TECHNICAL NOTES AND RESEARCH BRIEFS

Paul B. Ostergaard 10 Glenwood Way, West Caldwell, NJ 07006

Editor's Note: Original contributions to the Technical Notes and Research Briefs section are always welcome. Manu- scripts should be double-spaced, and ordinarily not longer than about 1500 words. There are no publication charges, and consequently, no free reprints; howe. ver, reprints may be purchased at the usual prices.

Advanced-degree dissertations in acoustics Editor's note: Abstracts of Doctoral and Master's theses will be wel-

comed at any time. Please note that they must conform to the usual limit of 200 words, as for archival papers, must be double spaced, and must bear the appropriate PACS classification numbers. It would be useful to provide the name of the thesis supervisor, and to indicate how a copy of the thesis may be obtained.

Quantitative ray methods for scattering of sound by spherical shells [43.20.Fn, 43.40.Ey]•Steven G. Kargl, Department of Physics, Washington State University, Pullman, WA 99164-2814, August 1990 (Ph.D.]. The application of ray methods to the scattering of high-frequency plane waves from evacuated elastic spherical shells is investigated. The in- vestigation of ray methods for spherical shells is a precursor to the applica- tion of such methods to shells having more complicated shapes. The scat- tered pressure in the far field of the shell is p• = p, (a/2r)f(O)exp(ikr) where p• is the plane-wave amplitude. The outer radius of the shell is a, h = a-b is the shell's thickness, and r is the distance to an observation point. Ray models are developed to synthesize the form function f(O, ka) where k is the wave number of the incident wave and 0 is the scattering angle. The forward scattering amplitude, f(0 = 0), is related to the extinc- tion cross section, %, by the optical theorem. If the absorption by the scat- terer is negligible, then (Ye is equal to the total scattering cross section %. A ray synthesis partitions f(0 = 0) into a component for ordinary forward diffraction about the shell,f•, and contributions from surface guided elas- tic waves. For high-frequency scattering, the relevant surface guided elastic waves are leaky Lamb waves. A similar ray synthesis of the backscattering amplitude f(0 = •r) contains a specular reflection component, •p (0 = •r), and leaky Lamb wave contributions. A generalization of the geometrical theory of diffraction is employed to synthesize f• (0 = 0, ka) and f• ( 0 = •r, ka) for the I th leaky Lamb wave contribution. The syntheses for forward and backwards scattering correctly describe the leaky Lamb wave contributions and are expressible in a Fabry-Perot resonator form. While the ray description ofbackscattering ordinarily accurately reproduces exact computations and experiments with tone burst, certain anomalies are dis- cussed. A ray synthesis off•p demonstrates a significant longitudinal reso- nance effect when k,• h -- mr, n = 1,2 ..... where k,• = w/c,• is the longitudi- nal wave number within the shell. The analysis of •p is for an elastic material with vanishing shear velocity. The relevant range of ka is 7•ka• 100. The shell is surrounded by water and is composed of 440 c stainless steel with inner-to-outer radii ratio b/a = 0.838.

Thesis advisor: Philip L. Marston.

Wavefields near transverse cusp caustics produced by reflecting ultrasonic transients and tone bursts from curved surfaces

[43.20.Fn, 43.20.Px]--Carl K. Frederickson, Department of Physics, Washington State University, Pullman, WA 99164-2814, August 1991 (Ph.D.). Ultrasonic wavefields reflected from curved surfaces were studied in the vicinity of caustics. Acoustical and optical transverse cusp diffraction catastrophes produced by reflections from a curved metal surface in water were imaged by displaying the amplitude or intensity in an observation plane transverse to the general direction of propagation. The optical image was used to locate the cusp point in the observation plane. Acoustical dif- fraction patterns for sine waves, described by the Pearcey function, were calculated with the parameters determined by the experimental setup leav- ing no adjustable scaling parameters. The calculated and experimental acoustical diffraction patterns showed good agreement near the cusp point.

The acoustical diffraction pattern showed the expected mirror symmetry about an axis. The pattern was shown to scale properly with frequency.

The transverse cusp caustic separates space into a region with three rays and a region with one ray. Inside the caustic there are three rays, on the curve two of the rays merge and disappear leaving one ray outside. Tran- sient signals reflected from curved surfaces exhibited the merging and dis- appearance of rays on the caustic. Relative arrival times for signals in calcu- lated and recorded time traces agree well. The relation to the wavefront parameters of the temporal orientation of the travel time surface is dis- cussed. The general shape of the travel time surface is that of the swallow tail caustic surface.

The temporal shape of the transient echoes was seen to be generally that of the incident signal or of its Hilbert transform. The Hilbert transform shape identifies the signals that have touched the caustic. The observed arrival sequence of the transient signals was shh inside the caustic and one h outside, where s stands for a signal with the general shape of the incident signal and h for its Hilbert transform. The relation between the surface and wavefront parameters and the arrival sequence is given.

Thesis advisor: Philip L. Marston.

Scattering of tone bursts from spherical shells: Computations based on Fourier transform method [43.20.Fn, 43.20.Px]--Ligang Zhang, Department of Physics, Washington State University, Pullman, WA 99164-2814, August 1991 (M.S.). An algorithm to compute the transient scattering of sound by elastic spheres and shells has been developed and tested. Short tone bursts incident on elastic spherical shells under various conditions have been investigated. Previous experiment results for elastic spheres and shells have been confirmed. Some interesting physical aspects concerning the basics of the scattering mechanism have been detected. A midfrequency enhancemerit has been examined for thin shells and com- pared with the ray model results. The ray model is found to closely approxi- mate the enhanced backscattering for tone bursts associated with a subsonic wave on thin shells. A related filterlike effect of thin shells for the selected

frequencies has been detected find quantitatively described and the impulse response has been computed. The present computations can be of practical use and can be compared with observations or ray models of the scattering from shells under the same conditions if such observations or models be-

come available later on. The scattering of tone bursts from shells was calcu- lated when the carrier frequency is at or close to the frequency of resonance associated with a reverberation of longitudinal waves across the thickness of the shell. When the shell is a fluid, the results are easily interpreted in terms of an existing ray model. When the shell is elastic, they suggest the presence of a mechanism for prompt radiation not involving complete circumnaviga- tion of the sphere by guided elastic waves.

Thesis advisor: Philip L. Marston.

Asymptotic description of the acoustic microscopy of a surface- breaking crack [43.35.Sx, 43.35.Pt]--Douglas Alexander Rebinsky, De- partment of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, 216 Talbot Lab., 104 S. Wright St., Urbana, IL 61801, October 1991 (Ph.D}. An asymptotic description of the acoustic signature of a crack, breaking the surface of an otherwise homogeneous, isotropic elastic matehal, determined using either a line focus or a point focus scanning acoustic microscope is constructed. The incident focused beam is construct- ed as a Fourier integral that produces a specified profile in the focal plane. The wavefields scattered from the specimen are also represented as Fourier integrals. Because the lenses of the acoustic microscopes are characterized by a large Fresnel number and a F number of order one, the Fourier inte-

3374 J. Acoust. Soc. Am. 90(6), Dec. 1991 0001-4966/91/123374-02500.80 ¸ 1991 Acoustical Society of America 3374

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grals can be asymptotically approximated to obtain explicit expressions for the incident wavefield and the wavefield scattered from a defect-free sur-

face. The latter wavefield contains the leaky Rayleigh wave that is incident to the surface-breaking crack. The surface-breaking crack is characterized by assigning it reflection and transmission coefficients. The wavefield scat- tered from the crack is estimated by tracing the leaky Rayleigh waves re- flected and transmitted by the crack. Lastly, the acoustic signature is calcu- lated by using the approximate incident and scattered wavefields in an electromechanical reciprocity identity that links the voltage measured at the microscope's transducer to the scattered acoustic wavefields at the sur- face of the specimen. Expressions for the acoustic signatures made using the line focus and point focus microscopes are compared. Moreover, from the expression for the acoustic signature, the leaky Rayleigh wave reflection and transmission coefficients can be extracted.

Thesis advisor: John G. Harris.

Outdoor sound propagation near ground surfaces [43.28.Fp, 43.20.Bi, 43.20.Fn]--Karsten Bo Rasmussen, The Acoustics Laboratory, Technical University of Denmark, Building 352, DK-2800 Lyngby, Den- mark 1990/1991 [Dr. Techn. J. Theoretical models for outdoor propagation close to impedance surfaces is developed. Various effects are modeled such as ( 1 ) the influence of a simple impedance discontinuity in the surface; (2) the influence of screens and earth berms; (3) the influence of wind and temperature gradients in the atmosphere. A number of different mathemat- ical approaches is used ranging from various diffraction theories to direct numerical integration of Helmholtz equation solutions. The mathematical models are compared to measured data for point sources. In addition, a very simple model for point source propagation is presented for the case of a flat impedance surface. This model is approximate but well suited for practical purposes. The thesis consists of previously published papers along with a very thorough summary in which the work by the author is commented on and related to work by other authors.

Official opponents: Jens Holger Rindel and Sven Lindblad.

Application of active noise cancellation for source identification and monitoring in a modal environment [43.40. Le, 43.40.Vn]--Wcn- Shyang Chiu, Graduate Program in Acoustics, The Pennsylvania State Uni- versity, University Park, PA 16802, May 1990 (Ph.D.). Faulty bearing detec- tion and diagnosis in complex machines often encounter a problem in that the bearing signal may be masked by excessive noise. The ability to process the diagnosed signal to improve its signal-to-noise density ratio (SNR) is critical in detecting and diagnosing the bearing's fault in its early stage. The objective of this research was to develop a real-time monitoring technique for the detection and diagnosis of an incipient beating failure when the bearing signal is corrupted by the presence of significant background noise.

The original contribution of this work is a new approach to separate the diagnosed signal from the structural noise based on the adaptive noise cancellation technique (ANC). The ANC makes use of an adaptive filter- ing process which is based on the least mean square algorithm (LMS) of Widrow and Hoff. A real-time, PC-hosted adaptive noise canceller with the capability of high-frequency range application has been developed using the Motorola DSP56000/56200 system. Power spectrum, kurtosis, and cep- strum are used to detect and diagnose the bearing's fault subsequent to the application of the ANC.

This real-time monitoring technique was applied to monitor the oper- ating conditions of a ball bearing in a motor/pump system. The bearing signal is masked by structural noise from structural resonances and from the pump. Results show that the ANC can remove the structural noise from the signal so that the statistical and spectral analysis techniques for bearing monitoring can be effectively used.

Thesis advisor: Jiri Tichy.

The prediction and measurement of acoustic absorption in high temperature (up to 1200 ø K) atmospheric gas mixtures using a spe- cially designed plate-diaphragm capacitive high temperature acoustic transducer [43.20.Hq, 43.35.Ae]--Wa]]ac½ R. A. G½or;e, Graduate Program in Acoustics, The Pennsylvania State University, Univer- sity Park, PA 16802, May 1990 (Ph.D.). This research is an in-depth study of the absorption of acoustic energy by arbitrary gas mixtures of N2, 02, CO2, H20, and Ar, at temperatures up to 1200 *K. Special attention is given to vibrational molecular relaxational acoustic absorption. This dissertation consists of three parts. The first is the design and the modeling of the re- sponse of a capacitive annular plate-diaphragm high temperature acoustic (HTA) transducer. The second is the discussion, modeling, and/or predic- tion of the acoustic dissipative mechanisms applicable to acoustic propaga- tion in cylindrical ducts. The third aspect of this research involves the mea- surements of absorption in high temperature (less than 1200 *K) gas mixtures using the high temperature acoustic (HTA) transducer and the comparison with predicted results.

A complete discussion of acoustic dissipation processes in cylindrical ducts is presented. The eigenproblem matrix formulism to predict the mo- lecular relaxational absorption in gas mixtures is developed; physical intu- ition on the subject is also developed, and the linearly independent energy transfer pathways are clearly identified. Eigenproblem perturbation tech- niques are used for the sensitivity analysis of the relaxation parameters to the assumed energy transfer rates.

A semi-empirical prediction for the tube wall boundary layer wall ab- sorption is developed. Some of the first acoustic absorption measurements at temperatures up to 1200 øK are reported. Experiments were fully com- puter controlled. Pulse technique, spectral analysis, and time (ensemble) averaging are used. Predicted results are compared with the measured re- sults and found to be reasonable.

Thesis advisor: Gary Koopmann.

Angle sample variance of azimuthally spread scattering pro- cesses using a two-element array [43.30.Vh]--James Robert Johnescu, Graduate Program in Acoustics, The Pennsylvania University, University Park, PA 16802, May 1990 {M. S.J. Active echo energy received by a two-element array may be comprised of both spatially coherent and spatially spread scattering processes (such as clutter or reverberation) and isotropic noise. Such inputs may be filtered by a correlation receiver from which range, Doppler, and angle estimates can be made. In many cases, these estimates display azimuthal support, such that angle estimates of spa- tially spread scattering processes are stochastically distributed across the array beamwidth, whereas angle estimates of spatially coherent scattering processes tend to be azimuthally compact.

A scattering function model is used to relate the geometry and scatter- ing distributions to the angle estimation problem when a two-element array is used as the receiver. The angle estimate statistics are described by proba- bility density functions which depend upon array geometry, scattering dis- tribution, scattering strength, and ambient noise. At low levels of interfer- ence, spatially coherent scattering processes display low angle variance. Consequently, realizations of measured angle from spatially compact pro- cesses tend to be consistent while those from spread scatterers tend to be distributed across the receive beam support. When multiple measurements of angle are available, the sample variance can be useful as a means to characterize the underlying scattering distribution.

Probability density functions of angle sample variance as a function of coherent scattered energy, diffuse scattered energy ambient noise are devel- oped through a multistep statistical transformation and verified with Monte Carlo estimations. Errors introduced by assumptions regarding correlation between angle measurement realizations are discussed and examples are provided.

Thesis advisor: Dennis Ricker.

3375 J. Acoust. Soc. Am. 90(6), Dec. 1991 0001-4966/91/123375-01500.80; @ 1991 Acoust. Soc. Am.; Notes and Briefs 3375

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