Volume 49, Issue 1B, January 1971

A Novel Technique for Measuring the Strength of Liquids
View Description Hide DescriptionA novel technique has been effectively utilized in studying the properties of liquids under conditions that are not ordinarily accessible. This technique involves the use of an acoustic standing‐wave field established in a column of one liquid in order to trap an immiscible droplet of another liquid. In the experiment reported here, a filtered ether droplet suspended in filtered glycerine was superheated and acoustically stressed until the combination produced an explosive liquid‐to‐vapor phase transition. The experiment was performed under atmospheric conditions at which the normal boiling point of ether is 35.6°C. The measured tensile strength varied linearly from 17 bars at 130°C to 0 bars at 146°C. Previous measurements of the tensile strength of liquids have not come within a factor of 2 or 3 of the theoretical predictions based on homogeneous nucleation theory, a theory which describes the vaporization conditions for pure liquids. The results reported here are in good agreement with that theory. This novel agreement is attributed to the ability to obtain pure liquid samples by utilizing small (0.5‐mm‐diam) filtered droplets.

Spectral Analysis of Cavitation Noise in Cryogenic Liquids
View Description Hide DescriptionSpectra of ultrasoniccavitation noise were obtained in liquid helium and liquid nitrogen. A subharmonic response at half the driving frequency was found to be present at all times. In the case of liquid helium, the relative intensity of this subharmonic showed a peak at the λ point. The background noise intensity was also higher in heliumII. A tendency for the half‐order subharmonic to increase with static pressure was also found both for heliumI and nitrogen. A correlation between the onset of the subharmonic audible‐frequency noise and the white‐noise background was also found. The variation of the intensity of the first overtone with increasing driving voltage was found to be different in heliumII than in other liquids. It is argued that many of these phenomena arise from the effect on bubble dynamics of the efficient heat transport in heliumII.

Effects of Input Amplitude Profile upon Diffraction Loss and Phase Change in a Pulse‐Echo System
View Description Hide DescriptionThe particle velocity profile V (ρ) across the face of a transmitting transducer is shown to have large effects upon the diffraction loss and phase change in the ultrasonic field of the transducer. Various functions V (ρ), monotonic decreasing from the center to the rim of a circular transducer, were employed. The pulse‐echo response of the transducer was calculated by numerical integration on an electronic computer. It was found that the functions V (ρ) chosen caused the diffraction‐loss and phase‐change curves to be smoother than in the piston case and caused the respective peaks and plateaus to shift with distance in the Fresnel region.

Propagation of Sound through a Variable‐Area Duct with a Steady Compressible Flow
View Description Hide DescriptionThe equations governing the progagation of sound in a nonconstant area duct with a one‐dimensional fluid flow are derived by a linearizing perturbation technique. The governing equations are transformed successively into two decoupled linear ordinary differential equations with a variable coefficient. By the appropriate choice of duct shape, the variable coefficient is made constant. The duct shape chosen is semi‐infinite, diverging from the sonic throat. Solutions are obtained for several choices of the parameter ωL/2a _{s}, which relates frequency, duct shape, and speed of sound. The solutions exhibit standing‐wave characteristics and reveal certain aspects of energy transfer between the mean flow and sound. The study bears on noise growth and decay in the input and output ducts of certain fluidic amplifiers.

Scattering of Acoustic Waves by a Periodic Thermal Field
View Description Hide DescriptionOne‐dimensional scattering of acoustic waves by the thermal field produced by a sinusoidal spatial distribution of heat sources in a perfect gas is examined analytically. The scattered field is found to consist of a transmitted acoustic wave, a reflected wave, and an entropywave. When the thermal‐field wavenumber is near the entropy wavenumber or twice the acoustic wavenumber, resonance‐like phenomenon occurs, resulting in large‐amplitude scatteredwaves.

Beam Behavior within the Nearfield of a Vibrating Piston
View Description Hide DescriptionA numerical investigation of the nearfield region of a vibrating piston was conducted. While existing literature is not exactly clear about how close to a transducer a regular beam pattern is formed, the results of this investigation show the limits of operation one can expect. From one interpretation of literature, a −3‐dB beam with a minimum spot size equal to the transducer diameter would be expected to form beyond an axial distance z = 3.89 a ^{2}/λ. This investigation shows that such a beam forms at z = 0.75 a ^{2}/λ and has a minimum spot size equal to one‐quarter the transducer radius. These results are verified for transducers with a/λ's ranging from 1 to 20 and can be extended with confidence to higher a/λ's. Similar results are also obtained for −1.5‐, −4.5‐, −6.0‐, −7.5‐, −9.0‐, −10.5‐, and −12‐dB beams.

Generalized Maxwell Spherical Structural Systems in Fluid Media
View Description Hide DescriptionThe dynamic response and stability of a single‐degree‐of‐freedom structural system composed of a hollow or solid sphere connected by a massless supporting member and submerged in a viscous fluid medium is studied. The constitutive relationship between the connecting member and the base is considered to be of a generalized Maxwell model type. Basset's fluid reaction is included in the integro‐differential equation of motion and a closed‐form solution is obtained by means of Laplace transforms. Response curves illustrating the effect of each dimensionless parameter on the response of the system are presented, and a dynamic stability criterion based on the character of the solution is employed to develop a stability profile for the system. It is demonstrated that the dynamic response of the system is significantly influenced by the character of the surrounding fluid medium while the stability or instability of the structure is determined by the relative values of the load parameter and the stiffness‐coefficient ratio.

Propagation of Axially Symmetric Waves in Hollow Elastic Circular Cylinders Subjected to a Step‐Function Loading
View Description Hide DescriptionAxially symmetric waves in semi‐infinite hollow elastic circular cylinders, with traction‐free lateral surfaces and subjected to a pressure‐step loading, are considered on the basis of the equations of motion derived by McNiven, Shah, and Sackman [J. Acoust. Soc. Amer. 40, 784–792; 1073–1076 (1966)]. By using double integral transforms, asymptotic solutions are obtained for the strains as functions of time and material and geometric parameters. Strains are presented for times near the head of the pulse of the extensional mode at the same distance from the finite end for various radii ratios a* and for different distances but for the same radius ratio. It is of interest to note that, for thin cylinders (a* less than approximately 1.7, owing to its slight dependence on Poisson's ratio), the maximum group velocity of the radial mode is slightly higher than that of the extensional mode although less than the dilatational wavevelocity.

Approximate Theory of Torsional Wave Propagation in Elastic Circular Composite Cylinders
View Description Hide DescriptionAn approximate one‐dimensional theory is developed for axially symmetric torsional deformation of elastic circular composite cylinders. The cylinders are composed of a core perfectly bonded to an outer casing. The equations of motion accommodate the first two frequency branches of the dispersion relation for symmetric torsional waves propagating along the axis of the cylinder. Important parameters are the ratios of densities, shear moduli, and radii of the core and casing. Dispersion relations obtained from this approximate theory are studied for ranges of values of these parameters, and a comparison made with the results of the “exact” theory, i.e., three‐dimensional elasticity. In order to match closely the results from the exact analysis, two correction factors are introduced, and values are tabulated for typical material and geometric properties. Sufficient conditions at the ends of finite cylinders are obtained to provide a unique solution.

Propagation of Harmonic Waves in a Composite Elastic Cylinder
View Description Hide DescriptionIn this paper, the propagation of harmonic waves with an arbitrary number of circumferential nodes in an infinitely long two‐layered composite circular elastic rod is investigated. The composite rod is made of a circular solid rod encased by a circular shell having different material properties. The frequency equation derived on the basis of the three‐dimensional linear isotropic elastictheory is presented. The reduction of this equation to the frequency equations for some special problems, such as longitudinal wave propagations, torsional wave propagations, flexural wave propagations, axial‐shear vibrations, and plane‐strain vibrations is discussed. Simplified equations for phase velocities of longitudinal and torsional waves at very long wavelength are obtained. Numerical results, in terms of frequency and real wavenumber, are given for a composite rod made of a soft core with a stiff casing.

Dispersion of Waves in Transversely Isotropic Rods
View Description Hide DescriptionThe axisymmetric motions in an infinitely long circular rod made of a transversely isotropic material are studied, and the frequency equation governing such motions is established. The relationship between frequency and wavelength contained in the equation is not explored in detail. Instead, exploration is limited to information that will be useful in a subsequent study in developing an approximate theory that will govern the same motions. By studying the distribution of cutoff frequencies on the frequency wave‐propagation constant plane, the conclusion is reached that the three lowest modes of motion strongly influence each other and are in turn influenced to a much lesser degree by the fourth and higher modes. Accordingly, numerical analysis is made of only the three lowest spectral lines.

Ensemble and Time Averages of Reverberation from a Sea Surface: A Computer Study
View Description Hide DescriptionA realistic computer simulation of reverberation from a moving sea surface has been used to compare time and ensemble averages. The experiment simulated has a directional source and an omnidirectional receiving hydrophone located at a depth of 350 yd (320 m). The surface is insonified in a strip of constant width independent of range. The reverberation is calculated in three “windows” of width 0.1 sec located at 0.5, 1.0, and 1.5 sec for a fully developed sea resulting from wind velocities of 10 and 20 kt (5.1 and 10.3 m/sec). The pulse waveform is two cycles of a 1‐kHz sinusoid. The sea surface is generated by using random phases in a Fourier polynomial of 100 terms. It is shown that, when the reverberation is reduced in the manner suggested by Ol'shevskii, the derived process is not stationary, but behaves like a narrow‐band noise of constant amplitude and random phase. The lack of stationarity arises because the statistical properties of the phase change with time. The backscattering strengths of the sea surface, computed for six combinations of grazing angle and sea state, agree only moderately well with experimental measurements at sea.

On the Acoustic Study of Nucleation by Energetic Particles in Fluids
View Description Hide DescriptionThe absorption of a small‐amplitude sound wave in a liquid can furnish a method for studying the size distribution of microcavities produced by energetic particles. In contrast to ultrasoniccavitation, this method is nondestructive and therefore allows the following of time variations of the distributions. The method has been improved to detect cavities of radii of the order of 2 μm, such as those created in water by fast neutrons.

Variable‐Focus Liquid‐Filled Hydroacoustic Lens
View Description Hide DescriptionA large fluid lens with accompanying reservoir and pump arrangement is described, with emphasis on its underwater acoustic‐imaging application. Pertinent properties are cited of the neutrally buoyant lens fluid, the elastomeric containment membranes, and the composite lens. The liquid‐filled lens potentially provides better over‐all acoustic transmissivity than does a comparable solid lens and has an equivalent acoustic refractive index. Focusing, achieved without physical motion of the lens proper, occurs in a manner analogous to the operation of the human eye. Introduction or removal of fluid changes the curvature of the lens‐membrane surfaces. Theoretical consideration reveals the stretched‐membrane surface configuration to be approximately spherical. Thus, standard spherical lens equations are combined with appropriate mensuration formulas to obtain lens calibrationequations. A hydroacoustic image taken with the liquid lens is displayed. This image is compared with that formed under identical circumstances by means of an equivalent Lucite lens. Beamwidth and spherical aberration of the fluid lens are discussed. A field stop for use with the liquid lens and a technique for immunizing the lens to water‐wave action are noted.

On Arrays with Nonrigid Interstices
View Description Hide DescriptionThe radiation from an infinite phased planar array of rectangular pistons with nonrigid interstices is considered. Numerical calculations for exact equations are compared with a simple approximation, derived for small pistons close together. The comparisons show that the approximate expressions agree well with the exact results even for pistons of practical size, if (1) the array is steered to an angle near broadside, (2) the interstitial impedance is not very low, and (3) the interstices occupy a small fraction of the total array area.

Effect of a Random Bottom on Acoustic Propagation in a Two‐Dimensional Ocean
View Description Hide DescriptionThe effect of a stochastic ocean bottom on underwater acoustic propagation is examined in two previous papers by the authors [J. Acoust. Soc. Amer 43, 1395–1403 (1968); 44, 1103–1114 (1968)]. In those investigations, the first and second moments of the random acoustic intensity are determined for various source and receiving‐point geometries. In a more recent study by the authors [J. Stat. Phys. 2, 279–289 (1970)], the amplitude and decibel amplitude, as well as the intensity, of a random acoustic field are examined. There, each of the three measures of acoustic strength is shown to differ from the others in the analytic properties of its mean value and standard deviation. Therefore, in the present paper, the random‐bottom problem of the two earlier studies is reexamined. In particular, the first and second moments of the total‐field amplitude and decibel amplitude are studied under certain restrictions and are compared with those of the intensity. Furthermore, the first and second moments of the total‐field phase are treated.

Sound Attenuation between 200 Hz and 10 kHz
View Description Hide DescriptionTrials have been conducted in the Western Mediterranean to confirm the excess attenuation of sound at frequencies between 200 Hz and 10 kHz. As sound propagation along the deep refracted path in the isothermal deep water of the Mediterranean is affected only by geometrical spreading and attenuation, it is possible to measure the attenuation separately for each frequency. The trials used explosive sound sources at different depths and at accurately determined ranges between 200 m and 30 km. Special care has been taken to separate the effects of finite amplitude from the attenuation and it is shown that the former are not responsible for the excess attenuation found at low frequencies. The authors have reported the analysis more thoroughly in SACLANTCEN Technical Report No. 156, “Sound Attenuation Between 200 Hz and 10 kHz.”

An Approach to Computing Time‐Dependent Interaction Forces and Mutual Radiation Impedances between Pistons in a Rigid Planar Baffle
View Description Hide DescriptionAn approach is presented to computing the time‐dependent force acting on a piston as a result of the velocity of an adjacent piston which may be any specified time‐dependent function. The method is based on a Green's functionsolution to the time‐dependent boundary‐value problem for an impulsive piston velocity motion. An asymptotic expression for the mutual radiation impedance between square pistons has been obtained using the method. A numerical approach is also presented to obtain the mutual radiation impedance coefficients from the time‐dependent solution of the boundary‐value problem. Numerical results obtained from the asymptotic expression are shown to agree with previously published numerical results and the results obtained using the numerical approach indicated in the paper. Numerical results for time‐dependent interaction forces resulting from sinusoidal piston velocities are also presented and discussed.

Dynamic Interaction between an Elastic Cylindrical Shell Subjected to Point Loadings and an Acoustic Medium
View Description Hide DescriptionThis investigation is concerned with the three‐dimensional interaction between an infinitely long elastic circular cylindrical shell, subjected to point loading and an acoustic medium. The formal solution to the problem was obtained by solving the governing field equations of the shell and the acoustic medium through the application of integral‐transform and series‐solution techniques. The resulting Fourier Laplace inversion integral was evaluated by means of numerical‐inversion methods. Detailed numerical results are presented for the dynamic response of a steel shell immersed in water when it is subjected to a point loading having the form of a step function of finite duration. Since there are no approximate relations introduced in the fluid‐shell phenomena, the result obtained from this investigation is the exact solution to the problem within the scope of linear‐acoustic and thin‐shell theory, and the approximation errors introduced by the numerical techniques.

Response of a Nonlinear Form of the Mathieu Equation
View Description Hide DescriptionThis communication presents the results of an investigation of the response of a nonlinear form of the Mathieu equation in the first unstable region. The equation of interest is a Mathieu equation plus a cubic nonlinearity. The response consists of a modulated one‐half subharmonic of the parametric‐excitation frequency. The envelope of the subharmonic is approximately a sinusoid. The magnitude and frequency of this sinusoid are determined by the method of harmonic balance. The results are compared with the results of computer simulation.