Volume 44, Issue 1, July 1968

Establishment of Objective Criteria Reflecting Subjective Response to Roller‐Bearing Noise
View Description Hide DescriptionIn recent years, the question of noise generated by rolling‐element bearings has been given considerable attention. That a certain irreducible “minimum” noise is created by a properly functioning bearing has been pointed out in earlier work. Acceptable roller‐bearing noise levels above this minimum are regarded in this paper as being, of necessity, set by subjective standards. The paper addresses itself first to the validity or consistency of certain subjective evaluations of bearing noise made by a group of observers in representative circumstances. Next, the question is examined as to what quantitative objective measurements are to be made in order to reflect accurately the character of the subjective evaluations. Finally, correlations between objective and subjective data are shown to be good. A representative method is thus defined for providing objective criteria that reflect subjective appraisal in this type of problem.

Method of Axial Testing for Roller‐Bearing Noise Qualities
View Description Hide DescriptionA number of investigators have studied the vibration of rolling element bearings by taking samples of bearing‐race vibratory velocity, acceleration, or displacement at one point on the race, the bearing being run in a somewhat isolated environment. While such methods have led to considerable progress in the evaluation and amelioration of bearing‐generated noise, there has been a constant trend toward improvement of the methods. One promising step in this process is reported here. The present paper discusses the replacement of accelerometer radial testing by accelerometer axial testing, the new connecting link between bearing and accelerameter being a metallic exponential horn. The horn technique avoids problems of accelerometer strain sensitivity and dependence of results upon accelerometer angular orientation with respect to specific bearing anomalies.

Detection of Noiselike Sounds in Telephone Speech
View Description Hide DescriptionA method of separating noiselike sounds from vowel/vowellike sounds where the speech is of telephone quality is presented. This procedure involves the use of the χ^{2} nonparametric test, which analyzes the fluctuations of the time waveform and separates the speech into two classes depending on the randomness of the waveform. Initial computer simulations show the feasibility of the method, but since the recognition networks must operate in real time and the χ^{2} test is nonlinear, a linear model to the χ^{2} test is constructed that can be easily implemented, operate in real time, and obtain an efficiency close to that of the χ^{2} test. The false‐alarm and false‐recognition rates obtained using the linear model on a test sentence of 45 phonemes and 6‐sec duration are in the order of 12% and 85%, respectively.

Speech Recognition as a Function of Channel Capacity in a Discrete Set of Channels
View Description Hide DescriptionThere have been many attempts to perform a frequency analysis of speech and to use the outputs of this analysis to provide cutaneous stimulation. The results of these tests have left in doubt the issue of whether or not cutaneous recognition of speech is actually possible. In addition to other difficulties, an optimum frequency analysis has never been achieved. Instead, filtering configurations have been chosen essentially arbitrarily. The systems considered may well have had insufficient channel capacity for speech recognition even in the event that the tactile stimulators were arranged in an optimum manner. In this paper, several sets of finite frequency band to discrete channels filters were considered. The frequency of each discrete channel was constrained to the fixed center frequency of the corresponding band so as to be directly translatable to the position of a tactile stimulator. Tests were conducted to measure the auditory recognition rate of speech, resynthesized as the sum of these discrete channel signals. From these measurements with different numbers of channels, a representation of recognition rate as a function channel capacity was obtained. It is anticipated that these results will be helpful in the choice of the optimum filtering configuration for test in actual tactile recognition.

Design of a Concentrator by an Ultrasonic‐Ray Technique
View Description Hide DescriptionAn experimental study is made of the design parameters and the construction of a power ultrasonic concentrator. The technique is that of generating “rays” at the surface of a ferroelectric short cylinder vibrating in its lowest‐frequency mode. A plot is made of the surface motion components of the cylinder, and it is found that the predominant components are radial rather than axial. The disseminator shape is determined by the internal ultrasonic‐ray configuration that involves direction, reflection, and impingement upon the surface of a processing cavity. The resulting body is, essentially, a truncated ellipsoid of revolution whose outer surface is made of conic segments to facilitate construction. A ferroelectric disk is bonded at the center of the truncated flat surface and is driven by an oscillator and a power amplifier. In operation, a strong sonic field was observed within the cavity whose center is that of one focal point of the ellipsoid of revolution. The other focus determines the normal truncating plane that contains the driving transducer. Two devices are constructed where the number of reflecting planes is varied, and their feasibility as particulate‐aerosol generators is disclosed. A simplified version of the device, where three reflecting surfaces are used, is able to form an aerosol cloud made from 0.5 gm of 100‐μ aluminum platelets within 3 sec after initiation. The frequency of the devices tested is 46.6 kHz, which coincides with that of a disk 5.1 cm in diam by 3.8 cm thick, coupled to a large piece of aluminum. A photographic study of the disseminator environment disclosed the formation of unexplained concentric rings about this vibrating device and visible on the surface containing said device.

Azimuth and Elevation Errors Inherent in Sound‐Ranging Calculations
View Description Hide DescriptionA square army of four microphones can be used to detectacoustic signals propagated through the atmosphere. Use of such an array allows the determination of the azimuth and elevation angle of the acoustic wave. Possible errors in these angles and the means of determining their respective values are considered in this paper. By making use of the known arrival times of the signals of each microphone, expressions for the error in azimuth and elevation angle are derived.

Fundamental Results Concerning Integral Representations in Acoustic Radiation
View Description Hide DescriptionAttention has of late been drawn to the use of integral equations for obtaining numerical solutions to problems of steady‐state harmonic acoustic radiation. Essentially, three distinct methods have been reported: the Simple Source Method, the Surface Helmholtz Integral Equation, and the Interior Helmholtz Integral Relation. The present paper contains two major theoretical results. Firstly, nonexistence failure at certain frequencies of the simple‐source method is clearly indicated. Secondly, it is shown that the surface Helmholtz integral equation fails by nonuniqueness at the same frequencies. In both cases, failure occurs at each of the discrete Dirichlet eigenfrequencies for the region enclosed by the vibrating surface. Physical interpretations and examples of the theoretical results are included.

Relation of the Exact Transient Solution for a Line Source near an Interface between Two Fluids to Geometrical Acoustics
View Description Hide DescriptionThe exact transient solution obtained by the Lamb‐Cagniard‐Smirnov‐Sobolev‐Pekeris method is summarized for waves from a line source of arbitrary time dependence near an interface between two fluids of different sound speeds and densities. The solution is used to give an alternate derivation of the pressure (or dp/dt for the refracted arrival wave) increments at times of onset of the reflected, refracted arrival, and transmitted waves originally obtained by the geometrical acoustics theory of Friedrichs and Keller for incident weak shocks. The exact theory shows that the Friedrichs‐Keller results (rigorously valid at onset times) may be extended to give an asymptotic approximation for waveforms following onset times. The strength of the logarithmic singularity accompanying the refracted arrival wave when the incident pressure is discontinuous is also derived from the exact theory.

Acoustic‐Wave Propagation past a Sinusoidal Surface
View Description Hide DescriptionThe acoustic field produced by a plane wave propagating in a direction parallel to a sinusoidal surface is examined analytically. When the surface wavenumber is larger than twice the acoustic wavenumber, it is found that the disturbance produced by the surface decays exponentially with distance from the surface. However, when the surface wavenumber is smaller than twice the acoustic wavenumber, it is found that a portion of the disturbance propagates to infinity.

Improved Integral Formulation for Acoustic Radiation Problems
View Description Hide DescriptionThree different integral formulations have been used as a basis for obtaining approximate solutions of the exterior steady‐state acoustic radiation problem for an arbitrary surface whose normal velocity is specified: (1) the simple‐source formulation, adapted from potential theory; (2) the surface Helmholtz integral formulation, based on the integral expression for pressure in the field in terms of surface pressure and normal velocity; and (3) the interior Helmholtz integral formulation, in which the surface pressure is determined by making a certain integral vanish for all points interior to the radiating surface. For certain characteristic wavenumbers, it is shown that no solution of the simple‐source formulation exists in general and that there is no unique solution of the surface Helmholtz integral formulation. The interior Helmholtz integral formulation is subject to similar difficulties and has undesirable computational characteristics. A Combined Helmholtz Integral Equation Formulation (CHIEF) that overcomes the deficiencies of the first two methods and the undesirable computational characteristics of the third, is described. The significant improvement over the previous three methods, which is accomplished through the use of CHIEF, is illustrated by numerical examples involving spheres, finite cylinders, cubes, and a steerable array mounted in two different boxlike structures.

Response of an Elastic Plate to a Cyclic Longitudinal Force
View Description Hide DescriptionEnergy supplied to the edge of a semi‐infinite plate by a sinusoidal in‐plane force, uniform across the thickness, is found to be divided among the various propagating modes in such a manner that one type of mode receives most of the energy. Because the mode shapes change with frequency, the same mode is not dominant at all frequencies. The dominant mode, at any frequency, is that mode that most closely resembles the symmetrical Goodier‐Bishop wave having a dilatational portion independent of the thickness coordinate. Computations were performed over a range of frequencies, extending to frequencies where five propagating modes are involved, and graphs of results are presented.

Pulse Shapes of Spherical Waves Reflected and Refracted at a Plane Interface Separating Two Homogeneous Fluids
View Description Hide DescriptionA review is given of Cagniard's method for determining the shapes of the reflected and transmitted waves resulting from a point source of spherical waves of arbitrary waveform located in one of two homogeneous fluids separated by a plane interface. Symmetry relations enable the basic Cagniard solutions for reflection to be obtained from those or transmission, and a reciprocity relation shows that the formulas for transmission when the source is located in one of the two fluids can easily be obtained from the formulas for transmission when the source is located in the other fluid. An Appendix lists explicit solutions for all cases (reflection or transmission with the source located in the fluid of higher or lower soundvelocity). The propagation of jump discontinuities the Cagniard solution is shown to be in agreement with geometrical ray theory. Impulse reflection and transmission coefficients are obtained from the asymptotic values of the basic Cagniard solutions. It is then demonstrated that these same coefficients can be deduced from a solution to Laplace's equation.

Pulse Shape of Totally Reflected Plane Waves as a Limiting Case of the Cagniard Solution for Spherical Waves
View Description Hide DescriptionThe well‐known solution for the pulse shape of a totally reflected plane wave is shown to be identical with the leading term in an asymptotic expansion of the Cagniard solution for spherical waves. This extreme approximation does not yield the correct impulse required by a general theorem. The second‐order term in the asymptotic expansion yields an impulse contribution comparable to that of the first term, and the sum has the correct value. A specific illustration of the expansion procedure is given for the case of a triangular pulse at grazing incidence and the results are compared with the exact solution obtainable for this case.

Influence of Nonlinearities on the Degenerate Vibration Modes of a Square Plate
View Description Hide Descriptionvon Karman's nonlinear plate equations are used to investigate the effects of nonlinearities on the degenerate vibration modes of a square plate. Galerkin's procedure is used to reduce the problem to two coupled nonlinear differential equations, and approximate solutions are obtained by the method of harmonic balance. For linear vibrations, the degenerate modes can be superimposed to form an infinite variety of nodal patterns. However, the nonlinear analysis shows that for finite amplitude vibrations the modes combine to give only four distinct nodal patterns. These nodal patterns are oriented along the lines of symmetry of the plate.

Diffraction of Antiplane Shear Waves by a Finite Crack
View Description Hide DescriptionThe scattering of polarized harmonic shear waves by a sharp crack of finite length under antiplane strain is considered. Use is made of integral transforms, which reduce the problem to the evaluation of a system of coupled integral equations. Special emphasis is placed on obtaining the detailed structure of the crack‐front stress and displacement fields, which control the instability behavior of cracks in brittlematerials. While the dynamic stresses around the singular crack point are found to be qualitatively the same as those encountered under statical loading, they differ quantitatively in that the intensity of the dynamical stress field, which may be regarded as a measure of the force tending to cause crack propagation, depends on the incident wavelength. At certain wavelengths, this intensification is shown to be larger than the static case. The method of solution in this paper applies equally well to boundary value problems in electromagnetic and acoustic theory.

Modified, More Rapidly Converging Modal Series Representation for Mechanical Admittance
View Description Hide DescriptionThe standard modal series representation of mechanical admittance may be slowly convergent, especially at antiresonance, for structures that may exhibit a spatially localized response to a spatially localized excitation, e.g., beams on elastic foundation as well as plates and shells. A William's modal acceleration approach is used to arrive at a modified, faster converging, modal series representation for the displacement admittance of a general, finite, linear elastic structure which contains damping. A freely supported, damped, circular cylindrical shell, driven by a radial point force, is employed as an example for a comparison of the modified and the standard modal representations for driving‐point and transfer displacement admittance in various frequency bands. At a shell antiresonance, the convergence of the modified driving‐point admittance representation is very rapid in comparison to that of the standard modal representation. This is particularly true for that shell antiresonance that lies between the two most widely separated shell resonances. As one proceeds from the case of very light to intermediate shell damping, the convergence, at antiresonance, of both types of admittance representation improves considerably.

Experiment on Sound Propagation in Shallow Water with Velocity Structure
View Description Hide DescriptionAn investigation into the propagation of sound in shallow, isovelocity water was carried out previously using an extensive area of the continental shelf off the west coast of New Zealand. This area has been re‐examined when a negative velocity gradient was present in the water layer. The results obtained show that this area provides a classic example of normal‐mode propagation in shallow water under conditions of both constant sound velocity and a negative gradient. The values of attenuation obtained are on the whole greater when a negative gradient occurs, but their general behavior with frequency is similar in both cases. In addition, the attenuations are comparable with those obtained in other shallow‐water areas and are consistent with the predictions of normal‐mode theory.

Domed Sonar System
View Description Hide DescriptionAn analysis of the changes that are induced by a dome in the signal to‐noise (S/N) ratio of a sonar system is performed. Both the transducer system and the dome are idealized in this analysis. A blanket dome and a plate dome are considered. It is shown that a properly designed dome can be made transparent to supersonic spectral components in the external pressure field and can reduce the response of the transducer system to subsonic spectral components in this pressure field. A dome can thus be emp oyed to increase the S/N ratio of a sonar system that is subjected to noise‐pressure fields that possess high density of subsonic spectral components. The external pressure field considered in this paper is composed of the blocked pressure field induced by an incident plane acoustic‐pressure field (the signal‐pressure field) and the blocked pressure field of a subsonic turbulent boundary layer (the noise‐pressure field).

Uniform Spherical Radiation through Thick Shells
View Description Hide DescriptionWave propagation from a spherical transducer through a fluid medium and a concentric viscoelastic spherical shell (not necessarily thin) to a fluid medium of infinite extent has been analyzed. Formulas for the acoustic field when the transducer is driven with constant‐amplitude sinusoidal radial velocity, have been derived. Numerical results show that the insertion loss due to the presence of the shell is an oscillatory function of frequency, indicating the existence of regions of favorable and unfavorable transmission, which are primarily controlled by the transducer‐shell spacing. The magnitudes of the maxima and minima of the insertion loss are determined primarily by the mass per unit area of the shell. The insertion‐loss function does not depend strongly upon the elastic constants or the material dissipation of the shell. A simple model consisting of a fluid‐filled tube with a piston and a spring‐supported “masslike” wall exposed to ambient fluid has been found to be a useful tool for interpreting the results. The analysis has been extended to the case of uniform radiation in the presence of a multilayered viscoelastic spherical shell. Numerical results show that by properly choosing the parameters, a low‐pass filter effect can be obtained.

On the Detection of a Known Signal in a Non‐Gaussian Noise Process
View Description Hide DescriptionIn this paper, three receiver designs for the detection of a known signal in an additive non‐Gaussian noise process are considered. The noise process consists of white Gaussian noise modulated by a random‐spectrum level. The first receiver considered is an optimum (likelihood) processor and the remaining two receivers are suboptimum designs consisting of a cross correlator and a likelihood correlator. The basic processing operations of the three receivers are investigated and compared on the basis of their effects in observation space. The performance of each receiver is evaluated and presented in terms of ROC curves. A comparison of the performance curves indicates a loss in optimum performance as compared to the Gaussian noise case and a significant loss in performance of the suboptimum receivers relative to the optimum receiver.