4
TECHNICAL NOTES AND RESEARCH BRIEFS Paul B. Ostergaard 10 Glenwood Way, West Caldwell, New Jersey 07006 Editor’s Note: Original contributions to the Technical Notes and Research Briefs section are always welcome. Manuscripts should be double-spaced, and ordinarily not longer than about 1500 words. There are no publication charges, and consequently, no free reprints; however, reprints may be purchased at the usual prices. A cost effective degassing system for use in ultrasonic measurements: The multiple pinhole degassing system [43.80.Vj, 43.58.Vb, 43.35.Yb, 43.35.Ei] Adam R. Kaiser and Charles A. Cain Department of Electrical Engineering and Computer Science, Biomedical Ultrasonics Laboratory, University of Michigan, Ann Arbor, Michigan 48109 Emma Y. Hwang and J. Brian Fowlkes Department of Radiology, Basic Radiological Sciences Division, University of Michigan Medical Center, Ann Arbor, Michigan 48109-0553 Russell J. Jeffers Naval Undersea Warfare Center, Newport, Rhode Island 02841 The multiple pinhole degassing (MPD) system discussed below is an inex- pensive method for lowering the dissolved oxygen concentration of water to levels acceptable for ultrasonic research. Several methods of degassing wa- ter for ultrasonic measurement and operation are available. However, many of these degassing systems are expensive to purchase and are complex, sometimes requiring considerable maintenance. The system described here is ideal for degassing large volumes of water in circulating applications. It degasses 80 liters of water to below 4 ppm O 2 in 5 h and to about 2 ppm O 2 in 24 h. It also enables easy collection of removed gases. At the time of this writing the system requires a standard pump and about ten dollars of hardware supplies. INTRODUCTION For ultrasound measurement and operation purposes, water must often be degassed to prevent uncontrolled cavitation events. Unexpected cavita- tion can cause equipment damage, erroneous measurements, and irreproduc- ible results. The AIUM ~American Institute of Ultrasound in Medicine! suggests that measurement of diagnostic ultrasound equipment should be performed in water with a dissolved gas concentration as low as practical ~,5–8 ppm O 2 !. For ultrasonic powers greater than 10 W AIUM recom- mends the use of water with a dissolved O 2 concentration below 4 ppm. 1 For in vitro and in vivo animal ultrasound experiments involving a water cou- pling path, degassing the water reservoir also serves to eliminate the possi- bility of cavitation outside the treated exposure volume. Because an effective yet inexpensive method for degassing water was needed, a degassing system was devised that consists of a standard pump, customized degassing head, and common laboratory tubing. This method requires few and inexpensive components, yet is as effective or better at degassing water as some of the currently known, more costly, degassing procedures. 2 I. MATERIALS The components used to build the degassing apparatus are readily available. The degassing head ~Fig. 1! consists of a noncorrosive metal plate, a PVC pipe cap, and a barb fitting. A 2-in. PVC pipe cap was drilled and tapped through its top to accommodate a 3/8 in. nylon barb fitting ~NPT 1/4 in.! which was sealed to the pipe cap with silicone sealant. The 6.4-cm- diam30.51-mm-thick stainless steel plate was drilled at its center with twelve 0.51-mm holes in a 2.5-cm32.5-cm grid. The plate was affixed to the open end of the pipe cap with silicone sealant. This completed degassing head was connected to a 3/8-in. brass barb fitting ~NPT 1/4 in.! at the pump inlet via a 2.13-m length of reinforced flexible PVC tubing ~3/8 in. i.d. 5/8 in. o.d.!~Fig. 2!. The pump used in this experiment was a 130-000 micro- pump head ~Micropump Corp., Concord, CA! driven by a magnetically coupled console drive ~Cole–Parmer Instrument Co., Chicago, IL!. The out- let of the pump was connected to a 1.5-m length of flexible PVC tubing ~3/8 in. i.d. 1/2 in. o.d.! via another brass barb fitting. A digital field-work dissolved oxygen meter ~Cole–Parmer Instrument Co., Chicago, IL! was used for measurement of O 2 concentration. A mer- cury thermometer was attached to the inside of each tank to monitor water temperature throughout the experiments. II. METHODS The performance of this system was evaluated with two experiments. The first experiment was performed to evaluate the single pass characteris- tics of the degassing system ~Fig. 3!. A 24-cm358-cm acrylic tank was filled with 10 l of reverse osmosis water. One-liter water samples were repeatedly degassed into a 1.5-l beaker. Once the measurements were taken, the water in the beaker was returned to the tank, lowering the O 2 concentration for the next round of degassing. A final data point was ob- tained by continually circulating 1 l of water until a steady-state O 2 con- centration was obtained. At this value both the inlet and outlet O 2 concen- trations are equal. Water temperature was approximately 22 °C throughout the experiment. In the second experiment, the performance of this system was evalu- ated by degassing 80 l of water in a circulating experiment ~Fig. 4!. An acrylic water tank, measuring 35.6 cm361.0 cm340.6 cm, was filled with 80 l of reverse osmosis water ~Fig. 2!. To ensure gas saturation at room temperature, the water was aerated over a 24-h period before the degassing experiment began. Air saturation was achieved by circulating the water through a waterfall-type fish-tank filter with its filter element removed. This circulator brought the water in continuous contact with the room air. The water temperature naturally reached room temperature ~22 °C!. Plastic air-filled balls were used to cover the entire water surface in order to minimize in-gassing at the air–water interface at the start of the experiment. The degassing head was placed in the water tank with its side oriented down at the base of the tank or with its bottom oriented down with the head suspended, allowing unobstructed flow of water through the pin- holes. The top 3-cm rim of a Styrofoam cup was cut off and placed in the tank to make a small portion of air–water interface free of the plastic balls ~Fig. 2!. The outlet of the tubing was placed into the water and fixed so that the outgoing water would flow up toward the free surface created by the FIG. 1. Degassing head assembly. A 5-cm PVC pipe cap was drilled and tapped to accommodate a 3/8-in. barb fitting ~NPT 1/4!. A metal plate drilled with twelve 0.51-mm holes in a 2.5-cm32.5-cm grid was attached with silicone sealant. 3857 3857 J. Acoust. Soc. Am. 99 (6), June 1996 0001-4966/96/99(6)/3857/4/$6.00 © 1996 Acoustical Society of America Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 137.207.120.173 On: Fri, 21 Nov 2014 20:33:05

Estimating acoustic radiation from a Bernoulli–Euler beam using shaped polyvinylidene fluoride film

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Page 1: Estimating acoustic radiation from a Bernoulli–Euler beam using shaped polyvinylidene fluoride film

TECHNICAL NOTES AND RESEARCH BRIEFS

Paul B. Ostergaard10 Glenwood Way, West Caldwell, New Jersey 07006

Editor’s Note: Original contributions to the Technical Notes and Research Briefs section are alwayswelcome. Manuscripts should be double-spaced, and ordinarily not longer than about 1500 words. Thereare no publication charges, and consequently, no free reprints; however, reprints may be purchased atthe usual prices.

A cost effective degassing systemfor use in ultrasonic measurements:The multiple pinhole degassing system[43.80.Vj, 43.58.Vb, 43.35.Yb, 43.35.Ei]Adam R. Kaiser and Charles A. CainDepartment of Electrical Engineering and Computer Science,Biomedical Ultrasonics Laboratory, University of Michigan, AnnArbor, Michigan 48109Emma Y. Hwang and J. Brian FowlkesDepartment of Radiology, Basic Radiological Sciences Division,University of Michigan Medical Center, Ann Arbor,Michigan 48109-0553Russell J. JeffersNaval Undersea Warfare Center, Newport, Rhode Island 02841

The multiple pinhole degassing (MPD) system discussed below is an inex-pensive method for lowering the dissolved oxygen concentration of water tolevels acceptable for ultrasonic research. Several methods of degassing wa-ter for ultrasonic measurement and operation are available. However, manyof these degassing systems are expensive to purchase and are complex,sometimes requiring considerable maintenance. The system described hereis ideal for degassing large volumes of water in circulating applications. Itdegasses 80 liters of water to below 4 ppmO2 in 5 h and to about 2 ppmO2 in 24 h. It also enables easy collection of removed gases. At the time ofthis writing the system requires a standard pump and about ten dollars ofhardware supplies.

INTRODUCTION

For ultrasound measurement and operation purposes, water must oftenbe degassed to prevent uncontrolled cavitation events. Unexpected cavita-tion can cause equipment damage, erroneous measurements, and irreproduc-ible results. The AIUM~American Institute of Ultrasound in Medicine!suggests that measurement of diagnostic ultrasound equipment should beperformed in water with a dissolved gas concentration as low as practical~,5–8 ppm O2!. For ultrasonic powers greater than 10 W AIUM recom-mends the use of water with a dissolved O2 concentration below 4 ppm.1 Forin vitro and in vivo animal ultrasound experiments involving a water cou-pling path, degassing the water reservoir also serves to eliminate the possi-bility of cavitation outside the treated exposure volume.

Because an effective yet inexpensive method for degassing water wasneeded, a degassing system was devised that consists of a standard pump,customized degassing head, and common laboratory tubing. This methodrequires few and inexpensive components, yet is as effective or better atdegassing water as some of the currently known, more costly, degassingprocedures.2

I. MATERIALS

The components used to build the degassing apparatus are readilyavailable. The degassing head~Fig. 1! consists of a noncorrosive metalplate, a PVC pipe cap, and a barb fitting. A 2-in. PVC pipe cap was drilledand tapped through its top to accommodate a 3/8 in. nylon barb fitting~NPT1/4 in.! which was sealed to the pipe cap with silicone sealant. The 6.4-cm-diam30.51-mm-thick stainless steel plate was drilled at its center withtwelve 0.51-mm holes in a 2.5-cm32.5-cm grid. The plate was affixed tothe open end of the pipe cap with silicone sealant. This completed degassing

head was connected to a 3/8-in. brass barb fitting~NPT 1/4 in.! at the pumpinlet via a 2.13-m length of reinforced flexible PVC tubing~3/8 in. i.d. 5/8in. o.d.! ~Fig. 2!. The pump used in this experiment was a 130-000 micro-pump head~Micropump Corp., Concord, CA! driven by a magneticallycoupled console drive~Cole–Parmer Instrument Co., Chicago, IL!. The out-let of the pump was connected to a 1.5-m length of flexible PVC tubing~3/8in. i.d. 1/2 in. o.d.! via another brass barb fitting.

A digital field-work dissolved oxygen meter~Cole–Parmer InstrumentCo., Chicago, IL! was used for measurement of O2 concentration. A mer-cury thermometer was attached to the inside of each tank to monitor watertemperature throughout the experiments.

II. METHODS

The performance of this system was evaluated with two experiments.The first experiment was performed to evaluate the single pass characteris-tics of the degassing system~Fig. 3!. A 24-cm358-cm acrylic tank wasfilled with 10 l of reverse osmosis water. One-liter water samples wererepeatedly degassed into a 1.5-l beaker. Once the measurements weretaken, the water in the beaker was returned to the tank, lowering the O2

concentration for the next round of degassing. A final data point was ob-tained by continually circulating 1l of water until a steady-state O2 con-centration was obtained. At this value both the inlet and outlet O2 concen-trations are equal. Water temperature was approximately 22 °C throughoutthe experiment.

In the second experiment, the performance of this system was evalu-ated by degassing 80l of water in a circulating experiment~Fig. 4!. Anacrylic water tank, measuring 35.6 cm361.0 cm340.6 cm, was filled with80 l of reverse osmosis water~Fig. 2!. To ensure gas saturation at roomtemperature, the water was aerated over a 24-h period before the degassingexperiment began. Air saturation was achieved by circulating the waterthrough a waterfall-type fish-tank filter with its filter element removed. Thiscirculator brought the water in continuous contact with the room air. Thewater temperature naturally reached room temperature~22 °C!.

Plastic air-filled balls were used to cover the entire water surface inorder to minimize in-gassing at the air–water interface at the start of theexperiment. The degassing head was placed in the water tank with its sideoriented down at the base of the tank or with its bottom oriented down withthe head suspended, allowing unobstructed flow of water through the pin-holes.

The top 3-cm rim of a Styrofoam cup was cut off and placed in thetank to make a small portion of air–water interface free of the plastic balls~Fig. 2!. The outlet of the tubing was placed into the water and fixed so thatthe outgoing water would flow up toward the free surface created by the

FIG. 1. Degassing head assembly. A 5-cm PVC pipe cap was drilled andtapped to accommodate a 3/8-in. barb fitting~NPT 1/4!. A metal platedrilled with twelve 0.51-mm holes in a 2.5-cm32.5-cm grid was attachedwith silicone sealant.

3857 3857J. Acoust. Soc. Am. 99 (6), June 1996 0001-4966/96/99(6)/3857/4/$6.00 © 1996 Acoustical Society of America

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Page 2: Estimating acoustic radiation from a Bernoulli–Euler beam using shaped polyvinylidene fluoride film

Styrofoam ring. Removed gasses can be collected at the pump outlet or atthe end of this tubing with an inverted beaker. The degassing pump speedwas set to a measured flow rate of 1.5 liters/min.

The degassing system was run over a 24-h period, during which dis-solved O2 content measurements were made. Readings were taken every 30min for the first 6 h of theexperiment and every several hours after the first8 h. The water temperature remained almost constant at room temperaturethroughout the experiment, rising 0.8 °C from the starting temperature.

III. RESULTS

The single pass evaluation revealed that the relationship between theinlet water O2 concentration and the outlet water O2 concentration was ap-proximately linear in the range of O2 concentrations measured in this ex-periment ~8.1 to 1.9 ppm!. After continually circulating 1l of water, asteady-state value of 1.9 ppm O2 was obtained.

The circulating evaluation revealed that degassing 80l of waterprogresses more quickly at the start of the degassing procedure than at theend. Within 5 h, the oxygen content fell from 8.5 to 3.9 ppm~see Fig. 3! andat the completion of the experiment, the dissolved oxygen concentration was2.0 ppm. The degassing progress could be qualitatively evaluated by observ-ing the size of the bubbles appearing at the outlet of the system. Initially theair bubbles appeared both larger in mean diameter~;5 mm! and larger inmaximum diameter than at the completion of the experiment.

IV. DISCUSSION

The degassing system described here works slightly faster than theErma ERC 3300-W degasser~Erma Inc., Tokyo, Japan! in bringing thedissolved oxygen levels of the tank of water to acceptable levels. The rate ofdegassing for the data shown in Fig. 4 is greater than the curve fit for theErma performance from the degassing review of Fowlkes and Carson3 inthis range of O2 concentrations.

3 This system is also less complex and lesscostly than other vacuum degassing methods.2,3

From these two experiments several equations were derived to de-scribe the performance of the degasser. The single pass experiment demon-strated that in the measured range, the output O2 concentration is linearlyrelated to the input O2 concentration as follows:

@O2#output5m@O2#input1b. ~1!

The constantsm50.65 andb50.85 were determined by the best fit lineshown in Fig. 3. By using the fact that this relationship is linear, one canderive an equation to represent the expected performance of the system in acirculating experiment as

@O2#tan k5VC01 f tb

V2 f t1 f tm. ~2!

In this equation,V580 l is the total tank volume,@O2# is the oxygenconcentration at timet, C058.5 ppm is the initial oxygen concentration,f51.5 l /min is the flow through the degassing system, andm50.73 andb50.85 are the constants described previously. The data was fit usingm andb as the fitting parameters. The values ofm andb differed between the twoexperiments. This is probably due to the differences in the handling of thewater and in the amount of air surface area to which the water was exposedthroughout the experiments. Equation~2! approximates the observed datamore closely than an exponential model.

Degassing begins as water is pulled through the pinholes of the degas-sing head. Small bubbles are generated due to the pressure drop across thehead. Along the length of the tubing, these small bubbles then coalesce andgrow as gas diffuses into the bubbles. The larger bubbles will pass throughthe pump head and through the outlet of the system as the water is reintro-duced into the tank. The bubbles coming out will float to the surface andburst.

There are several parameters which govern the effectiveness of thedegassing apparatus, some of which were optimized by trial and error. Oneof the primary parameters is that the flow through the system must belimited by the number and diameter of holes in the degassing head. Eachpinhole allows approximately 0.12l /min of flow. The liquid pump selectedmust have some excess capacity to pump more than what can flow throughthese pinholes, since this will allow the greatest possible pressure drop tooccur across the degassing head.

The tubing on the inlet side of the pump must be rigid enough towithstand the low pressures that it will encounter without collapsing. Itsinner diameter must be small enough to cause the coalescing bubbles to beswept along its length by water flow, yet not so small that water flow isrestricted. Its length should be chosen to allow time for the bubbles tocoalesce and grow, since larger bubbles are absorbed less quickly.4

The liquid pump must be able to move water at low pressure and withintermittent cavitation in its pumping elements. Due to this restriction, posi-tive displacement pumps such as the gear pump used in this experiment arerecommended. This pump speed need not be variable. Several MPD systemsusing a variety of fixed speed pumps are also currently in use. The measuredflow rate of these pumps with the same degassing head was also found to be1.5 l /min. These systems should perform equally well with the same tubinglengths and degassing head.

The outlet tubing should be as short and as large in inner diameter aspractical to reduce the exposure of the degassed water to the removed gases.These parameters also reduce the pressure at the outlet of the pump. The

FIG. 2. MPD system evaluation for circulating applications. 80l of reverseosmosis water was added to a 35.6 cm361.0 cm340.6 cm tank and allowedto equilibrate to ambient conditions. The water was then circulated throughthe MPD system for 24 h.

FIG. 3. Input/output characteristic of the MPD system. 1.5-l samples ofwater from a 10-l tank were degassed through the MPD system. The@O2#of the water in the tank and of the sample was measured for each data point.

FIG. 4. Degassing in a circulating application. 80l of water was continu-ously circulated through the MPD system over a 24-h period while@O2#measurements were taken.

3858 3858J. Acoust. Soc. Am., Vol. 99, No. 6, June 1996 Technical Notes and Research Briefs

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Page 3: Estimating acoustic radiation from a Bernoulli–Euler beam using shaped polyvinylidene fluoride film

outlet tubing should, however, have a diameter small enough to cause theflow of water to sweep the developing bubbles out of the tubing.

This degassing apparatus is not suited to degassing liquids containingsurfactants. In fact, experience using Roccal~National Laboratories, Lehnand Fink Industrial Products Division, Montvale, NJ! and other detergents inwater tanks, shows that copious small bubbles are created at the outlet of thesystem when surfactants are used. Surfactants appear to reduce the ability ofthe small bubbles created at the degassing head to coalesce, thus defeatingthe principle of operation of the MPD system and reducing the efficiency ofdegassing.

V. CONCLUSION

This multiple pinhole degassing~MPD! system lowers the dissolvedoxygen concentration of water to levels acceptable for measurement and

operation of diagnostic ultrasound equipment, as specified by the AIUM. Inaddition, it allows easy collection of removed gases. This system is as effi-cient and effective in gas removal as much more costly and complex sys-tems.

1‘‘Acoustic Output Measurement and Labeling Standard for DiagnosticUltrasound Equipment,’’ AIUM, 1992.

2Guide for Medical Ultrasound Field Parameter Measurements~IEEE,New York, 1990!, Appendix B.

3J. B. Fowlkes and P. L. Carson, ‘‘Systems for degassing water used inultrasonic measurements,’’ J. Acoust. Soc. Am.90, 1197–1200~1991!.

4T. G. Leighton, ‘‘Cavitation Inception and Fluid Dynamics,’’ inTheAcoustic Bubble~Academic, London, 1994!, Chap. 2, pp. 75–76.

Advanced-degree dissertations in acoustics

Editor’s note:Abstracts of Doctoral and Master’s theses will be wel-comed at all times. Please note that they must be double spaced, limited to200 words, must include the appropriate PACS classification numbers, andformatted as shown below~don’t make the editor retype them, please!!. Theaddress for obtaining a copy of the thesis is helpful. Please submit twocopies.

Underwater linear horn-array simulator [43.30.Yj, 43.58.Bh]—Stephen C. Butler,Graduate Program in Acoustics, The Pennsylvania StateUniversity, University Park, PA 16802, May 1995 (M.S.).Sonar transducerswith a radiating face whose dimensions are smaller than one-half wave-length tend to have a low radiation impedance load and consequently anarrow transmitting bandwidth. Thus, when the transducer is tested alone,the measured results yield a poor representation of its intended performancein an array. The objective of this research was to develop a fluid means tosimulate array loading conditions on a single sonar transducer element. Themethod which accomplishes this is based on a linear-endfired waveguide,which imposes on a single element a radiation impedance that is essentiallyreal with value near ‘‘rcAp, ’’ where Ap is the piston radiation area andrcis the characteristic impedance of the fluid medium. This is accomplished bythe ‘‘underwater linear horn-array simulator’’ which is composed of a rigid-walled cylindrical tube with slots of equal area equally spaced along thelength of the tube. It is shown, based on an acoustical circuit model, that85% rc-loading over an octave bandwidth can be achieved with a twowavelength long horn with quarter wavelength spaced slots. The radiationimpedance response results obtained are as if the ‘‘ka’ ’ value of the trans-ducer piston has been increased. Complex admittance and ABCD param-eters measurements on a physical model confirm the prediction. MeasuredmechanicalQ’s of the sonar transducer are 7.5 without the horn, and 5 withthe horn, agreeing with the mechanicalQ of a modeled 85%rc-loadedtransducer. This loading condition approximates the ideal 79%rc-loadingcondition for a closely packed array of circular piston transducers.

Thesis advisor: W. Jack Hughes.

Determination of phase modulating function from a powerspectrum definition [43.60.Gk]—David George Kasper,GraduateProgram in Acoustics, The Pennsylvania State University, University Park,PA 16802, December 1994 (M.S.).A theoretical study and numerical simu-lations are performed to find a modulating signal to apply to the input of avoltage-controlled oscillator~VCO! such that the power spectral density~PSD! of the output of the VCO matches a desired PSD. The desired PSD iscomposed of discrete spectral components with specified frequencies andrelative amplitudes. The first step in each of two algorithms developed is todefine a phase modulated signal that is a sum of sinusoids so that the phasemodulated signal has a PSD equal to the desired PSD. The objective of eachalgorithm is to reproduce this desired phase modulated signal and thus re-produce the desired PSD. The second step in each of the algorithms is tocalculate a modulating signal from the desired phase modulated signalthrough direct analytic inversion. The first algorithm, entitled direct inver-sion ~DI!, uses this modulating signal as input to the VCO. The second

algorithm, entitled ‘‘modeling,’’ involves modeling the modulating signalobtained from the DI algorithm with a sum of weighted orthonormal func-tions. The model modulating signal is then used as input to the VCO. TheDI and modeling algorithms both yield PSDs that reproduce the respectivedesired PSDs with minimal errors in frequency and amplitude for periodicdesired phase-modulated signals of various time lengths. The DI and mod-eling algorithms are each more advantageous compared to the other depend-ing upon the exact means of implementation and the selection of the fre-quencies of the spectral peaks in the desired PSD.

Thesis advisor: Carter L. Ackerman.

The effects of fuzzy attachments on compressional and shearwaves in a plate [43.40.At, 43.40.Dx, 43.40.Tm]—Judith Lynn Rochat,Graduate Program in Acoustics, The Pennsylvania State University,University Park, PA 16802, December 1994 (M.S.).Although realistic com-plex structures are usually difficult to model theoretically, fuzzy structuretheory enables one to produce such a model without a detailed knowledge ofthe entire structure. Using the theory established by Pierce, Sparrow, andRussell@J. Vib. Acoust.~to be published!, also ASME 93-WA/NCA-17#, theeffects that fuzzy attachments have on different wave types in a plate areexamined. Their theory models a thin plate mounted in an infinite baffle; onone side are fuzzy attachments, represented as an array of point-attachedmass-spring-dashpot systems, excited by an incident plane pulse. Thisknown theory explains the effects of these attachments on bending waves inthe plate. In this thesis, the theory is extended to isolated compressional andshear waves in a plate. It is discovered that coupling effects occur when theplate and attachment properties are not uniform in the direction perpendicu-lar to the wave propagation. Hence, the new theory uses a thin plate infinitein one direction with line-attached oscillators also infinite in the same direc-tion. For both compressional and shear waves, it is found that fuzzy attach-ments add an apparent frequency-dependent mass and damping to the plate.These results are similar to those for the bending wave theory.

Thesis advisor: Victor W. Sparrow.

Estimating acoustic radiation from a Bernoulli–Euler beamusing shaped polyvinylidene fluoride film [43.40.Rj, 43.38.Fx]—Brian Lloyd Scott,Graduate Program in Acoustics, The Pennsylvania StateUniversity, University Park, PA 16802, May 1995 (M.S.).This thesis numeri-cally examines using an array of shaped polyvinylidene fluoride sensors toestimate the far-field radiated power from a clamped-clamped Bernoulli–Euler beam. An analytical expression for the beam displacements from asinusoidal point excitation is derived and this result is used to obtain thestrain response, displacement wave-number spectrum and strain wave-number spectrum of the beam. Since only structural wave-number compo-nents whose magnitude is less than the fluid wave number contribute to astructure’s radiated power, distributed sensors are designed that act as low-pass filters in the wave-number domain. Specifically, the shape of thepatches is that of the sine function multiplied by a Hamming window. Theshaped sensors provide a reasonable estimate of the strain transforms overthe region of interest, when compared to the exact theoretical predictions,

3859 3859J. Acoust. Soc. Am., Vol. 99, No. 6, June 1996 Technical Notes and Research Briefs

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Page 4: Estimating acoustic radiation from a Bernoulli–Euler beam using shaped polyvinylidene fluoride film

for the first five beam resonance frequencies and for frequencies locatedapproximately midway between resonance frequencies. The distributed sen-sors also give better predictions of the strain transforms for all frequenciesconsidered when compared to the point sensor results. The power predic-tions using shaped sensors ranged from23.2 to 4 dB relative to the exacttheoretical results for the frequencies analyzed, while power predictionsusing point sensors ranged from 33.6 to 57 dB.

Thesis advisor: Scott D. Sommerfeldt.

Acoustic scattering by two immersed elastic shells [43.20.Fn,43.40.Ey, 43.40.Rj]—El m’kaddem Kheddioui,Laboratoire d’AcoustiqueUltrasonore et d’Electronique, U.R.A. C.N.R.S. 1373 Universite´ du Havre,France, 8 June 1995 (Ph.D.).The aim of this thesis is the experimental andtheoretical study of the scattering by two identical and elastic cylindricalair-filled shells immersed in water. The shell axes are parallel. The directionof propagation of the incident plane wave is perpendicular to the axes. Thedistance between the shells ranges from 1 to 3 diameters of one shell. Thefrequency range investigated corresponds to the range in which theA waveresonances and the whispering gallery wave resonances (l52! can be de-tected. First the scattered pressure by the two elastic shells is computed inthe same way as J. W. Young and J. C. Bertrand@J. Acoust. Soc. Am.58,1190–1195~1975!# but applied here to the case of elastic shells. Then, thescattered pressure is rewritten in a new way explaining the contributions ofeach shell. It is analyzed in terms of multiple interactions. The configurationin eclipse is mainly studied~the direction of the incident wave contains theshell axes!. Numerical calculations of the temporal and frequency responsesof the target submitted to a pulse excitation are performed and comparedwith a good agreement to the experimental results. The geometrical andcircumferential waves involved in the scattering process allow us to explainthe temporal and frequency responses. Single shell resonances and interfer-ential ‘‘resonances’’ are detected. These results are confirmed by an experi-mental quasiharmonic study. In this case the complex structure of the back-scattered temporal signal is analyzed against frequency and the phenomenonof acoustic interference is clearly shown. Finally, at the resonance frequen-cies of one shell, the angular diagram in the free reemission regime iscompared to that provided by an analytic model involving interferences

between the scattering by each shell: there is a good agreement.

Thesis advisors: J. L. Izbicki, J. M. Conoir, and P. Pareige.

Copies of this thesis may be obtained from Professor J. L. Izbicki, LAUE,Universitedu Havre, Place R. Schuman, 76610 Le Havre, France.

Viscothermal coupling effects on sound attenuation inconcentrated colloidal dispersions [43.35.Yb, 43.35.Bf]—Wei Han,Department of Chemical Engineering, University of Maine, Orono, ME04469, December 1995 (Ph.D.).This thesis describes a unified coupledphase continuum~UCPC! model to analyze sound propagation through col-loidal dispersions. The effective complex wave number as a function offrequency and concentration is derived for the viscothermal coupling.Frequency- and concentration-dependent viscous and thermal coupling co-efficients are developed on the basis of a cell model. An approximate simi-larity between the ‘‘viscous skin drag’’ and ‘‘heat conduction flux’’ associ-ated with the suspended phase was used. Expressions for the couplingcoefficients explicitly account for particle size, shape factor, orientation aswell as concentration and sound frequency. The predictions of attenuationspectra provide satisfactory agreement with reported data on two concen-trated suspensions, two concentrated emulsions and two aerosols, covering awide range of relative magnitudes~from 1023–103! of thermal versus vis-cous contributions, for dispersed phase volume fractions as high as 50%.Attenuation spectra for 18 frequencies from 3–100 MHz are measured andanalyzed for eleven kaolin clay slurries with solid concentrations rangingfrom 0.6% to 35%~w/w!. With incorporation of particle size and shapedistributions~PSSD!, predictions agree quantitatively with observed attenu-ation coefficients. The effects of particle aspect ratio and orientation becomemore evident as particle concentrations and frequencies are increased.

Thesis advisor: Hemant P. Pendse.

For copies, write Hemant P. Pendse at Department of Chemical Engineer-ing, University of Maine, Orono, Maine 04469. Author is now at Electronicand Electrochemical Materials and Devices Group, MST-11, MS D 429, LosAlamos National Laboratory, Los Alamos, NM 187545.

3860 3860J. Acoust. Soc. Am. 99 (6), June 1996 0001-4966/96/99(6)/3860/4/$6.00 © 1996 Acoustical Society of America

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