Volume 89, Issue 6, June 1991

Aeroacoustics of large wind turbines
View Description Hide DescriptionThis paper reviews published information on aerodynamically generatednoise from large horizontal axis wind turbines operated for electric power generation. Methods are presented for predicting both the discrete frequency rotational noise components and the broadband noise components, and results are compared with measurements. Refraction effects that result in the formation of highfrequency shadow zones in the upwind direction and channeling effects for the low frequencies in the downwind direction are illustrated. Special topics such as distributed sourceeffects in prediction and the role of building dynamics in perception are also included.

Power flow for sound incident on a solid aluminum sphere in water
View Description Hide DescriptionPower flow is computed for sound incident on a solid aluminum sphere in water. First, power flow together with kinetic and potential energy distributions are investigated for the standing modes of free vibration of the sphere. The instantaneous power flow excited in the sphere by a continuous train of plane waves is examined next. Finally, timeaveraged power flow is investigated. Little has been done so far to compute soundpower flow in structures immersed in a fluid. Computations of this kind provide a new insight into the relation between the elastic waves in the structure and the sound radiated into the fluid.

Characterizing pulses reflected from rough surfaces using ultrasound
View Description Hide DescriptionA model for the scattering of wideband signals from threedimensional rough surfaces is presented. This development is an extension of the scattering based on the Kirchhoff approximation method for a monochromatic wave source. The usual planewave approximation is relaxed and the Kirchhoff method is extended to include spherically diverging waves from the scattering surface. The scattered signal is expressed in terms of the Fourier transform of the acoustic channel. The frequency correlation function of the channel is then derived for a rough surface having the Gaussian spectrum. The coherent and incoherent components of the scattered signal intensity are determined from the frequency correlation function. The theory is applied to the signals produced by the Polaroid transducer operating in air and mounted on a mobile vehicle capable of automatic translation and rotation. Theoretical results are compared with experimental observations from two different rough surfaces. The analytic results are verified over the observable range of incidence angles from 0° to 60°.

Wavevectortime domain and Kirchhoff integral equation methods to determine the transient acoustic radiation loading on circular cylinders
View Description Hide DescriptionTwo new methods are presented to determine the transient acoustic radiation loading on circular cylinders. The acoustic modal forces are expressed as a sum of the convolution of the modal radiation impulse responses and the modal velocities. In the wavevectortime domain method, the modal radiation impulse responses are obtained by using the radiation impulse responses of an infinite cylinder and the modes in wavevector space. The approach can thus be easily used for parametric studies on the effects of boundary conditions and normalized lengths on the modal radiation impulse responses. In the Kirchhoff integral equation method, space and time are discretized. The pressure and acceleration in each element are then expressed in the form of a Taylorseries expansion about points at which the pressure is obtained by marching forward in time. The radiation impulse responses of both infinite and simply supported finite cylinders are obtained by the two methods and compared.

Ray synthesis of the form function for backscattering from an elastic spherical shell: Leaky Lamb waves and longitudinal resonances
View Description Hide DescriptionAn acoustic ray analysis is employed in synthesizing the form function for backscattering, from a fluidloaded evacuated elastic spherical shell where k is the wave number of the incident plane wave and a is the outer radius of the shell. The synthesis contains a component associated with a specular reflection, and contributions from leaky Lamb waves. The contribution of the lth leaky Lamb wave is expressible in a Fabry–Pérot resonator form [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)]. A comparison of the ray synthesis for with the exact partialwave series representation for a 440c stainlesssteel shell verifies the usefulness of the ray synthesis for the present case of a shell. The present synthesis is also new in that it includes the effects of longitudinal resonances on A novel ray synthesis of indicates a significant resonanceeffect near the condition (n=1,2,…). The thickness of the shell is h, and is the longitudinal wave number where is the longitudinal speed of sound in the elastic material. The ray synthesis demonstrates that the curvature of the shell is essential to the modeling of longitudinal resonances. Although acoustic ray modeling is generally a highfrequency technique, the ray synthesis of for a 440c stainlesssteel shell appears to be applicable for ka as small as 7. Certain anomalies in the synthesis are investigated to better understand the limitations of the present ray model.

Acoustic scattering from submerged cylinders. MIIR Im/Re: Experimental and theoretical study
View Description Hide DescriptionTo recognize a target submerged in water, a spectroscopy based on the backscattering spectrum or on the resonance spectrum can be used. These spectra are experimentally obtained from the quasiharmonic or short pulse method of isolation and identification of resonances (MIIR). They show sharp amplitude variations that are related to the scatterer’sresonances. These resonances are related to the surface waves that propagate around the target. The backscattering spectrum and the resonance spectrum are power spectra. They are obtained from the computation of the modulus of the Fourier transform of the signal scattered by the target. In this paper, the computation of the phase tangent of the Fourier transform is presented. The spectra obtained are called the Im/Re spectra. The experimental results are compared with the computation of the ratio of the imaginary part over the real part of the complex pressure observed at a large distance from the target center. It is shown that the Im/Re spectra are highly useful for distinguishing resonances in scatterers with large absorptivity, where conventional backscattering or resonancespectra prove insensitive.

Reconstructing stratified fluid flow from reciprocal scattering measurements
View Description Hide DescriptionThis paper shows how an inversion formula can be derived for reconstructing the magnitude and direction of stratified fluid flow from two scattering measurements. The measurements are recorded by transmitting an acoustic pulse from a source below the region of stratified flow and then recording the scatteredwave at another point horizontally displaced from the source. A second measurement is performed with the source and receiver interchanged and the result is subtracted from the first scattering measurement. This difference is, within the Born approximation, independent of scattering that arises from stationary inhomogeneities and thus solely sensitive to scattering due to flow. As a byproduct, the sum of the two scattering measurements with source and receiver interchanged yields a quantity sensitive only to scattering from stationary inhomogeneities. This allows the stationary inhomogeneities to be recovered independently of flow.

Characterization of fibermatrix interface by guided waves: Axisymmetric case
View Description Hide DescriptionA hybrid method combining the finiteelement and eigenfunction expansions is proposed to study the guided waves in composite cylinders. This method is shown to be flexible in modeling generally anisotropic cylinders and computationally efficient. However, most of the analysis is confined to the case of a transversely isotropic cylindrical core surrounded by coaxial isotropic cylinders. The object is to model uniaxial fiberreinforced materials with interface zones between the fiber (which is anisotropic) and the matrix (which is isotropic). Numerical results are presented for the axisymmetric case for a graphite fiber in magnesium and epoxy matrices. In particular, the measurable and analyzable effects of imperfect bonding are investigated. The reduction of bond stiffness is found to have significant effect on the leaky waves.

Propagation of Love waves in an initially stressed medium consisting of a slow elastic layer lying over a liquidsaturated porous solid halfspace
View Description Hide DescriptionThe dispersion equation, for Love wave propagation in a slow elastic layer overlying a liquid saturated porous solid halfspace, is derived. Both the media are assumed to be under initial stress. The effect of porosity and initial stress on the phase velocity of Love waves has been discussed. Dispersion curves for the phase velocity have been plotted, both with the presence and absence of prestress, for different values of the sandiness parameter. Some special cases have also been deduced.

Generation of fluctuating normal stress in a viscoelastic layer by surface shear stress and pressure as in turbulent boundarylayer flow
View Description Hide DescriptionAt low wave numbers, according to recent indications, fluctuating wall shear stress generated by a turbulent boundary layer may be comparable with fluctuating wall pressure. Consideration is given here to the fluctuatingnormal stress generated within an elastic layer by both shearstress and pressure excitation on its outer face. The transfer level from surface shear to normal stress is shown to be comparable with or exceed that from surface pressure in a significant range of low to intermediate wave numbers. This transfer from surface shear stress is enhanced by the outer fluid loading and by the imposition of vanishing displacement at an inner rigid surface. Results of computations are presented and analyzed in numerical examples based on a configuration where an elastomer layer is bounded by a fluid halfspace at its excited surface and by a thin, damped plate at its inner surface, with a similar fluid halfspace below the plate. Results are given also for the limiting cases of a rigid inner surface and of an elastic halfspace with and without fluid loading. The transfer level from shear stress is computed also where a concomitant wall pressure is present and related to shear stress as recently determined from a theoretical treatment of the viscous boundary condition at low wave numbers in turbulent boundarylayer flow. It is thus suggested that the contribution of turbulent wallshear stress to flow noise on recessed hydrophones in the absence of a platelike element between these and the flow is likely an important one.

Effects of anisotropy upon the normal modes in a borehole
View Description Hide DescriptionElasticanisotropy affects the modes generated during acoustic logging. To study these effects, the wave equation was solved using a variational method for a model consisting of a fluidfilled borehole through a solid whose anisotropy is defined in the Cartesian coordinate system. The solution for each normal mode includes its phase velocity, group velocity, pressures in the fluid, and displacements in the solid. The most significant findings are: (1) two quasiflexural waves exist and have different phase and group velocities; (2) for the slow quasiflexural wave, the particle displacements in the plane perpendicular to the borehole, when viewed together, are aligned with the polarization of the slow, planar qSwave whose wavenumber vector is parallel to the borehole; and (3) for the fast quasiflexural wave, the particle displacements in the plane perpendicular to the borehole, when viewed together, are aligned with the polarization of the fast, planar qSwave whose wavenumber vector is parallel to the borehole.

Measurement and calculation of acoustic propagation constants in arrays of small airfilled rectangular tubes
View Description Hide DescriptionAn experimental and theoretical investigation of sound propagation in a porous sample composed of capillary tubes with rectangular cross sections is described in this paper. An experimental technique valid for low flow resistivity and high porosity porous samples was developed to measure the attenuation and phase velocity in the porous material. This technique uses transmission of a short pulse in a large tube through the porous sample and subsequent frequency domain analysis in the range 200–1300 Hz. Good agreement was obtained if an anomalous tortuosity factor of 1.1 is used in the theory. A scaling factor for relating cylindrical and square tube capillary theories, known as the dynamic shape factor, was investigated. Propagation constants computed from use of a near unity dynamic shape factor in the cylindrical pore theory agree favorably with calculations based on the square pore theory for the frequencies and pore radii used in the experiment.

Numerical errors associated with the method of superposition for computing acoustic fields
View Description Hide DescriptionThe method of “wave superposition” is based on the idea that an acoustic radiator can be approximately represented by the sum of the fields due to a finite number of interior point sources. The accuracy of this representation depends upon how well the velocityboundary condition on the surface of the body is approximated. The ultimate objective of this study, then, is to provide some guidelines for improving the accuracy of the surfacevelocityreconstruction and, consequently, the accuracy of the superposition solutions. In general, this is dependent upon the particular surfacevelocity distribution to be reconstructed, as well as other formulation factors such as the acoustic wave number, the number and locations of the surface nodes, and the number and locations of the point sources. Velocityinterpolation functions are introduced as a means of quantifying the dependence of reconstruction errors on the acoustic wave number and the placement of the surface nodes and point sources. Numerical experiments on cylindrical radiators with different velocity distributions are performed to further illustrate how the solution accuracy depends on the surfacevelocityboundary conditions as well as the other formulation factors.

Measurements of the effective nonlinearity parameter B/A of water containing trapped cylindrical bubbles
View Description Hide DescriptionThe effective nonlinearity paramter of water containing a threedimensional ensemble of randomly distributed uniformsized trapped cylindrical bubbles was measured. The experimental results indicate that the dramatic enhancement of the effective nonlinear parameter is due to the nonlinear resonance oscillation of the trapped bubbles. The measured effective for the system is of the magnitude of to

Plane sound waves of finite amplitude for intermediate Gol’dberg numbers
View Description Hide DescriptionBurgers equation provides a good description of the propagation of plane sound waves of finite amplitude for which nonlinear effects are important. Although an exact solution is known, simple asymptotic approximations are useful since they may provide starting points in the case of more general situations for which no exact solution is known. Approximation solutions of Burgers equation are sought by means of a “mixed asymptotic method” involving both the method of multiple scales and the method of strained coordinates. The main point is the introduction of a new slow variable binding the solution in the region before shock formation with the solution in the old age region. For an emitted monochromatic wave, the method yields a simple and complete description for Gol’dberg numbers up to 20, as it is shown by comparison to exact or other approximated solutions. For higher Gol’dberg numbers, the solution is valid up to the shock formation distance and it can be connected with Fay solution beyond.

Oblique reflection of a nonlinear P wave from the boundary of an elastic halfspace
View Description Hide DescriptionThis paper describes mode conversion effects and subsequent waveform distortion arising when a finite amplitude dilatational (P) wave that has already experienced nonlinear distortion is obliquely incident on a stressfree boundary of an isotropic elastic halfspace. A twoterm perturbation expansion is first employed to identify the dominant nonlinear effects. The understanding of wave interactions obtained from the perturbation analysis is then exploited to derive a successful solution using the method of characteristics for twodimensional wave. It is shown that the incident and reflected Pwaves undergo nonlinear amplitude dispersion along their ray paths. The orientation of the rays for the reflected waves are time dependent, being governed by a modified form of Snell’s law, in which the phase speed incorporates the nonlinear correction for the association particle velocity. The reflection coefficients are shown to resemble those of linear theory, except for the dependence on the variable angles of reflection. The nonlinear propagation and reflection laws are solved to determine temporal waveforms for the reflected P and (vertically polarized shear) waves. This requires an iterative procedure in order to trace rays arriving at a specified field point at an arbitrary instant back to their source.

Generating eigenray tubes from two solutions of the wave equation
View Description Hide DescriptionA method is presented for calculating the paths taken by sound between a source and receiver. These paths, which are called eigenray tubes, are obtained from two solutions of the wave equation at finite frequency, one propagated from the source and the other propagated from the receiver. The results are not restricted to the highfrequency limit as is the case with classical ray traces. This generalization of classical ray tracing could be an important new tool in acoustic tomography. A numerical example is included with plots of 11 eigenray tubes.

A narrowband approximation to the acoustic pressure field
View Description Hide DescriptionBroadband theoretical calculations of the acoustic pressure field generally suffer from the need to perform a large number of calculations at each of several frequencies across the frequency band and to, subsequently, construct the required time series through a Fourier synthesis. The computational load for such a series of calculations can be prohibitive especially for high frequencies. This paper presents a theoretical approach within the framework of normalmode theory that significantly reduces the computational requirements for broadband calculations. The limits of the applicability of this method have been examined, and the technique has been used in comparisons with experimental data. The method is easily extended to accommodate range dependence in the environment.

A new algorithm for sound speed in seawater
View Description Hide DescriptionTravel times of acoustic pulses across a 3000km section in the northeast Pacific are used to estimate an algorithm for the speed of sound in seawater. This algorithm, derived from tomographic techniques, is inconsistent both with the international standard algorithm derived by Chen and Millero [J. Acoust. Soc. Am. 62, 1129–1135 (1977)] and with the algorithm of Del Grosso [J. Acoust. Soc. Am. 56, 1084–1091 (1974)]. Both previous algorithms were derived from laboratory experiments. The additive correction, to Del Grosso’s sound speeds between 0 and 4km depth is with p being pressuregauge units in kg The rms error of is about and between the intervals of 0 to 2 km and 2 to 4 km, respectively. At about 3km depth, sound speeds predicted by Chen and Millero and Del Grosso are about and too fast, respectively. An accurate algorithm for sound speed is of fundamental importance in acoustics and in tomographic measures of oceantemperature.

Modeling compressional wave velocity and attenuation in carbonate sediments
View Description Hide DescriptionThe Biot poroelastic theory is used to model ultrasonic (1 MHz) compressional wavevelocity and specific attenuation for carbonate sediment sequences from three Deep Sea Drilling Project (DSDP) sites 288, 289, and 316 on the Ontong–Java Plateau in the western Pacific ocean. The sediments are assumed to be represented by a granular frame containing tortuous capillary tubes of a constant radius. Experimental data for the variation of shear velocity and bulk density ρ with depth are used as input parameters for the model. Assumptions of the frame Poisson’s ratio grain bulk modulus and tortuosity α are necessary. The lowfrequency asymptote of the Biot theory is adequate in modeling the variation of with depth for sites 288 and 289. Modeled velocities agree to within 8% of experimental. The sensitivity of the modeled velocities to the uncertainty in the input parameters is investigated. The equations of motion are partially differentiated with respect to each parameter and the resulting equations are used in conjunction with each parameter’s uncertainty or error. The uncertainty in the modeled velocities is on average 11% and is mostly dependent upon the uncertainties in and The assumption of constant for the chalklimestone sequences from sites 288 and 289 is then tested. It is found to remain constant at a value of 0.2 for the chalk, and decreases to approximately 0.1 for the transition to limestone. Modeled values for are found to be sensitive to and ρ, in addition to the pore space parameters, and are considerably smaller than the experimental observations from sites 288, 289, and 316.