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Feb 1980

Volume 67, Issue 2, pp. 377-751

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Free‐wave propagation through combinations of periodic and disordered systems

A. S. Bansal

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 377-389 (1980); (13 pages) | Cited 2 times

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A method has been developed for the analysis of free‐wave propagation through a combination of two different semi‐infinite, monocoupled, periodic systems joined together without or through a finite periodic/disordered system. The general expressions derived from the analysis have subsequently been adapted to study the free flexural wave propagation in beam‐type systems. Results have been computed and discussed for different combinations of beam systems which include semi‐infinite periodic beams joined (i) through different periodic and disordered finite beams and (ii) without an additional beam at the junction. Attenuation of free waves in such systems, caused by six‐span finite beam disorders, has been studied and compared to the attenuation of free waves in an infinite periodic beam and when one of its elements is different from the rest. Although multispan finite beam disorders generally attenuate the propagating incident waves, at certain discrete frequencies they offer no obstruction to such waves. The conditions under which this can happen have been identified and explained. It has been pointed out what type of finite disordered beams can be employed to prevent vibrational energy from flowing from one periodic system to another. The energy flow through the combined system, as governed by the transmitted free wave, has been discussed. The conditions have been explained under which two interacting attenuating flexural waves can transmit energy, although they are incapable of doing so individually.
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43.20.Bi Mathematical theory of wave propagation

Scattering of stationary acoustic waves by an elastic obstacle immersed in a fluid

Anders Boström

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 390-398 (1980); (9 pages) | Cited 8 times

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The scattering of stationary acoustic waves by a bounded elastic obstacle in an inviscid fluid is considered. The developed formalism is an extension of the transition matrix method, which has been given by Waterman for acoustic, electromagnetic, and elastic scattering. In fact the problem at hand is more complex than the elastic case, something which is apparent in the solution. It is possible to obtain some different forms for the transition matrix, depending upon whether the Rayleigh hypothesis enters or not. It is worthy of notice that the more general formalism, i.e., the one not assuming the Rayleigh hypothesis, is also the more efficient numerically. Numerical results are given for spheroids and an object resembling the number ’’8.’’
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43.20.Fn Scattering of acoustic waves
43.20.Tb Interaction of vibrating structures with surrounding medium
43.20.Bi Mathematical theory of wave propagation

Multiple scattering of elastic waves by bounded obstacles

Anders Boström

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 399-413 (1980); (15 pages) | Cited 4 times

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The transition matrix method for stationary elastic waves is extended to a great class of obstacles characterized by piecewise constant properties. First, the translation properties of the basis functions is used to treat two and, then, several homogeneous obstacles, and thereafter an obstacle with consecutively enclosing layers is considered. It is then indicated how these two basic methods of combination can be applied to treat more complex cases, including an obstacle consisting of several nonenclosing parts. Finally, we give some numerical applications to configurations of spherical and nonspherical obstacles in and below the resonance region.
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43.20.Fn Scattering of acoustic waves
43.20.Bi Mathematical theory of wave propagation

Resonance theory of elastic shear‐wave scattering from spherical fluid obstacles in solids

D. Brill, G. Gaunaurd, and H. Überall

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 414-424 (1980); (11 pages) | Cited 3 times

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The vector potential for an arbitrarily polarized shear wave in an elastic (lossless) medium incident on, and scattered by, a spherical fluid occlusion is expanded in vector spherical harmonics. The boundary conditions are dealt with for this incident vector potential in terms of two (scalar) Debye shear potentials ψ and χ giving rise to what we have termed ’’s and t waves,’’ respectively. The s wave scatters into both another s wave and also mode‐converts into a compressional p wave. The t wave scatters only into another t wave with no mode conversion. Scattering amplitudes are cast in a series of resonance terms. The scattered p and s waves exhibit resonances; however, the t wave does not. We exhibit monostatic and bistatic plots of the first few partial‐wave amplitudes (n=1,2,3,...) for the sp, ss, and tt scattering modes. When the background amplitude corresponding to scattering from an evacuated spherical cavity is removed from each partial‐wave contribution, the remaining portion of the amplitudes is a clear series of liquid‐sphere resonances. We display these resonances as functions of the acoustic size kda of the cavity, and of the order n of each mode. This work completes the determination of the scattering matrix elements for a fluid sphere in an elastic medium which was commenced by us earlier with the study of resonance effects in pp and ps scattering.
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43.20.Fn Scattering of acoustic waves
43.20.Ks Standing waves, resonance, normal modes
43.35.Mr Acoustics of viscoelastic materials
43.40.Ph Seismology and geophysical prospecting; seismographs

Acoustic propagation in aperiodic transition layers and waveguides

Georges Canévet

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 425-433 (1980); (9 pages)

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Wave propagation in inhomogeneous media is studied by a new method, the ’’cutting‐out’’ Jessel’s method. Emphasis is on transition layers, where both the sound velocity and density variations are taken into account. Several classes of layers are studied and impedance matching by a smooth dioptre is described. By using the analogy between inhomogeneous media and waveguides, this property of impedance matching has been extended to connecting horns, thus leading to the definition of a new family : the aperiodic horns.
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43.20.Mv Waveguides, wave propagation in tubes and ducts
43.20.Bi Mathematical theory of wave propagation

Transient scattering of a piezoelectric wave from a crack

Harold A. Sabbagh

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 434-445 (1980); (12 pages)

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The problem of the scattering of transient antiplane shear electroelastic waves from a crack in a piezoelectric medium possessing 6‐mm symmetry is solved by determining the electric dipole density induced on the crack by the incident wave. An integral equation satisfied by the Laplace‐transformed dipole distribution is derived by appealing to the piezoelectric reciprocity relation. The solution of the integral equation is accomplished by expanding the dipole distribution in a series of first‐order spline functions with unknown coefficients and then applying the method of moments to transform the problem to a vector‐matrix one, which is readily handled by a computer. Inversion back into the time domain is effected by an efficient numerical method of inverting Laplace transforms. Results are given for the cases of normal and oblique incidence of the wave onto the crack.
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43.20.Bi Mathematical theory of wave propagation
43.38.Fx Piezoelectric and ferroelectric transducers
43.20.Px Transient radiation and scattering
62.30.+d Mechanical and elastic waves; vibrations

Asymptotic analysis for dispersive fluid filled tubes

T. Bryant Moodie and J. B. Haddow

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 446-452 (1980); (7 pages) | Cited 1 time

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In a previous paper [J. Acoust. Soc. Am. 64, 522 (1978)] we obtained a new approximate equation governing the propagation of small perturbations to the pressure in a thin‐walled fluid filled elastomer tube. There, the spatial fluctuations in the pressure perturbation for fixed time were evaluated numerically by a procedure based on the Fast Fourier Transform (FFT) algorithm. Here, by means of an asymptotic analysis, based on a modified steepest descent method, we explain an apparent anomaly in the numerical results by exhibiting the existence of a forerunner wave and investigate the accuracy of the large time asymptotic results, for times which may be regarded as small or intermediate, by comparing them with the results from the FFT algorithm. It is found that the results obtained from the asymptotic analysis are in close agreement with those obtained from the FFT for moderate times and in qualitative agreement for relatively small times. For nondimensional times greater than 100 the positions of the zeros of the pressure perturbation agreed with those obtained from the FFT to better than four significant figures for the main part of the disturbance.
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43.20.Bi Mathematical theory of wave propagation
43.20.Mv Waveguides, wave propagation in tubes and ducts
43.40.Ey Vibrations of shells

Scattering of a plane wave by a Schroeder diffusor: A mode‐matching approach

Hans Werner Strube

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 453-459 (1980); (7 pages) | Cited 1 time

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The two‐dimensional, scalar diffraction theory is developed for a diffusing surface as suggested by Schroeder, consisting of an array of ’’wells’’ of equal widths but different depths, separated by hard, thin walls. Diffusors of finite size as well as infinite, periodic ones are treated. Matching the plane waves in the free half‐space to the wave modes in the wells yields an infinite but discrete linear equation system in either case. For a periodic diffusor based on a quadratic‐residue (QR) sequence, numerical results are compared with measurements on a finite diffusor comprising two periods. The results are also compared with those obtained by approximating the diffusor as a locally reacting surface. The differences are, at most, a few decibels; the mode‐matching results are usually closer to the measurements. The uniformity of scattering is tested over a range of wavelengths of 1:4; QR sequences are superior to pseudorandom sequences.
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43.20.Fn Scattering of acoustic waves
43.20.Bi Mathematical theory of wave propagation
43.55.Br Room acoustics: theory and experiment; reverberation, normal modes, diffusion, transient and steady-state response

Diffraction by a planar, locally reacting, scattering surface

Hans Werner Strube

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 460-469 (1980); (10 pages) | Cited 1 time

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The integral equation for the diffraction of a plane scalar wave by a locally reacting, planar, finite scattering surface is treated, the surrounding being either a free space or a uniform locally reacting plane. The surface is described by a ’’generalized reflectivity’’—a bilinear function of the reflection factor containing two free parameters. By proper choice, the validity of Kirchhoff’s Fourier approximation of the diffraction pattern can be extended. Also the analytical treatment of some simple scattering and inverse scattering problems is alleviated. Numerical solution methods are then considered; apart from the direct method, only applicable to small equation systems, an iteration procedure is developed, based on Neumann’s successive‐approximation method. Proper choice of the two free parameters leads to fast convergence in most cases. The methods are tested with Schroeder’s quadratic‐residue‐sequence diffusors. Agreement with the measurements is acceptable but not perfect.
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43.20.Fn Scattering of acoustic waves
43.20.Bi Mathematical theory of wave propagation

Backscattering of short ultrasonic pulses by solid elastic cylinders at large ka

P. J. Welton, M. de Billy, A. Hayman, and G. Quentin

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 470-476 (1980); (7 pages) | Cited 1 time

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Backscattering measurements from solid brass, aluminum, and lucite cylinders in water have been performed at a ka of approximately 240 using short acoustic pulses. Numerous discrete echoes are received due to multiple internal reflections of the acoustic pulse at the boundary of the cylinders. Excellent agreement between the measured echo arrival times and the echo arrival times predicted by the theory of Brill and Überall [J. Acoust. Soc. Am. 50, 921 (1979)] is obtained for all of the cylinders. The amplitudes of the backscattered echoes from the brass and aluminum cylinders are also compared with theory and fair agreement is obtained.
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43.20.Fn Scattering of acoustic waves

A coupled system for subharmonics of any order

Ferial T. El‐Mokadem, Omotayo A. Seriki, and Robert W. Newcomb

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 477-483 (1980); (7 pages)

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A set of two coupled differential equations with square law nonlinearities is shown to have dominant and stable subharmonic solutions. Mathematical expressions characterizing the subharmonic solutions and their regions of stability are obtained. It is further shown that under appropriate choice of system parameters a resulting system described through these coupled differential equations possesses an exact stable subharmonic of any real order. From this, a design theory is obtained for a system which yields an arbitrary dominant subharmonic. The theory is also directly applicable to the creation of arbitrary stable harmonics.
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43.25.Ts Nonlinear acoustical and dynamical systems

Nonlinear interaction of two collinear, spherically spreading sound beams

Jacqueline Naze Tjötta and Sigve Tjötta

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 484-490 (1980); (7 pages) | Cited 1 time

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Nonlinear interaction of two collinear, spherically spreading sound beams is considered and applied to a discussion of parametric acoustic arrays. A general solution is given in the quasilinear approximation in terms of spherical harmonics and used to discuss the asymptotic behavior of the generated sound. Other expansions are also discussed. The main results, however, are obtained by introducing perturbation methods and deriving simplified equations governing the generated sound field, taking into account diffraction, absorption, and nonlinearity. From these equations, solutions are obtained and matched to give a solution valid in the whole space of propagation. Analytical and numerical results are presented and compared with available observations by different authors.
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43.25.Lj Parametric arrays, interaction of sound with sound, virtual sources

Sonomagnetic pulses from underwater explosions and implosions

J. F. Bird

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 491-495 (1980); (5 pages)

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The magnetic field that is generated by the sound field of a transient acoustic source immersed in electrically conducting fluid in the presence of ambient magnetism is calculated from a recent theory of such ’’sonomagnetic’’ phenomena. A general solution for the sonomagnetic pulse emitted by an arbitrary transient source is derived in terms of the acoustic pressure field directly (as opposed to a less certain source description). For a model pressure pulse, representative of underwater explosion/implosion pulses, the solution is reduced to tabulated functions. The result consists of a sonomagnetic shock plus precursor and relaxation waves, whose properties are discussed analytically and illustrated numerically.
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43.30.Qd Global scale acoustics; ocean basin thermometry, transbasin acoustics
43.35.Rw Magnetoacoustic effect; oscillations and resonance

A numerical simulation of the effects of oceanic finestructure on acoustic transmission

Terry E. Ewart

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 496-503 (1980); (8 pages) | Cited 2 times

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A simple numerical simulation model is presented which includes the effects of oceanic finestructure together with previously developed theoretical treatments of the effects of internal waves on acoustic transmission. The wave equation solution to particular layer geometries developed by Brekhovskikh [Waves in Layered Media (Academic, New York, 1960)] is combined with the theoretical model of acoustic scattering based on internal waves developed by Desaubies [J. Acoust. Soc. Am. 64, 1460–1469 (1978)]. In this treatment it is assumed that a single finestructure layer is passively advected by internal waves. The layer modulates the effects of internal waves. Experiments carried out at Cobb Seamount over a fixed, horizontal, wholly refracted path indicate that the power spectrum of the phase fluctuations is fit almost exactly by models based on internal waves only, while the power spectrum of the log amplitude fluctuations is not. In the present treatment the predictions of the phase fluctuations remain unaffected by the presence of finestructure, and the predicted power spectrum of the log amplitude is in considerably better agreement with observation.
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43.30.Bp Normal mode propagation of sound in water
43.20.Dk Ray acoustics
43.20.Wd Analogies

Averaging of fish target strength functions

Kenneth G. Foote

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 504-515 (1980); (12 pages) | Cited 5 times

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A general model for averaging the acoustic target strength functions of fish is stated in calculable form. It accounts for the influences of the distribution of generally coupled spatial and orientation states of fish, geometric perspective, and beam patterns on observations of target strength. The model is developed and applied to observation of fish by directional, downward‐looking sonars. A particular example is considered in which the sonar is represented by an ideal circular piston, the spatial distribution of fish is homogeneous, and the orientation distribution is spatially homogeneous and characterized by a uniformily distributed azimuthal variable and an independent, essentially normally distributed tilt angle variable. Averaged and averaged‐squared backscattering cross sections are computed from high quality gadoid target strength functions measured at two ultrasonic frequencies. Results for a sonar half‐beamwidth of 2.5 deg for three different realizations of the tilt angle distribution are expressed in the logarithmic domain and regressed linearly on fish length. The significance of species, frequency, and orientation distribution differences among the regressions is noted. Estimates of the mean ratio of averaged‐squared backscattering cross section and squared‐averaged backscattering cross section are presented.
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43.30.Dr Hybrid and asymptotic propagation theories, related experiments
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.30.Vh Active sonar systems
43.80.Jz Use of acoustic energy (with or without other forms) in studies of structure and function of biological systems

Source level model for propeller blade rate radiation for the world’s merchant fleet

Leslie M. Gray and David S. Greeley

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 516-522 (1980); (7 pages) | Cited 3 times

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A model is developed for the acoustic source strength of blade rate line energy produced by single‐screw merchant vessels. These source strengths are based on observed cavitation time histories on merchant vessels and on limitations imposed by considerations of propeller design procedures and ship vibration criteria. Relationships are presented for the expected value of the blade rate source strength for ships of different lengths, expressed both as a monopole source strength located at a known depth below a free surface and as a dipole source strength that describes the pressure radiated to the farfield. These relationships are based on a small sample of merchant ship characteristics and are exercised for the estimated population of ships at sea. This calculation yields a statistical description of the distribution of source level and frequency of propeller blade rate acoustic energy for the fleet of single‐screw merchant vessels.
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43.30.Nb Noise in water; generation mechanisms and characteristics of the field
43.50.Ed Noise generation

An experimental investigation of the parabolic reflector as a nearfield calibration device for underwater sound transducers

M. Jean McKemie and Chester M. McKinney

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 523-529 (1980); (7 pages)

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Results are presented of an experimental investigation of the use of thin metal parabolic reflectors to form underwater quasiplane wave regions in the nearfield of the reflector. This quasiplane wave volume is then used to calibrate underwater sound transducers in terms of directivity and sensitivity. Such reflectors, mass produced for use with electromagnetic wave devices, are readily available, inexpensive, and rugged. Experiments were conducted with reflectors ranging from 45 to 122 cm in diameter at frequencies from 30 to 300 kHz. It might be noted that at the higher frequencies the acoustic wavelength is approximately an order of magnitude shorter than that for which the reflectors were designed. Test transducers, typically half the size of the reflectors, were calibrated both in the nearfield of the reflector and in the farfield (using conventional techniques) and the results were compared. It was found that for the major lobe there was excellent agreement and that the levels of the minor lobes were in acceptable agreement but that the fine detail of the minor lobe structure differed for the two types of measurements. Sensitivity measurements differed by about ±1.0 dB. For low‐frequency operation the metal reflector needs to be backed by air or other pressure release material in order to be an efficient reflector. It is concluded that the parabolic reflector technique has useful accuracy for many applications.
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43.30.Yj Transducers and transducer arrays for underwater sound; transducer calibration
43.58.Dj Sound velocity
43.20.Fn Scattering of acoustic waves

Ambient noise depth‐dependence models and their relation to low‐frequency attenuation

David E. Weston

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 530-537 (1980); (8 pages)

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Both a deterministic dipole model and the law of conjugate depths are applied to study the depth dependence of the low‐frequency ambient noise in the main sound channel and, when used together, a reasonable agreement with experiment is obtained. Scattering or diffusion models for the region below critical depth agree well with experiment. Complete area and line source models for the ambient level are derived. Three approximate predictions of the low‐frequency attenuation come from the deep ambient depth dependence, ambient differences with site position, and ambient differences with site and depth, respectively. All three are consistent with conventional measurements and with the scattering diffusion and bottom loss mechanism.
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43.30.Nb Noise in water; generation mechanisms and characteristics of the field
43.30.Bp Normal mode propagation of sound in water

Experiments on the transmission paths and dynamic behavior of engine structure vibrations. I. Background and static tests

Hideo Okamura

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 538-545 (1980); (8 pages)

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In order to establish a method of estimating the engine structure surface responses, a series of experiments was made on a four‐cylinder (bore: 86 mm, stroke: 84 mm), in‐line, water‐cooled high‐speed diesel engine. The results obtained in static conditions are summarized with the necessary background. The propagation behavior of excitation forces in the engine structure, the vibration behavior of the vibration transmission paths, and the transfer functions of the transmission paths were examined in static conditions. The distribution of the damping in the engine structure, the influence of cooling water, the lubrication oil, the oil pressure, and the crank position on the transfer functions were also examined. After the experiments, we found that (a) a different excitation force induces different responses on the engine structure surfaces because of its different transmission paths and their transmission behavior; (b) the forces applied on the cylinder head can be transmitted along the cylinder head bolts, and the engine structure can be excited by this force just as strongly as by the identical force applied on the piston top; and (c) most of the damping in the engine structure is induced by the oil film existing around the main moving parts such as the pistons, the connecting rods, and the crankshaft.
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43.40.At Experimental and theoretical studies of vibrating systems
43.50.Ed Noise generation
43.50.Lj Transportation noise sources: air, road, rail, and marine vehicles

Experiments on the transmission paths and dynamic behavior of engine structure vibration. II. Motoring tests

Hideo Okamura

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 546-550 (1980); (5 pages)

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In order to gain a better understanding of the transmission behavior of the excitation forces in the engine structure, such as the gas forces, the inertia forces, the piston slap forces, and the valve seating impact forces, a series of motoring tests was carried out on a four‐cylinder (bore: 86 mm, stroke: 84 mm), in‐line, water‐cooled high‐speed diesel engine. The motoring tests were carried out by changing the combinations of the excitation forces, and at different engine speeds. Under the motoring tests, it could be seen that even the cylinder block bottom sides could be steadily excited by the valve seating impact forces. The transmission behavior of each of the excitation forces can be identified distinctly by the particular frequency components in the power spectral density diagrams of the engine structure responses. Finally, new types of transfer functions were proposed in order to identify the relationship between the kinetc energy of the impulsive excitation forces (such as the piston slap forces and the valve seating impact forces) and the induced engine structure responses. These new transfer functions could be determined under motoring conditions and can greatly overcome the difficulties in estimating the engine structure responses.
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43.40.At Experimental and theoretical studies of vibrating systems
43.50.Lj Transportation noise sources: air, road, rail, and marine vehicles
43.50.Ed Noise generation

Analytical method to predict noise radiation from vibrating machine systems

N. D. Perreira and S. Dubowsky

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 551-563 (1980); (13 pages)

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A fundamental study of noise generation in high‐speed mechanical systems is undertaken. The objective being the development of modeling techniques for the prediction of mechanical system noise levels. Recently developed dynamical procedures are used to obtain the motions of linked mechanical systems with elastic elements and connection clearances. The ranges of critical system parameters are identified and classical acoustical analysis methods are used in determining the most significant acoustic sources. Detailed acoustic models are analytically developed for these significant sources. These methods and models are then used to predict the farfield radiation of a simple, yet representative, mechanical system; an elastic link with connection clearances in a nominal motion container.
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43.40.At Experimental and theoretical studies of vibrating systems
43.50.Ed Noise generation
43.50.Jh Noise in buildings and general machinery noise

Power series for the reverberation time

W. B. Joyce

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 564-571 (1980); (8 pages) | Cited 8 times

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The reciprocal of the reverberation time T is expressed as a power series in the absorptivity of the enclosure. The leading term of the series is found to be the Sabine–Franklin expression, and the procedure is thus interpreted, for weakly absorbing enclosures, as a new derivation and confirmation of that still controversial expression. The next term of the series then provides a correction to the Sabine–Franklin value in many practical cases of intermediate absorptivity where the Sabine–Franklin value is reasonably accurate but not accurate enough. Four other formulas which have been advanced as improvements on Sabine–Franklin are shown to yield unreliable corrections which are even of the wrong sign in some enclosures. Finally, it is shown that T bears a simple relation to the gain g of a laser, and, thus, existing evaluations of either gor T are immediately interpreted as evaluations of the other.
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43.55.Br Room acoustics: theory and experiment; reverberation, normal modes, diffusion, transient and steady-state response

Array gain for signals and noise having amplitude and phase fluctuations

L. I. Kleinberg

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 572-577 (1980); (6 pages)

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One of the causes of the deviation of the signal‐to‐noise array gain from its ideal value is the existence of random amplitude and phase fluctuations of the signal and noise waveforms arriving at the elements of the array. The effect of normally distributed fluctuations on both the signal and noise gains is examined in this paper. An equation is developed which gives the gain, when there are fluctuations, as a function of the ideal gain for both the signal and noise. The expressions for the signal and noise gains used in this paper are valid for all single‐frequency fluctuations arising between the source and the point in the array where the output is measured. It is shown that under certain conditions the total signal gain degradation due to fluctuations can be approximated by the sum of the degradation due to fluctuations in the medium and the degradation due to fluctuations in the equipment.
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43.60.Gk Space-time signal processing, other than matched field processing
43.30.Vh Active sonar systems

Combining acoustic holography with space‐frequency equivalence

Winston E. Kock

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 578-580 (1980); (3 pages)

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Space‐frequency equivalence, a 1958 concept involving either electromagnetic or acoustic detection systems, states that the physical complexity of a system is interchangeable with the frequency complexity of the system so that the use of a multiplicity of discrete frequencies permits a significant reduction in the physical (space) extent of the system. The implications of combining this equivalence with holography are here examined.
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43.60.Gk Space-time signal processing, other than matched field processing

Fourier efficiency using analytic translation and Hilbert samples

Jack R. Williams

J. Acoust. Soc. Am. Volume 67, Issue 2, pp. 581-588 (1980); (8 pages) | Cited 1 time

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The discrete Fourier transform (DFT) inherently accepts complex data; yet signals to be processed are usually real. This necessitates special accommodations if efficient computation is to be achieved. Further accommodation is necessary for efficiency when processing bandpass data. Both accommodations can be made by generating analytic signals using Hilbert transforms. The generation of such signals around zero frequency can be accomplished by analytic band translation where the bandpass can afterwards be defined at baseband by a pair of matched filters. After baseband processing, the spectrum can be translated back up to an arbitrary frequency or can enter after Hilbert sampling directly into the complex DFT for the most efficient spectrum analysis. The analytic translation to the zero‐centered baseband frequencies provides the most conveniently normalized spectrum and facilitates the most efficient use of computational resources. The analytic band translator applies to either digital or analog implementation and is useful in both spectrum analysis and other processes.
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43.60.Gk Space-time signal processing, other than matched field processing
43.60.Cg Statistical properties of signals and noise
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