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Nov 1999

Volume 106, Issue 5, pp. 2321-L52

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An analytic secondary source model of edge diffraction impulse responses

U. Peter Svensson, Roger I. Fred, and John Vanderkooy

J. Acoust. Soc. Am. Volume 106, Issue 5, pp. 2331-2344 (1999); (14 pages) | Cited 17 times

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A new impulse-response model for the edge diffraction from finite rigid or soft wedges is presented which is based on the exact Biot–Tolstoy solution. The new model is an extension of the work by Medwin et al. [H. Medwin et al., J. Acoust. Soc. Am. 72, 1005–1013 (1982)], in that the concept of secondary edge sources is used. It is shown that analytical directivity functions for such edge sources can be derived and that they give the correct solution for the infinite wedge. These functions support the assumption for the first-order diffraction model suggested by Medwin et al. that the contributions to the impulse response from the two sides around the apex point are exactly identical. The analytical functions also indicate that Medwin’s second-order diffraction model contains approximations which, however, might be of minor importance for most geometries. Access to analytical directivity functions makes it possible to derive explicit expressions for the first- and even second-order diffraction for certain geometries. An example of this is axisymmetric scattering from a thin circular rigid or soft disc, for which the new model gives first-order diffraction results within 0.20 dB of published reference frequency-domain results, and the second-order diffraction results also agree well with the reference results. Scattering from a rectangular plate is studied as well, and comparisons with published numerical results show that the new model gives accurate results. It is shown that the directivity functions can lead to efficient and accurate numerical implementations for first- and second-order diffraction. © 1999 Acoustical Society of America.
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43.20.Bi Mathematical theory of wave propagation
43.20.Fn Scattering of acoustic waves
43.20.Px Transient radiation and scattering

Surface waves over a convex impedance surface

Qiang Wang and Kai Ming Li

J. Acoust. Soc. Am. Volume 106, Issue 5, pp. 2345-2357 (1999); (13 pages)

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The existence of the surface wave in an upward refracting medium has been predicted by Raspet et al. [J. Acoust. Soc. Am. 89, 107–114 (1991)]. Making use of an acoustic analogy, one is able to study the surface waves above a convex cylinder and, hence, to simulate the propagation of sound over an impedance ground in an upward refracting medium. A suitable comblike surface may be used to facilitate the generation of surface waves above the convex ground. This paper describes laboratory experiments for the observation of surface waves over a convex impedance ground. © 1999 Acoustical Society of America.
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43.20.Fn Scattering of acoustic waves
43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors

Sound propagation over concave surfaces

Qiang Wang and Kai Ming Li

J. Acoust. Soc. Am. Volume 106, Issue 5, pp. 2358-2366 (1999); (9 pages)

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Diffraction of sound by concave surfaces is investigated theoretically and experimentally. In an earlier study [J. Acoust. Soc. Am. 104, 2683–2691 (1998)], it has been demonstrated that a rigorous analogy exists for the sound field above a convex circular cylinder in an otherwise homogeneous medium. The predicted sound field corresponds to the situation where the sound speed of the medium decreases exponentially with height. Extending the previous work, this paper investigates of the sound field above a concave surface and explores the corresponding analogy. Normal mode solutions have been developed for a downward refracting medium with an exponential sound speed profile. The solutions are used to predict the sound fields diffracted by a cylindrical concave surface. A series of laboratory experiments is conducted using point monopole, horizontal dipole, and vertical dipole sources over cylindrical concave surfaces. The experimental measurements are compared with the normal mode predictions. For monopole and horizontal dipole sources, good agreement has been found between measurements and the normal mode predictions using an exponential profile. However, the agreement is less satisfactory where the sound field was due to vertical dipole sources. © 1999 Acoustical Society of America.
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43.20.Fn Scattering of acoustic waves
43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors

Shear-speed gradients and ocean seismo-acoustic noise resonances

Oleg A. Godin and David M. F. Chapman

J. Acoust. Soc. Am. Volume 106, Issue 5, pp. 2367-2382 (1999); (16 pages) | Cited 8 times

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Measurements of infrasonic seismo-acoustic ambient noise using an ocean bottom seismometer in shallow water have uncovered an unusual phenomenon: the noise spectrum of the horizontal component of seabed velocity shows several prominent peaks in the frequency range 0–8 Hz, whereas the noise spectra of both the acoustic pressure and the vertical component of seabed velocity show very weak or nonexistent features at the same frequencies. This structure is interpreted theoretically as resonances of shear waves of vertical polarization in the upper sediment layer, excited by the diffuse infrasonic sound field in the water. Independent interface wave dispersion studies at the site have revealed an approximate power-law profile of shear speed versus depth, having the form c(z) = c0zν, with c0 = 21.5 and ν = 0.60 (SI units). The theoretical development concentrates on exact analytic solutions for the resonance frequencies and wave field for power-law profiles and on the WKB and more advanced asymptotic solutions in the more general case of smooth shear-speed profiles with a power-law singularity. The experimental observations are interpreted in light of these analytic results, and are consistent with the previously determined power-law shear speed-profile. © 1999 Acoustical Society of America.
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43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves
43.25.Gf Standing waves; resonance
43.28.Dm Infrasound and acoustic-gravity waves
43.30.Ma Acoustics of sediments; ice covers, viscoelastic media; seismic underwater acoustics

Boundary conditions for the weak formulation of the mixed (u,p) poroelasticity problem

Patricia Debergue, Raymond Panneton, and Noureddine Atalla

J. Acoust. Soc. Am. Volume 106, Issue 5, pp. 2383-2390 (1999); (8 pages) | Cited 16 times

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This paper presents the boundary conditions that apply to the weak integral formulation of the Biot mixed (math,p) poroelasticity equations. These boundary conditions are derived from the classical boundary conditions of the Biot displacement (math,math) poroelasticity equations. They are applied to the surface integrals of the associated weak form to account for exterior excitations, supports, and couplings with exterior elastic, acoustic, poroelastic media, and a septum. It will be shown that the derived boundary conditions for the (math,p) formulation lead to simpler finite element equations compared to those obtained from the (math,math) formulation. Finally, two numerical examples are presented to validate the poroelastic-septum coupling condition, and to highlight the limitations of the free edge condition on a poroelastic medium. © 1999 Acoustical Society of America.
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43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves
43.50.Gf Noise control at source: redesign, application of absorptive materials and reactive elements, mufflers, noise silencers, noise barriers, and attenuators, etc.
43.20.Tb Interaction of vibrating structures with surrounding medium
43.40.Yq Instrumentation and techniques for tests and measurement relating to shock and vibration, including vibration pickups, indicators, and generators, mechanical impedance

Exact solution for sound propagation in ducts with an axial mean temperature gradient and particulate damping

B. Karthik, R. Krishna Mohanraj, Rajesh Ramakrishnan, and R. I. Sujith

J. Acoust. Soc. Am. Volume 106, Issue 5, pp. 2391-2395 (1999); (5 pages) | Cited 1 time

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An exact solution for one-dimensional sound propagation in ducts in the presence of axial mean temperature gradient and particulate damping is presented in this paper. The acoustic wave equation is derived starting from the one-dimensional momentum and energy equation. The application of appropriate transformations leads to an analytically solvable Whittaker’s differential equation for the case of a linear mean temperature gradient and Bessel’s differential equation for the case of an exponential mean temperature gradient. The derived analytical solutions are used to investigate the dependence of the acoustic field in a duct on temperature gradient and particulate damping. © 1999 Acoustical Society of America.
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43.20.Mv Waveguides, wave propagation in tubes and ducts
43.20.Tb Interaction of vibrating structures with surrounding medium

Analysis of transient wave scattering from rigid bodies using a Burton–Miller approach

A. A. Ergin, Balasubramaniam Shanker, and Eric Michielssen

J. Acoust. Soc. Am. Volume 106, Issue 5, pp. 2396-2404 (1999); (9 pages) | Cited 8 times

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Transient scattering from closed rigid bodies can be analyzed using a variety of time domain integral equations, e.g., the Kirchhoff integral equation and its normal derivative. Unfortunately, when the spectrum of the incident field includes one or more of the resonance frequencies of the corresponding interior problem, the solutions to these time domain integral equations become corrupted with spurious interior modes. In this article, this phenomenon is demonstrated via numerical experiments, and a Burton–Miller-type time domain combined field integral equation is proposed as a remedy. To verify that the solutions to this Burton–Miller-type equation are not corrupted by interior modes, various numerical results are presented. It is anticipated that this equation, when used in conjunction with fast time domain integral equation solvers (e.g., plane wave time domain algorithms), will enable the accurate analysis of transient wave scattering from acoustically large bodies. © 1999 Acoustical Society of America.
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43.20.Px Transient radiation and scattering
02.60.Cb Numerical simulation; solution of equations
02.60.Nm Integral and integrodifferential equations
02.70.Pt Boundary-integral methods

Fast transient analysis of acoustic wave scattering from rigid bodies using a two-level plane wave time domain algorithm

A. A. Ergin, Balasubramaniam Shanker, and Eric Michielssen

J. Acoust. Soc. Am. Volume 106, Issue 5, pp. 2405-2416 (1999); (12 pages) | Cited 4 times

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It is well known that the computational cost associated with the application of classical time domain integral equation methods to the analysis of scattering from acoustical targets scales unfavorably with problem size. Indeed, performing a three-dimensional scattering analysis using these methods requires O(NtNs2) operations, where Ns denotes the number of basis functions that model the spatial field distribution over the surface of the scatterer and Nt is the number of time steps in the analysis. Recently, novel plane wave time domain algorithms that augment these classical methods and thereby reduce their high computational cost have been introduced. This paper describes such a plane wave time domain algorithm within the context of the analysis of acoustic scattering from rigid bodies and outlines its incorporation into a time domain integral equation solver in a two-level setting. It is shown that the resulting scheme has a computational complexity of O(NtNs1.5 log Ns). Examples comparing the accuracy and computational efficiency of the conventional and accelerated methods are presented. The proposed two-level scheme renders feasible the broadband analysis of scattering from large and complex bodies. © 1999 Acoustical Society of America.
Show PACS
43.20.Px Transient radiation and scattering
43.20.Fn Scattering of acoustic waves
02.70.Pt Boundary-integral methods

Elucidation of the relationship between complex acoustic power and radiation efficiency for vibrating bodies

Pei-Tai Chen

J. Acoust. Soc. Am. Volume 106, Issue 5, pp. 2417-2423 (1999); (7 pages)

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This investigation examines the physical meaning of surface complex acoustic power and its relationship to acoustic radiation efficiency. It is shown that the radiated power is the power radiating out of a far-field surface where the plane wave relationship between pressure and particle velocity holds. Meanwhile, the reactive power pertains to the difference between kinetic energy and potential energy. A stationary condition of the ratio between the radiated power to the reactive power yields an eigenvalue problem, subsequently decomposing the surface acoustics into a modal representation. Doing so further allows the examination of the relationship between acoustic radiation efficiency and power factor of the complex power. According to the results, the radiation efficiency of the first radiation mode is nearly equal to the square of the first modal power factor. The modes beyond the first of the modal radiation efficiencies are relatively larger than the corresponding squared modal power factors. Numerical examples of elastic structures subjected to external forces illustrate the relationship between radiation efficiencies and power factors of complex powers. © 1999 Acoustical Society of America.
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43.20.Tb Interaction of vibrating structures with surrounding medium
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