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Abstract When avibratingstructureisrotatedwithrespecttoinertialspace,thevibratingpatternrotatesatarateproportionalto the inertialrateofrotation.Bryanfirstobservedthiseffectin1890.Theeffect,calledBryan’seffectinthesequel,has numerous navigationalapplicationsandcouldbeusefulinunderstandingthedynamicsofpulsatingstarsandearthquake series inastrophysicsandseismology.Bryan’sfactor(thecoefficientofproportionalitybetweentheinertialandvibrating pattern rotationrates)dependsonthegeometryofthestructureandthevibrationmodenumber.The‘‘gyroscopiceffects’’ of ahollowisotropicsolidspherefilledwithaninviscidacousticmediumareconsideredhere,butthetheoryisreadily adapted toahollowisotropicsolidcylinderfilledwithaninviscidacousticmedium.Alineartheoryisdevelopedassuming, among othermildconditions,thattherotationrateisconstantandmuchsmallerthanthelowesteigenfrequencyofthe vibrating system.Thuscentrifugalforcesareconsideredtobenegligible.Beforecalculatingsolutionsforthedisplacement of aparticleintheisotropic,spherical,distributedbody,Bryan’sfactorisinterpretedusingacomplexfunction.Hereitis demonstrated thatneitherBryan’seffectnorBryan’sfactorisinfluencedbyincludinglight,isotropic,viscousdampingin the mathematicalmodel.Hencedampingisneglectedinthesequel.Twoscenariosarethenidentified.Firstly,wemay assume thattheacousticmediumiscompletelyinvolvedintherotation(thespheroidalmode).Secondly,wemayassume that theacousticmediumremainsstaticwithrespecttotheinertialreferenceframe(thetorsionalmode).Weinvestigatethe spheroidal modeusinganumericalexperimentthatcomparestherotationalangularrateofasphere(filledwithaninviscid acoustic medium)withthoseofitsvibratingpatternsatbothhighandlowvibrationfrequency.

Thesis (M.S.)--Ohio State University, 1977. / Includes bibliographical references (leaves 153-155). Available online via OhioLINK's ETD Center

This thesis describes the development and testing of two apparatuses; a vibrating wire viscometer to measure the viscosity of fluids over a wide range of temperature and pressure; and a microwave cavity resonator to measure dew points, gas phase densities, and liquid drop out volumes. Viscosity and density of downhole fluids are very important properties as their values can determine the economic viability of a petroleum reservoir. A vibrating wire viscometer has been developed with an electrically insulating tensioning mechanism. It has been used with two wires, of diameters (0.05 and 0.150) mm, to measure the viscosity of methylbenzene and two reference fluids with viscosities of (10 and 100) mPa·s at T = 298 K and p = 0.1 MPa, at temperatures in the range (298 to 373) K and pressures up to 40 MPa, where the viscosity covers the range (0.3 to 100) mPa·s, with a standard uncertainty < 0.6 %. The results differ from literature values by < ±1 %. The results demonstrate that increasing the wire diameter increases the upper operating viscosity range of the vibrating wire viscometer, a result anticipated from the working equations. For the microwave cavity resonator, the method is based on the measurements of the resonance frequency of the lowest order inductive-capacitance mode. The apparatus is capable of operating at temperatures up to 473 K and pressures below 20 MPa. This instrument has been used to measure the dew pressures of {0.4026CH4 + 0.5974C3H8} at a temperature range from 315 K up to the cricondentherm ˜ 340 K. The measured dew pressures differ by less than 0.5 % from values obtained by interpolation of those reported in the literature, which were determined from measurements with experimental techniques that have quite different potential sources of systematic error than the radio-frequency resonator used here. Dew pressures estimated from both NIST 14 and the Peng-Robinson equation of state lie within < ±1 % of the present results at temperature between (315 and 337) K while predictions obtained from the Soave-Redlich-Kwong cubic equation of state deviate from our results by 0.4 % at T = 315 K and these differences increase smoothly with increasing temperature to be -2.4 % at T = 337 K. Densities derived from dielectric permittivity measurements in the gas phase lie within < 0.6 % of the values calculated from the Soave-Redlich-Kwong cubic equation of state and about 1 % from values obtained with the Harvey and Prausnitz correlation based on a mixture reduced density. The calculations with Kiselev and Ely parametric crossover equation of state (based on Patel-Teja EOS) gave deviations < 0.7 %. Liquid volume fractions, in the 2-phase region, were measured from (0.5 to 7) cm3 in a total volume of about 50 cm3 at different isochors. The measured liquid volume fractions differ from values obtained with the Soave-Redlich-Kwong cubic equation of state by between 0 and 3 % at T < 326 K and about 8 % on approach to the critical region. The large deviations observed in the critical region were anticipated because of the known poor performance of the cubic equations of state with regard to the calculation of the liquid density in the vicinity of the critical temperature.

Recently, granules under vertical vibrations receive many attentions due to their importance in theoretical research and engineering application. In this paper, a two-dimensional Particle Image Velocimetry (PIV) system was used to examine the f/2 stripe pattern forming in a vertically vibrated granular layer. Since the PIV sampling frequency does not match with the vibrating frequency, a special identification-coupling method was adopted to combine the images taken in different cycles to offer the information in one complete cycle. The measured velocity vectors showed exactly the particle motions at various stages of a motion cycle, illustrating the alternating peaks and valleys on the layer top. Furthermore, quantitative results on the temporal evolution of velocity profiles were obtained and some other interesting phenomena were observed, such as the appearance of local structures (e.g. dual-phase layer structure) and the moving feature of the 'standing point'. The mechanism accounting for the occurrence of stripes on the surface is also discussed. This work will be of interest to a better understanding on pattern formation in the vibrating granular bed. / Singapore-MIT Alliance (SMA)

When a body vibrates in a fluid, some of the fluid is carried with it and the mass loading lowers its resonant frequency. Similarly, when compression of the fluid occurs, there is an added stiffness which by design can be made to predominate. In addition, there is an energy dissipation arising from viscous losses and acoustic radiation. The starting point of this research was a tuning fork with flat rectangular tines, designed to trap a narrow laminar of gas which is forced to pump in and out as the tines vibrate. The increase in kinetic energy, contributed by this high velocity' gas, gives the device a relatively large sensi ti vi ty as a gas density transducer. The change in frequency between vacuum and atmospheric pressure is typically a few percent, during which period the mechanical "Q" remains high enough to keep the fork sharply resonant. A high stability oscillator incorporating the transducer as the frequency controlling element was built. Small piezoelectric Cp2t) elements were used to drive the transducer and pick up the vibrations. A typical stability, equivalent to a pressure change of 0. 05 mBar was achieved. The supporting equipment re qui red for the work centred around a vacuum system with facilities for introducing a range of gases at precise rates. Computer control enabled the transducer's temperature, frequency, and "Q" factor to be measured and stored as the gas pressure was increased from vacuum. Extensive experiments were carried out on a range of tuning fork transducers, including a circular one in which a pair of disks clamped at the center acted as the tines and gave a simple radial gas displacement. Common to all these transducers is, the linearity of 1/f 2 with gas density for pressures above about 50 mBar; a departure from. linearity below this pressure; and below 10 mBar an overriding stiffness effect, where from vacuum to a few mBar the frequency paradoxically increases. The resultant calibration to this non-linear response, while exhibiting high stablility, is unattractive for general use. It has however applications over limited ranges as for example, those of a barometer or altimeter. Insight gained from experience with the double disk resonator, led to a new geometry which has resulted in an extremely viable transducer, without calibration anomalies, and capable of operating in a pressure or dehsity mode. Here, the gas is confined in two cylindrical cavities above and below a thin circular diaphragm, clamped at the periphery and again made to vibrate using p2t elements. In the fundamental mode, the alternating change in cavity volume due to compression and rarefaction of the gas, adds stiffness to the diaphragm. In the next mode, there is no net volume change, but the gas is pumped across the cavities adding inertial loading. No anomalies were experienced in the empirical calibrations obtained for each mode- the fundamental being linear with pressure Cf 2 proportional to Pl, and the first overtone linear with density (1/f 2 proportional to pl. A simple theory, which is sufficiently accurate for general design purposes, has been developed. Future work, which is of a straightforward development nature, is proposed. The high degree of stability achieved for these vibrating structures was later realised in a different geometry. In this, a long rod was excited into a torsional mode so as to produce two nodes a quarter wavelength from. either end. By securing the rod at these points and immersing the lower length in a liquid, a sensitive, robust, viscometer was produced. Driving the rod with a burst of oscillations, shears the liquid in contact with it. By removing this drive and measuring the rate of vibrational decay under the action of viscous dissipatiop, an indication of the viscosity can be obtained. The features of a pure shearing force, and the real-time, on-line nature of the device, makes it attractive for the characterisation of both thick and thin liquids and automatic process control.

The purpose of this work is to study the effects of boundaries on granular flows down vibrating inclines, on segregation in granular mixtures induced by boundary vibrations, and on flows of granular mixtures through vibrating sieves. In each case, we employ techniques borrowed from the kinetic theory to derive an appropriate set of boundary conditions, and combine them with existing flow theories to calculate the profiles of solid volume fraction, mean velocity, and granular temperature throughout the flows. The boundaries vibrate with full three-dimensional anisotropy in a manner that can be related to their amplitudes, frequencies, and phase angles in three independent directions. At impenetrable surfaces (such as those on the inclines), the conditions derived ensure that momentum and energy are each balanced at the boundary. At penetrable surfaces (such as sieves), the conditions also ensure that mass is balanced at the boundary. In these cases, the momentum and energy balances also are modified to account for particle transport through the boundary. Particular interest in all the applications considered here is in how the details of the boundary geometry and the nature of its vibratory motion affect the resulting flows. In one case, we derive conditions that apply to a monosized granular material that interacts with a bumpy, vibrating, impenetrable boundary, and predict how such boundaries affect steady, fully developed unconfined inclined flows. Results indicate that the flows can be significantly enhanced by increasing the total energy of vibration and are more effectively enhanced by normal vibration than by tangential vibration. Regardless of the direction of vibration, the bumpiness of the boundary has a profound effect on the flows. In a second case, we derive conditions that apply to a binary granular mixture that interacts with a flat, vibrating, penetrable sieve-like boundary, and predict how such boundaries affect the process in which the particles pass through the sieve. In the special case in which the particles are all the same size, the results make clear that energy is more effectively transmitted to the assemblies when either the total vibrational energy or the normal component of the vibrational energy is increased, but that an increase in the energy transferred to the material can sometimes actually decrease the flow rates through the sieve. Consequently, at any instant of time in the sieving process, there is an optimum level of vibrational energy that will maximize the flow rate. For the sieving of binary granular assemblies, the physics associated with the effects of energy transfer on the flow rates still applies. However, in these cases, the flows through the sieve are also profoundly affected by segregation that occurs while the particles reside on sieve before the pass through. For this reason, we also isolate the segregation process from the sieving process by considering the special case in which the holes in the vibrating sieve are too small to allow any particles to pass through. In this case, the results show that under most circumstances the region immediately adjacent to the vibrating surface will be populated almost entirely by the smaller particles or by the more dissipative particles if there is no size disparity, and that the reverse is true in a second region above the first.

Background: Aerosol therapy has been established as an efficient form of drug delivery to pediatric and adult patients with respiratory diseases; however, aerosol delivery to the pediatric population is quite challenging. While some studies compare jet nebulizer (JN), vibrating mesh nebulizer (VMN), or JN and pMDI, there is no study comparing these three devices in pediatric and young children. The aim of this study quantifies aerosol deposition using JN, VMN, and pMDI/VHC in a simulated pediatric with active and passive breathing patterns. Methods: Each aerosol generator was placed between manual resuscitator bag (Ambu SPUR II Disposable Resuscitator, Ambu Inc, Glen Burnie, MD) and infant facemask (Mercury Medical, Cleanwater, FL), which was held tightly against the SAINT model. Breathing parameters used in this study were Vt of 100 mL, RR of 30 breaths/min, and I:E ratio of 1: 1.4. Active and passive breathing patterns were used in this study with aerosol device; active breathing pattern was created using a ventilator (Esprit Ventilator, Respironics/Philips Healthcare, Murrysville, PA) connected to a dual chamber test lung (Michigan Instruments, Grand Rapids, MI), which was attached to an absolute filter (Respirgard II, Vital Signs Colorado Inc, Englewood, CO), to collect aerosolized drug, connected to the SAINT model. Pediatric resuscitator bag was run at 10 L/min of oxygen and attached to aerosol generator with facemask. In passive breathing pattern, SAINT model was attached to test lung and ventilated using the resuscitator bag with the same breathing parameters. Each aerosol device was tested three times (n=3) with each breathing patterns. Drug was eluted from the filter and analyzed using spectrophotometry. The amount of drug deposited on the filter was quantified and expressed as a percentage of the total drug dose. To measure the differences in the inhaled drug mass between JN, VMN, and pMDI/VHC in active or passive breathing, one-way analysis of variance (one-way ANOVA) was performed. To quantify the difference in aerosol depositions between the two breathing patterns, independent t-test was performed. A p < 0.05 was considered to be statistically significant. Results: Although the amount of aerosol deposition with the JN was the same in passive and active breathing without any significant difference, the VMN was more efficient in active breathing than the JN (p = 0.157 and p = 0.729, respectively). pMDI/VHC had the greatest deposition in the simulated spontaneous breathing (p=0.013) Conclusion: Aerosol treatment may be administered to young children using JN, VMN, or pMDI/VHC combined with resuscitator bag. Using pMDI/VHC with resuscitator bag is the best choice to deliver albuterol in spontaneously breathing children. Further studies are needed to determine the effectiveness of these aerosol generators with different type of resuscitator bag and different breathing parameters.

The purpose of this thesis is to develop a novel design of the oscillatory type of wave-energy acquisition system. It is aimed to increase the efficiency of wave-power acquisition from random sea. The main feature of the new system structure is its flexibility to adjust the system dynamics to satisfy two optimal criteria. The effects of various system parameters on the system dynamics and acquired power were analyzed. To find the set of system parameters to acquire the highest power, an optimization searching method was adopted. Finally, a regression model was established to help the user to calculate the optimal system parameters under various application conditions. The study first indicated that to acquire high power from sea wave the dynamic characteristics of the system should satisfy two criteria. However, the study also revealed that the dynamic properties of a traditional acquisition system are difficult to fulfill the two criteria in a wide frequency band. Accordingly, a new system structure was proposed. It is composed of a traditional acquisition system and a vibrating platform. The platform is linked to the acquisition system through a spring. Because of the coupling effect, the dynamic characteristics of the acquisition system are altered. The effects of varying different system parameters on the locations of pole or zero of the transfer function of acquisition system were examined. It was shown that with a proper choice of system parameters, the frequency bandwidth satisfying or close to the two criteria may be increased. The study indicated that acquired power of the proposed system is higher than the traditional one by 34%.

The eigenvalue gaps and eigenvalue ratios of the Sturm-Liouville systems have been studied in many papers. Recently, Lavine proved an optimal lower estimate of first eigenvalue gaps for Schrodinger operators with convex potentials. His method uses a variational approach with detailed analysis on different integrals. In 1999, (M.J.) Huang adopted his method to study eigenvalue ratios of vibrating strings. He proved an optimal lower estimate of first eigenvalue ratios with nonnegative densities. In this thesis, we want to generalize the above optimal estimate. The work of Ashbaugh and Benguria helps in attaining our objective. They introduced an approach involving a modified Prufer substitution and a comparison theorem to study the upper bounds of Dirichlet eigenvalue ratios for Schrodinger operators with nonnegative potentials. It is interesting to see that the counterpart of their result is also valid. By Liouville substitution and an approximation theorem, the vibrating strings with concave and positive densities can be transformed to a Schrodinger operator with nonpositive potentials. Thus we have the generalization of Huang's result.