Motion Oscillatory

The instantaneous drag on a rigid spherical particle moving with velocity Lp in a fluid whose instantaneous velocity in the vicinity of the particle is follows from an extension to Eq. (11-30)  

Although its practical applicability is not so well established as that of Eq. (11-30) for motion from rest, it represents a convenient starting point for a discussion of oscillatory motion. If the fluid oscillates in the vertical direction, and velocities are positive downwards, the equation of motion for a freely moving particle follows from Eq. (11-43) as  

If the particle Re is always small, the creeping flow assumptions apply. Equation (11-44) then becomes  

The linearity of Eq. (11-45) implies that the mean terminal velocity is unaffected by oscillation (M7). The velocities may then be written as sums of mean values and variations from the mean, i.e., 

Molerus (M7) and Hjelmfelt and Mockros (H6) have developed complete solutions to Eq. (11-48). Velocities can be expressed as Fourier integrals. It therefore suffices to consider pure sinusoidal oscillations  

Gemant, in Frictional Phenomena, Chemical Publishing Co., Brooklyn, N. y., 1950. 

Friction and Wear Devices, Revised and Enlarged Report of the Subcommittee on Wear, Lubrication Fundamentals Committee, 2nd Edition, American Society of Lubrication Engineers, Park Ridge, 111., 1976. 

Bowden and D. Tabor, The Friction and Lubrication of Solids, Oxford University Press, 1950, Part I, p. 73. 

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Viscoelastic fluids that are more concentrated are characteri2ed with devices that are similar to the rotational viscometers described previously. However, instead of constant rotational motion in one direction, a sinusoidal oscillatory motion is provided. Some instmments allow both viscosity and viscoelastic measurements. 

Rheometric Scientific markets several devices designed for characterizing viscoelastic fluids. These instmments measure the response of a Hquid to sinusoidal oscillatory motion to determine dynamic viscosity as well as storage and loss moduH. The Rheometric Scientific line includes a fluids spectrometer (RFS-II), a dynamic spectrometer (RDS-7700 series II), and a mechanical spectrometer (RMS-800). The fluids spectrometer is designed for fairly low viscosity materials. The dynamic spectrometer can be used to test soHds, melts, and Hquids at frequencies from 10 to 500 rad/s and as a function of strain ampHtude and temperature. It is a stripped down version of the extremely versatile mechanical spectrometer, which is both a dynamic viscometer and a dynamic mechanical testing device. The RMS-800 can carry out measurements under rotational shear, oscillatory shear, torsional motion, and tension compression, as well as normal stress measurements. Step strain, creep, and creep recovery modes are also available. It is used on a wide range of materials, including adhesives, pastes, mbber, and plastics. 

Schwingungs-bewegung, /. vibratory (or oscillatory) motion, -bogen, m. arc of oscillation, dauer, /. time of vibration, -ebene, /. plane oC vibration, -ener e, /. vibrational energy. 

The only condition that results in oscillatory motion and, therefore, represents a mechanical vibration is underdamping. The other two conditions result in periodic motions. When damping is less than critical ji, < cP), then the following equation applies ... 

The changes in stress fields, and intensities of igneous and hydrothermal activities seem to correlate to oscillatory motion of the Pacific plate (Jackson s episodes) (Jackson et al., 1975 Jackson and Shaw, 1975) (Masuda, 1984). Masuda (1984) and Takeuchi (1987) pointed out that the oscillatory motion of Pacific plate during the least 42 Ma correlates with magmatism, the intensity of tectonism, the change of stress field and the history of sedimentary basin in arc-trench system (Fig. 1.147). The above arguments also suggest that the mineralizations in arc and back-arc systems relate to the oscillatory motion of the Pacific plate. 

Fig. 6. (a) Schematic view of an extruder channel with an undulating baffle, (b) B, C, D Steady flow streamlines with and without baffles for initial condition A. E, F Mixing in a cavity flow with an oscillating baffle. The upper plate moves with a steady velocity while the lower plate with the baffle undergoes linear oscillatory motion (Jana, Tjahjadi, and Ottino, 1994). 

Although the equilibrium configuration of a molecule can usually be specified, at ordinary temperatures, all of the atoms undergo oscillatory motions. The forces between the atoms in the molecule are described by a Taylor series of the intramolecular potential function in the internal coordinates. This function can then be written in the form... 

Womersley, J. R. Oscillatory motion of a viscous liquid in a thin-walled elastic tube. I. The linear approximation for long waves. Phil. Mag. Ser. 7 46 199-221, 1955. 

The other class of motion only now being introduced into interpretive models is oscillatory motion. Anisotropic oscillatory motions of substituent groups have been considered by Chachaty (12) but not in conjunction with a lattice description of backbone motion. No attempt to develop a model based on oscillatory backbone rearrangements is known to these authors, and this avenue may be very important for the interpretation of concentrated solutions, rubbery or amorphous solids, and especially glassy polymers... 

The maximum distance between the value of a periodic function (i.e., a function with repeated values for f(x) for all integer multiples of a constant displacement or increment along the independent variable axis) and the function s mean value. 2. A term used in classical mechanics to define the magnitude of the maximum displacement of a body experiencing an oscillatory motion. 3. A term used in relaxation kinetics to indicate the magnitude of displacement of a chemical reaction. 

Large drops (De =1 cm) of chlorobenzene will fall through water with a somewhat erratic oscillatory motion (L3). The drop pitches and rolls. The flight is not vertical but is erratically helical in nature. A series of oscillations, accompanied by waves moving over the interface, can cause the drop to drift several inches in a horizontal direction in a range of a foot or two of fall. Such drops can not oscillate violently as described above, due to the damping action of such movement by the sliding side-wise motion of the wobble. Motion pictures indicate that internal circulation is also considerably damped out by this type of oscillation. Rate of... 

As noted above, for Re greater than a value of order 100, a cylinder in free motion has a secondary oscillatory motion superimposed on its steady fall or rise. For cylinders with > 1, the axis oscillates in a vertical plane about the mean (horizontal) orientation, and the trajectory oscillates about the mean path in the same plane as the cylinder sideslips when its axis is not horizontal... 

In practice, this model is oversimplified since the exciting wake shedding is by no means harmonic and is itself coupled with the shape oscillations and since Eq. (7-30) is strictly valid only for small oscillations and stationary fluid particles. However, this simple model provides a conceptual basis to explain certain features of the oscillatory motion. For example, the period of oscillation, after an initial transient (El), becomes quite regular while the amplitude is highly irregular (E3, S4, S5). Beats have also been observed in drop oscillations (D4). If /w and are of equal magnitude, one would expect resonance to occur, and this is one proposed mechanism for breakage of drops and bubbles (Chapter 12). 

Although a number of workers [e.g. (C5, Dl, D2)] have considered flow around particles started impulsively from rest at constant nonzero velocities, this situation is of little practical interest. Attention is concentrated on free fall from rest and oscillatory motion. 

Consider a rigid sphere of radius a, executing rectilinear oscillatory motion relative to remote fluid with its velocity given by" ... 

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