Index of content:
Volume 57, Issue 5, May 1975

Sound radiated by low‐frequency vibrations of slender bodies
View Description Hide DescriptionSimple and practical formulas are derived for computing the near or far sound‐pressure field radiated by a slender body which vibrates in a low‐frequency whipping mode, or a low‐frequency accordion mode in water. The calculations can be made by simple quadratures, and require a specification of the modal vibration pattern along the length, the cross‐section area along the length, and a mean radiation impedance coefficient which can be estimated from independent data or calculated from an explicit formula derived here. Comparison is made with several other methods used to analyze these sound‐pressure fields. The analyses are specific examples of a general technique for transforming a solution for the incompressive field of a body in low‐frequency vibration to a solution that is valid in the near‐ or farfield of an acoustic compressible medium.
Subject Classification: 20.55; 40.20.

Acoustic response in a liquid overlying a homogeneous viscoelastic half‐space
View Description Hide DescriptionAn analytical model is developed for use in marine sediment identification on the Continental Shelf. The effects of rigidity and internal energy dissipation are taken into account by treating the subbottom as a viscoelastic solid. The acoustic response due to a harmonic point source is computed using a Green function formalism. Expressions are given for the frequency‐domain Green function for subcritical and supercritical incidence angles. The response is interpreted as the sum of direct, reflected, and refracted waves.
Subject Classification: 20.30; 20.15.

Calculation of the range‐Doppler plot for a doubly spread surface‐scatter channel at high Rayleigh parameters
View Description Hide DescriptionNo abstract supplied.
Subject Classification: 20.15, 20.30; 28.10; 60.20.

N‐parameter ducts
View Description Hide DescriptionThe exact solution to Webster’s differential equation for sound in an initial variable area duct is used to generate new families of duct shapes with their exact solutions. In most cases the shapes and their solutions may be expressed in terms of nth‐order determinants (Wronskians, in fact) whose elements are solutions to the initial duct and derivatives of these solutions. The nth‐order determinant contains 2n+1 arbitrary parameters which are available for the design of ducts. The initial duct may be any duct for which the solution to Webster’s equation is known. The method is applied to a uniform duct to derive new families of ducts where both the duct shape and its solution are expressed in closed form in terms of elementary functions. Special cases include filters, constrictions, and new horn shapes in addition to the well‐known conical horn, Bessel horns, the exponential horn, the Salmon horn, and the sinusoidal duct.
Subject Classification: 20.45; 85.60.

Acoustic waves in ducts with sinusoidally perturbed walls and mean flow
View Description Hide DescriptionAn analysis is presented of the propagation of acoustic waves in a hard‐walled duct with sinusoidally perturbed walls and carrying mean flow. The results show that resonance occurs whenever the wavenumber of the wall undulations is approximately equal to the difference between the wavenumbers of any two propagating modes. It is shown that neither of the resonating modes could exist in the duct without strongly exciting the other resonating mode.
Subject Classification: 20.45, 20.60; 28.60.

Some relations between energy yield of atmospheric nuclear tests and generated infrasonic waves
View Description Hide DescriptionThe relation between energy yield in megatons (MT) of atmospheric tests during 1968–1971 at French Polynesia and infrasonicwaves recorded at Peñas in Bolivia (a distance of approximately 7300 km) is studied. Yields were estimated from period and amplitude of the early portion of the waveforms using the theoretical relation of Pierce and Posey [Geophys. J. R. Astron. Soc. 26, 341–368 (1971)]. In the present paper, the relation of this derived yield to the Power spectrum of major portions of the waveforms is investigated. The magnitude of the square root of this spectrum that can be considered proportional to the Fourier Integral for a Yield Sample Time (i.e., spectral amplitude) typically has two characteristic peaks, the first of which appears to nearly directly proportional to yield, the proportionality constant being 300 μbar sec^{1/2}/MT. Another waveform feature exhibiting strong correlation with yield is the time duration of the gravity wave train which precedes the acoustic mode waves. For smaller yields, this also appears to vary nearly linear with yield, the proportionally constant being 1000 sec/MT up to about 1 MT. The application of these conclusions to other source–receiver geometries and to other meteorological conditions remains a topic for future study.
Subject Classification: 28.20, 28.30.

Perturbation theory for scattering of sound from a point source by a moving rough surface in the presence of refraction
View Description Hide DescriptionA general perturbation theory is presented which is valid for small surface waveheights and for acoustic wavelengths of the order of the ocean‐surface correlation length. Formal solutions for the perturbed field are given and are specialized, to the second order of approximation, for the case of a random oceansurface. The scattering reduces the intensity of the carrier (source) signal and creates signal sidebands that are not in general symmetric in amplitude about the carrier. A pair of system functions for the signal sidebands is defined.
Subject Classification: 30.40, 30.30, 30.25; 20.15.

Normal‐mode theory of underwater sound propagation from stationary multipole sources: results for a realistic sound‐speed profile
View Description Hide DescriptionA normal‐mode approach that solves the wave equation governing underwater sound propagation from a point source with directivity expressible as an expansion in spherical multipoles is summarized. The theory is extended by the development of a general theory of propagation loss for multipole sources of arbitrary order. Exact long‐range pressure field and propagation loss expressions are developed and presented for the first three multipole orders. Numerical results of the pressure fields and the propagation loss for monopole, dipole, and quadrupole sources are presented for the case of a realistic sound‐speed profile.
Subject Classification: 30.20; 20.15, 20.40.

Cancellation of turbulent boundary‐layer pressure fluctuations
View Description Hide DescriptionAn optimum beamforming scheme has been applied to a system of sensors flush mounted in a turbulent boundary‐layer pressure field. It is shown that flownoise propagating at subsonic velocities can be significantly discriminated against while passing, undistorted, a sonic signal. Two‐ and three‐sensor systems are evaluated and extrapolations to a N‐sensor case are made. Comparisons of the two‐ and three‐sensor cases are made with a single sensor of finite size as well as with some previously reported results from a method by Jorgensen and Maidanik (J. Acoust. Soc. Am. 43, 1390–1394 (1968)].
Subject Classification: 30.70, 30.85.

Sound‐velocity perturbations due to low‐frequency motions in the ocean
View Description Hide DescriptionThe properties of low‐ and intermediate‐frequency external and internal waves in the open ocean, and the nature of the acoustic velocity perturbations they produce, are examined. The basic principles are illustrated with theoretical calculations based on representative oceanic cases. Such calculations provide a rational estimate for the vertical and horizontal dependence of the perturbation of the acoustic velocity field due to external and internal waves. External waves can cause travel‐time fluctuations by their horizontal velocity fluctuations (or fluctuations in the total soundvelocity).Internal waves can cause acoustic travel‐time fluctuations both by their vertical displacement of isotherms (or isolines of sound speed) and by their velocity fluctuations (or fluctuations in total soundvelocity). Both external and internal waves can have horizontal wavelengths ranging from a fraction of a kilometer to hundreds of kilometers. The longer waves can be effective in producing travel‐time fluctuations over long propagation paths; the shorter waves are probably most influential in the scattering of acoustic energy.
Subject Classification: 30.20.

Amplitude shading of sonar transducer arrays
View Description Hide DescriptionAmplitude shading is an important technique for controlling the beamwidth and sidelobe level of transmitting and receiving arrays in sonar and radar. The traditional method of Dolph–Tchebyscheff synthesis for the determination of array amplitude shading or weighting coefficients is, however, highly restrictive despite the extension and generalizations by many workers following Dolph. This paper outlines an entirely new method of finding these shading coefficients by minimizing the power received by the array in an isotropic noise field exclusive of a three‐dimensional spatial slice around the mainbeam direction. The method is completely general in the sense that it is applicable to any discrete array of transducers arbitrarily distributed in a three‐dimensional space. As an illustrative example, nonuniformly spaced linear arrays (which are necessary for reasons of economy and operation over a band of frequencies) are shown to have been successfully shaded to acceptable pattern shape and sidelobe levels. In the special case of equally spaced linear transducer arrays, the new method of shading yields an essentially identical mainbeam shape as Dolph–Tchebyscheff’s for the same sidelobe level, while the total power received (or transmitted) via the sidelobes is actually slightly less than one half of that by the latter synthesis. Necessary detailed mathematical formulas for applying the method to circular or arc arrays are also suggested.
Subject Classification: 30.82; 20.15; 60.30.

Pulse‐echo method of investigating the properties of mechanical resonators
View Description Hide DescriptionVibrational sensors can be designed in such a way that the frequency of one of their modes of vibration is a function of temperature, pressure, density, or other parameter, making them the basis of various instrumentation transducers. These can be driven remotely by means of a line carrying bursts of plane waves of stress analogous to sonar or radar. The simple analysis of such a system, where only one mode at a time is considered, is unsatisfactory, and a complete general theory has been developed. This applies to an extended object with an arbitrary pattern of resonant frequencies, internal energy losses, and mechanical couplings to the line. The basic Navier–Stokes equation of motion was solved for this boundary‐value problem to give a pole‐zero diagram for the system. Computer programs were used to invert the function into the time domain and plot the echo‐return traces. The theory has been used to relate experimental observations of the spectra of isotropic disks of a variety of materials to recent theoretical studies. Accurate values of elastic constants and their temperature coefficients have been obtained. The special case of a line resonator, which has a harmonic spectrum, enables the internal friction losses to be evaluated absolutely. To make an automatic system where the drive frequency follows the resonant frequency, a number of control signals are possible. A computer program was prepared to determine the parameters of the various phase control loops available.
Subject Classification: 40.24.

Wave propagation in nonuniform elastic rods
View Description Hide DescriptionAsymptotic solutions are obtained for elastic waves propagating in any nonuniform rod, with an arbitrary cross section which varies slowly along the length of the rod. The solutions are valid when the variation in cross section along the rod is sufficiently slow. For each mode the result is of the WKB type, involving a phase function, an amplitude function, and a mode form. The phase velocity and the mode form at each cross section are obtained from the solution for the corresponding uniform rod. The amplitude function is obtained from an equation which is equivalent to conservation of energy. An application of the results is made to long waves. The linear theory of elasticity is used throughout.
Subject Classification: 40.20, 40.22; 20.15.

Motion of a three‐layered elastic–viscoelastic plate under fluid loading
View Description Hide DescriptionA mathematical model of a three‐layered plate structure is employed to study the vibration characteristics of a composite panel under the influence of fluid loading. The effects of heavy, in‐water fluid loading is adapted in the analysis by the definition of normal and cross‐coupling coefficients for the acoustic pressures which accompany the normal modes of vibration. The numerical solution is presented for relatively low‐mode resonant response. The results indicate that structural stiffness and damping constitute primary factors in the resonant response and radiated pressures displayed by a finite rectangular plate. It is shown that constrained‐layer damping, a normal‐mode component, affects a significant reduction in the degree of cross coupling between resonant and nonresonant modes.
Subject Classification: 40.24; 20.15.

Moment impedance of internally damped rectangular and square plates with simply supported boundaries
View Description Hide DescriptionTheoretical expressions for the moment impedances of simply supported, internally damped, rectangular and square plates are presented. The plates are driven either centrally or at an arbitrary point by a bending moment, the line of action of which has arbitrary direction. In calculations made to illustrate the frequency dependence of moment impedance, plate damping of the solid type has always been assumed. The expressions for moment impedance do not contain a logarithmic term that becomes infinitely large as the separation of the moment‐producing pair of forces normal to the plate surfaces is reduced to zero, and so contrast with prior expressions that have been derived for the moment impedance of infinite plates.
Subject Classification: 40.24.

Vibration of generally orthotropic skew plates
View Description Hide DescriptionThis paper presents a numerical method for finding the natural frequencies and mode shapes of generally orthotropic clamped skew plates subjected to in‐plane forces. As illustrations, two aspects are considered. First, the natural frequencies and mode shapes of a rhombic plate (without any in‐plane forces) are determined for different orientations of the axes of orthotropy. Marked changes in the mode shapes, which are not easily predictable, are found to take place. Secondly, the influence of in‐plane forces (both unidirectional tension/compression and uniform shear) on the natural frequencies is studied. The results indicate that in all cases but one the relationship between the square of the frequency and the in‐plane force is nonlinear. The numerical method employed makes use of integral equations of beams with appropriate boundary conditions, along the skew coordinates, for transforming the governing differential equation into a set of algebraic equations. These equations are then solved to find the eigenvalues and eigenvectors.
Subject Classification: 40.24.

Dispersion of flexural elastic waves in honeycomb sandwich panels
View Description Hide DescriptionThe phase velocity of flexural waves traveling along a 1‐in.‐thick honeycomb sandwich panel has been experimentally determined from 170 Hz to 50 kHz by using three techniques: measurement of resonant frequencies of beam‐shaped samples in forced vibration, measurement of nodal spacing in standing wave patterns on beam‐shaped samples, and measurement of the change in time delay of a particular phase feature of a wave packet as a function of propagation distance on large plate samples. The experimentally determined velocities ranged between 2.2×10^{4} cm/sec at 170 Hz to 1.18×10^{5} cm/sec at 40 kHz. This dispersion arises primarily from the geometrical effect of the finite thickness of the panel and agrees well with two theoretical models; a plate theory and an elasticity theory, each of which treats the core as a continuum. Above 40 kHz, the predictions of the two models differ greatly for the particular panel geometry studied. The experimental phenomena become more complex and appear to agree with neither model, quite possibly due to the neglect of the periodicity of the core. A brief description of these results is given.
Subject Classification: 40.24; 35.26.

Identification of structural parameters using low‐amplitude impulsive loading
View Description Hide DescriptionA parameter‐estimation procedure is developed using the average of the response of a structure to a sequence of impulsive force loadings. The finite Fourier sine and cosine transforms of the averaged response are computed. using a mathematical model of a linear one‐degree‐of‐freedom system, whose acceleration response has normal uncorrelated noise added to it, the joint probability density function of the Fourier coefficients is found. Applying the principle of maximum likelihood, estimates for the percent of critical damping, the natural frequency, and the magnitude of the impulse are computed using Marquardt’s method. Data were generated by digital simulation, analog simulation, and by exciting an experimental model. The resulting estimates and their confidence intervals are shown in tabular form. Error analysis due to random impulsive forces, finite pulse width of the force loading, and correlation of the noise are performed. The technique can be used in estimating the damping of systems in which the response to impulsive loading can be measured but is small relative to the ambient response.
Subject Classification: 45.40; 40.35.

Effects of flanking and test environment on lab–field correlations of airborne sound insulation
View Description Hide DescriptionPrevious attempts to correlate lab and field sound‐insulation performance have been based on a comparison of the lab sound‐transmission class (STC) and the field sound‐transmission class (FSTC). In this study comparisons of the 1/3‐octave‐bandwidth transmission loss (TL) values are made taking into account partition transmission, flanking transmission, and test‐environment factors. An experimentally determined flanking TL is obtained through a quantitative relationship between the partition, flanking, and field TL. This determination allows separation of test environment factors related to diffuseness and modal distribution from flanking transmission. Also noted under field conditions are interactions between the coincidence phenomena and the sound field under absorptive room conditions (reverberation time = 0.5 sec), demonstrating that the properties of a partition depend in part on the dwelling‐unit furnishings. Because all the test‐environment effects observed resulted in TL values higher than those of a properly adjusted classical lab, the conclusion is drawn that for replicate partitions field TL data may under certain conditions exceed lab TL data by as much as 5 dB when no flanking exists. Specific field TL values are likely to be lower than lab TL values owing to the accumulated effects of flanking, leaks, and assembly differences.
Subject Classification: 55.75.

Long‐aperture parametric receiving arrays
View Description Hide DescriptionThe nonlinear interaction of a strong high‐frequency local sound source with a weak low‐frequency sound signal can be used to construct a system (’’parametric receiving array’’) for passive reception of the signal. Analytic formulas exist which describe the behavior of such a system. In this note, we develop a design procedure using these formulas, which leads to optimal system parameters. The procedure is illustrated by the design of parametric arrays for the reception of underwater sound signals in the 25–100‐Hz band. Beamwidths of the order of 15 ° seem feasible, while beamwidths as narrow as 5 ° are probably not feasible. Such an array could be deployed in water without the necessity of phasing sensors along the (necessarily long) aperture.
Subject Classification: 25.35; 30.82; 60.10.