decreased the rates. A minimum velocity of the sphere moving in the liquid was required to produce any measurable change $\ensuremath{\Delta}R$ in the transfer rates. After increasing with increasing velocity of the sphere, $R$ was found to become independent of further increases in velocity. These results give further insight into the way in which transfer rates of liquid helium through the film depend on the state of turbulence of the bulk liquids which serve as the source and sink for the film.

Effective numbers of nucleon clusters in light nuclei determined from quasi-elastic knock-out reactions

The effective number N eff(X) of nucleon clusters of type X, occurring in high-energy quasi-elastic scattering reactions is calculated in the oscillator shell model with elimination of the c.m. motion. One finds N eff ( d)= 113 18 , 94 9 , 33 2 ; N eff ( t)= 52 9 , 106 9 , 184 9 ; N eff (α)= 103 32 , 231 32 , 437 32 for the target nuclei Be 8, C 12 and O 16, respectively. The distribution of N eff( α) shows concentration towards the surface. One finds N eff(Li 6, Li 7, Li 8, Be 8) = 0.09, 0.13, 0.005, 0.3 f r O 16. The integral momentum distributions are calculated for the knock-out of alpha;-particles from C 12. The results of these calculations are compared with available experimental data. A comparison of the shell model, cluster model and α-model approaches is outlined on the basis of the example of the deuteron knock-out from Li 6. A method for calculating the fractional parentage coefficients 〈 A| A− X, X〉 in the translational invariant oscillator shell model is considered in the appendix.

Steady and Unsteady Motions and Wakes of Freely Falling Disks

The motions and wakes of freely falling disks were studied and it was found that the diverse motions of the disks exhibit a systematic dependence on the Reynolds number Re, and the dimensionless moment of inertia I*. The relation between I* and Re along the boundary separating stable and unstable pitching oscillations of the disk was determined. The Reynolds number for stable motion of a disk with large I* is 100, in agreement with the Reynolds number for stability of the wake of a fixed disk. Slightly unstable disks of large I* were stabilized by reducing the moment of inertia. The highest Reynolds number for stable disk motion was 172. At higher Reynolds numbers the disks exhibited periodic pitching and translational oscillations. The laminar wake behind certain of the oscillating disks consisted of a staggered arrangement of two rows of regularly spaced vortex rings similar to the wake observed behind liquid drops by Margarvey and Bishop. The dependence of the dimensionless frequency of oscillation on I* and Re was determined along the boundary for stable motion and at higher Reynolds numbers when the wake was turbulent. Tumbling motions of the disks were observed when the Reynolds number was large, Re > 2000, and I* was greater than a certain value, I* =̇ 10−2.

ANALYSIS OF THE RESPONSE OF OFFSHORE-MOORED SHIPS TO WAVES

A vessel moored at sea will experience complicated series of translational and rotational oscillations due to sea waves. These motions can be considered as the summation of six components, three translational and three rotational. In the presently available analyses of motions of unmoored ships, differential equations can be written for each mode of movement. Unfortunately, motions in one of these modes are coupled to motions of other modes, and the analysis becomes rather complicated. Generally, the problem is simplified by neglecting some of the coupling effects and by specifying the position of the vessel in the wave system. This study develops and analyzes a model for a moored ship restrained by mooring lines, using the presently available mathematical models for the free ship and the force-displacement relationship of the cable-holding points on the ship. The coupled movement (three degrees of freedom) in a vertical plane through the longitudinal axis of the vessel and the generated mooring-line forces are considered in detail. The general case of six degrees of freedom in arbitrary heading is discussed briefly in general terms.