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Journal of the Acoustical Society of America

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Dec 1979

Volume 66, Issue 6, pp. 1593-1918

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Electromagnetic field reciprocity applied to the excitation and detection of elastic waves in an electromagnetic cavity resonator

A. McNab and J. Richter

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1593-1600 (1979); (8 pages)

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This paper discusses the generation and detection of acoustic waves in a piezoelectric material by cavity excitation. By invoking electromagnetic field concepts whereby the acoustic waves appear as equivalent current sources, the reciprocal nature of both problems can be proved. Also, from a knowledge of the cavity electric field and the acoustic excitation vector, the detected cavity responses can be evaluated, showing that two distinct responses (even and odd) are obtained for differing electric fields on the piezoelectric surfaces.
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43.38.Fx Piezoelectric and ferroelectric transducers

Two theoretical results suggesting a method for calibrating ultrasonic transducers by measuring the total nearfield force

Eric B. Miller and Arthur D. Yaghjian

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1601-1608 (1979); (8 pages) | Cited 1 time

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Theory and preliminary experiments are outlined relating to a nearfield method of evaluating electroacoustic transducers. The theoretical results are conveniently organized into two theorems: (1) The total complex force on all parallel infinite planes to one side of a transducer and perpendicular to an arbitrary direction, has a constant magnitude equal to the magnitude of the farfield pressure in that same direction multiplied by the wavelength. (2) The output voltage of a baffled, reciprocal, plane‐piston receiver is proportional to the total incident force normal to its face. These two theorems suggest a compact and relatively simple method for evaluating directive or moderately directive ultrasonic transducers. It is demonstrated experimentally that there is good agreement between the farfield pattern of a directive transducer in the main beam region, measured by a large, plane‐piston transducer in the nearfield, and the pattern measured directly with a small probe in the approximate farfield. Further, it is experimentally demonstrated that, as a piston receiver is moved axially, with respect to a transmitter, no discernible change in the output voltage of the receiver is detected, provided the nearfield beam of the transmitter is intercepted by the receiver (even though the nearfield of either transducer differs significantly from that of a plane wave).
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43.38.Ar Transducing principles, materials, and structures: general
43.35.Yb Ultrasonic instrumentation and measurement techniques
43.30.Yj Transducers and transducer arrays for underwater sound; transducer calibration

Dependence of the electromechanical coupling coefficient on the width‐to‐thickness ratio of plank‐shaped piezoelectric transducers used for electronically scanned ultrasound diagnostic systems

J. Sato, M. Kawabuchi, and A. Fukumoto

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1609-1611 (1979); (3 pages) | Cited 7 times

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A finite element analysis method is used to obtain the electromechanical coupling coefficient ke for plank‐shaped piezoelectric transducers with a width W to thickness T ratio of not more than two. Calculation results for typical piezoelectric ceramics show that there exist maximum values of ke at certain values of W/T. For PCM‐5R material the maximum value of ke is 0.69 at a W/T of 0.6. It is shown that only one vibrational mode is very strongly coupled around this value of W/T. This vibrational mode is very useful for application to electronically scanned arrayed transducers.
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43.58.Kr Spectrum and frequency analyzers and filters; acoustical and electrical oscillographs; photoacoustic spectrometers; acoustical delay lines and resonators
43.38.Fx Piezoelectric and ferroelectric transducers
43.80.Qf Medical diagnosis with acoustics
43.35.Yb Ultrasonic instrumentation and measurement techniques

Some voicing adjustments of flue organ pipes

A. W. Nolle

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1612-1626 (1979); (15 pages) | Cited 2 times

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The investigation uses a flue organ pipe designed so that mouth height Y, position of the upper lip in the air stream X, and width of the air passage are adjustable. Other dimensions can be altered with interchangeable parts. Rectangular and circular resonators of several lengths, open and stopped, are used. Speaking frequencies are 125 to 500 Hz. Speech for a supply pressure of 55‐mm water is described for the useful X,Y range in qualitative terms, and also in terms of sound‐pressure level and harmonic content. Behavior is related to resonance frequencies. Stable oscillation of longer pipes occurs in a limited X,Y range unless the first resonance frequency is some 2% lower, relative to harmonic relationship with the next few modes of vibration. As X is varied, for the speaking pipe, the second harmonic has an amplitude minimum, where the phase relative to the fundamental reverses. The acoustic pressure is proportional to mass flow rate over a range of at least 4:1 in tests involving reduction of air pressure or narrowing the passage. Threshold operating pressure for 7‐mm mouth height is 5‐mm water, in good agreement with Coltman’s flute data. Air supply energy is converted to radiation with about 0.5% efficiency for the stopped pipe.
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43.75.Np Pipe organs

Speech waveform coding: Techniques and performance

Ronald E. Crochiere and Yasuo Kato

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1627-1627 (1979); (1 page)

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43.72.-p Speech processing and communication systems

Topics on speech waveform coding activities in Japan

Atsushi Tomozawa and Kazuo Ochiai

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1628-1632 (1979); (5 pages)

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Current activities on speech waveform coding technique developments in Japan are reviewed. The following topics of the activities on ADPCM and ADM are discussed. (1) An ADPCM code sequence optimization method by Fushikida for an ADPCM with an adaptive quantization and fixed predictor. The method uses a technique reminiscent of dynamic programming and optimizes code sequence. It is shown that about 3 dB SNR improvement is obtainable for speech at 32 kbps (4 bits/sample). (2) Another ADPCM technique by Araseki and Ochiai. This technique is suitable for use at the bit rate less than 32 kbps. Two adaptive predictors connected in a cascaded form are used. One of the predictors has an ordinary small number of prediction taps. However, the other predictor possesses a considerably larger number of predictor taps and is used to predict the speech waveform which is one pitch period apart. (3) Performance improvement techniques and LSI implementation by Tomozawa and Niwa for a discretely variable slope 32 kbps ADM (DVSD). Yatsuzuka’s residual encoder and Hosokawa and Yamashita’s adaptive predictive DM are also discussed briefly.
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43.72.-p Speech processing and communication systems

Predictive and residual encoding of speech

John Makhoul and Michael Berouti

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1633-1641 (1979); (9 pages)

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This paper surveys recent developments in adaptive predictive coding (APC) of speech. Prominent among these developments are the use of a three‐point pitch predictor, a pitch‐adaptive quantizer, entropy coding of the residual, and adaptive shaping of the quantization‐noise spectrum. APC systems produce high quality speech at around 16 kbit/s; their quality diminishes rapidly at 9.6 kbit/s or less. For those lower data rates, some form of baseband coding system becomes desirable. In such systems, a low‐frequency baseband is transmitted. The high‐frequency regeneration of the excitation spectrum from the baseband is of special importance. Traditional regeneration techniques have used some form of nonlinear distortion (usually rectification) of the baseband, followed by spectral flattening. We introduce a new set of regeneration based on duplication of the baseband spectrum at high frequencies. The audible signal distortions in rectification and spectral folding are compared.
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43.72.-p Speech processing and communication systems

Frequency domain techniques for speech coding

R. E. Crochiere and J. M. Tribolet

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1642-1646 (1979); (5 pages)

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Frequency domain techniques for speech coding have recently received considerable attention. The basic concept of these methods is to divide the speech into frequency components by a filter bank (subband coding) or by a suitable transform (transform coding) and then encode them using adaptive PCM. Four basic operations are involved in the design of these coders: (1) the type of transform or filter bank (analysis/synthesis), (2) the adaptive quantizer design (quantization theory), (3) the choice of bit allocation used by the quantizers (noise shaping and auditory masking), and (4) the control of the step‐size of the quantizers (spectral estimation). This paper briefly reviews the basic aspects of the design of these four operations particularly as they apply to low bit‐rate adaptive transform coding.
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43.72.-p Speech processing and communication systems

Optimizing digital speech coders by exploiting masking properties of the human ear

M. R. Schroeder, B. S. Atal, and J. L. Hall

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1647-1652 (1979); (6 pages) | Cited 8 times

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In any speech coding system that adds noise to the speech signal, the primary goal should not be to reduce the noise power as much as possible, but to make the noise inaudible or to minimize its subjective loudness. ’’Hiding’’ the noise under the signal spectrum is feasible because of human auditory masking: sounds whose spectrum falls near the masking threshold of another sound are either completely masked by the other sound or reduced in loudness. In speech coding applications, the ’’other sound’’ is, of course, the speech signal itself. In this paper we report new results of masking and loudness reduction of noise and describe the design principles of speech coding systems exploiting auditory masking.
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43.72.-p Speech processing and communication systems
43.70.Dn Disordered speech

Practical implementations of speech waveform coders for the present day and for the mid 1980s

Aaron J. Goldberg

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1653-1657 (1979); (5 pages)

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This paper discusses practical implementations of low bit‐rate speech waveform digitizers for the pre‐1980 and post‐1985 time periods. Based on requirements of expected mathematical complexity, accuracy, and redundance of these coders, the basic hardware speeds and amount of logic to implement them are given for today’s implementations. Issues important to the commercial and military users are examined to ascertain how they can radically alter the architectures and hardware chosen for implementation. Then assuming that the speech digitization algorithms remain at least as complex as today’s techniques, well‐known procedures for forecasting LSI improvements and cost reductions are used in estimating the hardware needed to implement these systems in the mid 1980s.
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43.72.-p Speech processing and communication systems

Objective measures for speech quality testing

Thomas P. Barnwell, III

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1658-1663 (1979); (6 pages)

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This paper presents a discussion of the philosophy and practice of speech quality testing using objective measures. The emphasis in the paper is on the problems of designing effective objective quality measures and the inherent limitations of such measures. Both traditional and recent techniques are discussed, along with the issues of implementation and evaluation. Experimental results on the correlation between objective quality measures and subjective quality measures are also presented.
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43.72.-p Speech processing and communication systems
43.71.Gv Measures of speech perception (intelligibility and quality)

Evaluation of a segmental SNR measure as an indicator of the quality of ADPCM coded speech

Paul Mermelstein

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1664-1667 (1979); (4 pages)

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Two objective measures of speech quality, the traditional signal to quantization noise ratio (SNR) and a segmental SNR, are compared from the point of view of their ability to predict subjective preference ratings of PCM and ADPCM coded speech. The SNR shows an 8‐dB bias for PCM coding, i.e., the SNR of the PCM has to exceed the SNR of ADPCM by 8 dB before the two are judged to be equally preferable. In contrast, the segmental SNR shows no such bias. The segmental SNR is considered a better perceptual model since it evaluates the quantization noise with respect to the energy in each underlying speech segment.
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43.72.-p Speech processing and communication systems
43.71.Gv Measures of speech perception (intelligibility and quality)

Speech perception in early infancy: Perceptual constancy for spectrally dissimilar vowel categories

Patricia K. Kuhl

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1668-1679 (1979); (12 pages) | Cited 3 times

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While numerous studies on infant perception demonstrate the infant’s ability to discriminate individual speech‐sound pairs, very few demonstrate the infant’s ability to recognize the similarity among phonetic units when they occur in different phonetic contexts, in different positions in a syllable, or when they are spoken by different talkers. In two studies, six‐month‐old infants demonstrated the ability to distinguish two spectrally dissimilar vowel categories (/a/ and /i/) in which the vowel tokens were generated to simulate tokens produced by a male, a female, and a child talker. In experiment I, the infants were initially trained to discriminate the /a/ and /i/ tokens produced by the computer‐simulated male voice. They were then gradually exposed to a number of novel tokens in a progressive transfer‐of‐learning task. In experiment II, the infants were initially trained to discriminate the same vowel contrast, but were then immediately tested with all of the tokens in both vowel categories. In both experiments the infants demonstrated rapid transfer of learning from the traning tokens produced by the male talker to the tokens produced by female and child talkers. Both experiments provide strong evidence that the six‐month‐old infant recognizes acoustic categories that conform to the vowel categories perceived by adult speakers of English.
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43.70.Dn Disordered speech
43.70.Fq Acoustical correlates of phonetic segments and suprasegmental properties: stress, timing, and intonation

Some effects of deafness on the generation of voice

Randall B. Monsen, A. Maynard Engebretson, and N. Rao Vemula

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1680-1690 (1979); (11 pages)

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Glottal volume–velocity waveform data were collected from twenty male and female hearing‐impaired adolescents by means of a reflectionless tube. The subjects each provided samples of phonation in normal‐ and soft‐voice modes and in a three‐syllable word with primary stress on the medial syllable. Analysis of the data, in comparison with characteristics of phonation produced by normally hearing subjects, indicates that deafness affects primarily the time‐varying characteristics of the glottal source. Among the hearing‐impaired subjects, the following abnormalities were noted: diplophonia and creaky‐voice episodes at the onset or middle of phonation, and irregular patterns of change in the frequency and intensity of the glottal waveform. For some subjects, the period‐to‐period changes of frequency and intensity may be greater than normal. For the hearing‐impaired subjects, the shape of the isolated glottal pulse and its spectrum are similar or identical to normal, while striking abnormalities may be seen in the way the glottal pulse changes over time. The effect of deafness is thus that it may prevent a speaker from learning the phonatory consequences of the muscular gestures which maintain and alter vocal‐fold tension and subglottal air pressure dynamically in the production of voice.
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43.72.Ar Speech analysis and analysis techniques; parametric representation of speech
43.70.Jt Instrumentation and methodology for speech production research
43.66.Sr Deafness, audiometry, aging effects
43.70.Bk Models and theories of speech production

Formant frequency patterns in Russian VCV utterances

Edward T. Purcell

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1691-1702 (1979); (12 pages)

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Previous studies have sought to establish the significance of various parameters in the determination of the patternings of Russian formant frequency trajectories in vowel‐consonant‐vowel (VCV) syllables. In the present study, 9600 measurements of first and second formant frequency were made on Russian VCV nonsense words. Variance for speakers was controlled through regression. Stepwise multiple regression was employed to determine the relative contributions of six predictors to the explanation of the patternings of first and second formant frequency in the test words. The six predictors included the height of the first and second vowels, the front/back dimensionality of the first and second vowels, the place of articulation of the consonant, and the palatalization or nonpalatalization of the consonant. Results of the regression analyses are summarized. The regression coefficients for the useful predictors of the various dependent variables comprise a model of formant frequency patterns in Russian VCV utterances.
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43.72.Ar Speech analysis and analysis techniques; parametric representation of speech
43.70.Fq Acoustical correlates of phonetic segments and suprasegmental properties: stress, timing, and intonation

Analysis of stop consonant production errors in developmentally dysphasic children

Rachel E. Stark and Paula Tallal

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1703-1712 (1979); (10 pages)

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The speech production skills of 12 dysphasic children and of 12 normal children were compared. The dysphasic children were found to have significantly greater difficulty than the normal children in producing stop consonants. In addition, it was found that seven of the dysphasic children, who had difficulty in perceiving initial stop consonants, had greater difficulty in producing stop consonants than the remaining five dysphasic children who showed no such perceptual difficulty. A detailed phonetic analysis indicated that the dysphasic children seldom omitted stops or substituted nonstop for stop consonants. Instead, their errors were predominantly of voicing or place of articulation. Acoustic analyses suggested that the voicing errors were related to lack of precise control over the timing of speech events, specifically, voice onset time for initial stops and vowel duration preceding final stops. The number of voicing errors on final stops, however, was greater than expected on the basis of lack of differentiation of vowel duration alone. They appeared also to be related to a tendency in the dysphasic children to produce final stops with exaggerated aspiration. The possible relationship of poor timing control in speech production in these children and auditory temporal processing deficits in speech perception is discussed.
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43.72.Ar Speech analysis and analysis techniques; parametric representation of speech
43.70.Fq Acoustical correlates of phonetic segments and suprasegmental properties: stress, timing, and intonation

A system for evaluating auditory function from 8000–20 000 Hz

Stephen A. Fausti, Richard H. Frey, Deborah A. Erickson, B. Z. Rappaport, Edward J. Cleary, and Robert E. Brummett

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1713-1718 (1979); (6 pages) | Cited 3 times

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A system for the measurement of auditory function from 8000–20 000 Hz is described. This system introduces advances in: (a) maximum power output, (b) signal fidelity, and (c) transducer characteristics. Two case studies are presented to illustrate the clinical information gained from the measurement of high‐frequency auditory sensitivity, which is not readily apparent in conventional threshold assessment.
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43.66.Yw Instruments and methods related to hearing and its measurement
43.66.Sr Deafness, audiometry, aging effects
43.58.Fm Sound level meters, level recorders, sound pressure, particle velocity, and sound intensity measurements, meters, and controllers
43.66.Cb Loudness, absolute threshold

Forward masking with equal‐energy maskers

M. J. Penner

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1719-1724 (1979); (6 pages) | Cited 2 times

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Temporal masking of clicks by noise was investigated using a forward‐masking paradigm. The temporal separation ΔT between the click and the noise ranged from 0.3 to 100 msec. The duration of the noise varied from 3 to 500 msec while its energy remained fixed. For fixed ΔT (ΔT≳3msec), the masking effect may actually increase for the longer, less intense noises despite the fact that, for long maskers, there is less masker energy near the signal in time. These results are interpreted in terms of the modified version of the running‐average hypothesis [M. J. Penner, J. Acoust. Soc. Am. 63, 195–201 (1978)] in which it is argued that the auditory system compresses the intensity of the stimulus prior to integrating it. If the temporal integrator depends on stimulus intensity, then these results may be easily predicted. As an alternative explanation we show that compression may reduce the effective intensity of short maskers to such an extent that they do less masking than the longer ones. Such reduction in masking effectiveness will occur if the time between the masker and the signal is long enough so that the effects of compression and integrator shape do not counterbalance each other.
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43.66.Mk Temporal and sequential aspects of hearing; auditory grouping in relation to music
43.66.Dc Masking
43.66.Ba Models and theories of auditory processes

Psychophysical frequency resolution in the cat as determined by simultaneous masking and its relation to auditory‐nerve resolution

J. O. Pickles

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1725-1732 (1979); (8 pages) | Cited 2 times

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Critical bandwidths were measured behaviorally at 1 and 2 kHz by simultaneous masking in four cats. Three methods were used. They were (i) the masking of a tone by noise of variable bandwidth, (ii) the masking of a narrow‐band signal by two tones, and (iii) the masking of a tone by noise of rippled spectrum. The three methods agreed closely and gave a mean critical bandwith of 410 Hz at 1 kHz and 690 Hz at 2 kHz. These values were about three times as great as the electrophysiologically‐determined effective bandwidths of single fibers of the auditory nerve at the same frequencies, both as measured in other animals, and in one of the animals that had been tested behaviorally as well. Psychophysical tuning curves were also determined behaviorally; in contrast, they agreed closely with auditory‐nerve fibers in both bandwidth and slope. The results suggest that the critical band as measured by simultaneous masking is not a close relation of the frequency‐threshold curve of auditory‐nerve fibers, but that the psychophysical tuning curve possibly may be. Possible reasons and implications are discussed.
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43.66.Gf Detection and discrimination of sound by animals
43.66.Dc Masking
43.66.Ba Models and theories of auditory processes
43.66.Fe Discrimination: intensity and frequency

Discrimination of symmetric time‐intensity traded binaural stimuli

B. Robert Ruotolo, Richard M. Stern, Jr., and H. Steven Colburn

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1733-1737 (1979); (5 pages) | Cited 7 times

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Experiments were conducted to determine the extent to which listeners can discriminate between different combinations of interaural time and intensity for binaural stimulus configurations which eliminate loudness, lateralization, and image‐diffuseness cues. A two‐interval forced choice paradigm was used, and the task of the subject was to determine the order of two stimuli, each of which was a slowly gated 500‐Hz tone with a combination of interaural time and intensity differences that resulted in a centered primary spatial image. The two stimuli to be discriminated were symmetric in that they differed only in the polarity of their interaural differences. Also, in order to reduce artifacts introduced by variations in the coupling of the earphones to the head, acoustic monitoring and compensation was performed both before and after each experimental run. The performance of the two most highly trained subjects is consistent with previous experimental results that indicate an incomplete trading of interaural time and intensity information. The subjective perceptions of these observers are not consistent with previous studies that describe a ’’time image’’ and a ’’time‐intensity traded’’ spatial image.
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43.66.Qp Localization of sound sources
43.66.Pn Binaural hearing
43.66.Rq Dichotic listening

A neural‐counting model incorporating refractoriness and spread of excitation. I. Application to intensity discrimination

Malvin Carl Teich and Gerard Lachs

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1738-1749 (1979); (12 pages) | Cited 3 times

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We consider in detail a new mathematical neural‐counting model that is remarkably successful in predicting the correct detection law for pure‐tone intensity discrimination, while leaving Weber’s law intact for other commonly encountered stimuli. It incorporates, in rather simple form, two well‐known effects that become more marked in the peripheral auditory system as stimulus intensity is increased: (1) the spread of excitation along the basilar membrane arising from the tuned‐filter characteristics of individual primary afferent fibers and (2) the saturation of neural counts due to refractoriness. For sufficiently high values of intensity, the slope of the intensity‐discrimination curve is calculated from a simplified (crude saturation) model to be 1−1/4N, where N is the number of poles associated with the tuned‐filter characteristic of the individual neural channels. Since 1?N<∞, the slope of this curve is bounded by 3/4 and 1 and provides a theoretical basis for the ’’near miss’’ to Weber’s law.
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43.66.Ba Models and theories of auditory processes
43.66.Fe Discrimination: intensity and frequency
43.66.Lj Perceptual effects of sound

Measurements of binaural echo suppression

P. M. Zurek

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1750-1757 (1979); (8 pages) | Cited 9 times

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The notion of binaural echo suppression that has persisted through the years states that when listening binaurally, the effects of reverberation (spectral modulation or coloration) are less noticeable than when listening with one ear only. This idea was tested in the present study by measuring thresholds for detection of an echo of a diotic noise masker with the echo presented with either a zero or a 500‐μsec interaural delay. With echo delays less than 5–10 msec, thresholds for the diotic echo were about 10 dB lower than for the dichotic signal, a finding opposite that of the usual binaural masking‐level difference but consistent with the notion of binaural echo suppression. Additional echo‐threshold measurements were made with echoes of interaurally reversed polarity, producing out‐of‐phase spectral modulations. The 10–15 dB increase in thresholds for the reverse‐polarity echo, over those for the same‐polarity echo, indicated that the apparent ’’hollowness’’ associated with spectral modulations can be partially canceled centrally. Overall, the results of this study are consistent with a model in which: (1) the monaural representations of spectral magnitude are nonlinearly compressed prior to being combined centrally; and (2) neither monaural channel can be isolated in order to perform the detection task.
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43.66.Qp Localization of sound sources
43.66.Pn Binaural hearing
43.66.Dc Masking
43.66.Rq Dichotic listening

Analysis of the vibratory excitation of gear systems. II. Tooth error representations, approximations, and application

William D. Mark

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1758-1787 (1979); (30 pages) | Cited 2 times

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The second part of a theory is presented for predicting the vibratory excitation of gear systems from fundamental descriptions of gear tooth elastic properties and deviations of tooth faces from perfect involute surfaces. The first part of the theory [J. Acoust. Soc. Am. 63, 1409–1430 (1978)] provides expressions for the Fourier‐series coefficients of the vibratory excitation, which was shown to be described by the static transmission errors of all pairs of meshing gears in a system. The present paper provides expressions for these Fourier‐series coefficients in terms of easily interpreted gear tooth metrics that are readily evaluated from tooth‐face measurements. Detailed results are given for rectangular tooth‐face contact regions using two‐dimensional Legendre polynomial expansions of local tooth‐pair stiffnesses and stiffness–weighted deviations of tooth faces from perfect involute surfaces. A rigorous transfer function approach is developed that permits separation of the effects of gear tooth errors and gear design parameters, thereby permitting independent assessment of the effects of gear design parameters on the vibratory excitation. The theory is applicable to both helical and spur gears and is illustrated using measurements of tooth‐spacing errors and tooth profiles obtained from a pair of spur gears.
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43.40.At Experimental and theoretical studies of vibrating systems

Vibration of a plate having a circular inside edge and a cornered outside edge consisting of arcs

Kosuke Nagaya

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1788-1794 (1979); (7 pages)

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This paper is concerned with a transverse vibration problem of a thin plate having a circular inside edge and a cornered outside edge consisting of some arcs. The classical plate theory is applied and the eigenvalue problem of the plate is solved by the use of the exact solution of the equation of motion which satisfies the inner boundary conditions. The boundary conditions at the outer edge are satisfied by means of the Fourier expansion method. Numerical calculations are carried out for a plate having a clamped circular inside edge and a free outer one consisting of three arcs. Experimental results are also given as an additional check of this analysis.
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43.40.Dx Vibrations of membranes and plates

On the analysis of the doubly connected problem of vibrating polygonal plates

Kosuke Nagaya

J. Acoust. Soc. Am. Volume 66, Issue 6, pp. 1795-1800 (1979); (6 pages)

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In this paper a method for solving vibration problems of thin polygonal plates, with circular inside edges, is presented. The frequency equations of the polygonal plates are given for various combinations of outer and inner boundary conditions. Numerical calculations are carried out for cases of triangular, square, pentagonal, and hexagonal plates.
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43.40.Dx Vibrations of membranes and plates
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