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May 2001

Volume 105, Issue 5, pp. 2388-L12

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Variational formulation using integral equations to solve sound scattering above an absorbing plane

C. Granat, M. Ben Tahar, and T. Ha-Duong

J. Acoust. Soc. Am. Volume 105, Issue 5, pp. 2557-2564 (1999); (8 pages) | Cited 2 times

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The boundary element method is used to model two-dimensional acoustic radiation and scattering from a body of arbitrary shape above an infinite plane of flat surface and homogeneous impedance. The particularity of the study is the use of an indirect integral representation of the solution, given in terms of the jumps of pressure and its normal derivative through the boundaries. A variational formulation is associated with the boundary indirect integral equations modeling our problem. The major difficulty in the formulation is the infinite feature of the plane, which is avoided by introducing an appropriate Green’s function. Numerical results of the attenuation of sound by noise barriers are presented. They show good agreement with other results in the literature. © 1999 Acoustical Society of America.
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43.20.-f General linear acoustics
43.20.Fn Scattering of acoustic waves

On the radiation of ultrasound into an isotropic elastic half-space via wavefront expansions of the impulse response

Dmitri Gridin

J. Acoust. Soc. Am. Volume 105, Issue 5, pp. 2565-2573 (1999); (9 pages) | Cited 4 times

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The problem of propagation of pulses in the radiating near zone of a large circular normal transducer directly coupled to a homogeneous and isotropic elastic half-space is re-visited. It is shown that for certain observation angles the impulse response approach is computationally inefficient. A new method based on the so-called wavefront expansions of the impulse response is developed instead. The expansions are obtained by the analytical harmonic synthesis of the high-frequency asymptotics of the transducer field. Unlike these asymptotics the wavefront expansions are expressed in terms of elementary functions only. The direct P, edge P and S waves as well as the transition regions (penumbra and axial region) are described. The uniform asymptotic expansions applicable throughout the radiating near zone are derived as well. The code based on the time convolution of the pressure input function with the wavefront expansions is compared to a direct numerical code. It is thousands of times faster but practically just as accurate except that the phenomena related to the head waves are not described. Formulas pertaining to the far field are also offered. © 1999 Acoustical Society of America.
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43.20.Bi Mathematical theory of wave propagation
43.20.Dk Ray acoustics
43.35.Zc Use of ultrasonics in nondestructive testing, industrial processes, and industrial products

The full-field equations for acoustic radiation and scattering

Martin Ochmann

J. Acoust. Soc. Am. Volume 105, Issue 5, pp. 2574-2584 (1999); (11 pages) | Cited 13 times

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The source simulation technique or related approaches like the multipole method, the superposition method, etc. are used for calculating the sound field radiated (or scattered) from complex-shaped structures. However, it is known that these techniques can lead to ill-conditioned systems of equations, and their numerical treatment requires extreme care. A new stabilized variant of the source simulation technique—called the full-field method—has been developed by using the exterior instead of the interior Helmholtz integral formulation or, equivalently, by expanding the sound field into special trial and weighting functions. These functions are chosen in such a way that the resulting matrix becomes more diagonally dominant. The full-field method is applied to the acoustic radiation from a pulsating sphere and to the high-frequency scattering from a cylinder and a nonconvex structure. The numerical results are compared with calculations obtained from other methods. It is shown that the improved method leads to better conditioned sets of equations which can be solved directly without singular-value decomposition, since the associated condition numbers are decreased strongly, in some cases by a few orders of magnitude. © 1999 Acoustical Society of America.
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43.20.Fn Scattering of acoustic waves
43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.30.Jx Radiation from objects vibrating under water, acoustic and mechanical impedance
43.40.Yq Instrumentation and techniques for tests and measurement relating to shock and vibration, including vibration pickups, indicators, and generators, mechanical impedance

Interface conditions for Biot’s equations of poroelasticity

Boris Gurevich and Michael Schoenberg

J. Acoust. Soc. Am. Volume 105, Issue 5, pp. 2585-2589 (1999); (5 pages) | Cited 17 times

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Interface conditions at a boundary between two porous media are derived directly from Biot’s equations of poroelasticity by replacing the discontinuity surface with a thin transition layer, in which the properties of the medium change rapidly yet continuously, and then taking the limit as the thickness of the transition layer approaches zero. The interface conditions obtained in this way, the well known “open-pore” conditions, are shown to be the only ones that are fully consistent with the validity of Biot’s equations throughout the poroelastic continuum, including surfaces across which the medium properties are discontinuous. But partially blocked or completely impermeable interfaces exist; these may be looked upon as the case of a thin layer with its permeability taken to be proportional to the layer thickness, again in the limit as layer thickness approaches zero. This approach can serve as a simple recipe for modeling such an interface in any heterogeneous numerical scheme for poroelastic media. © 1999 Acoustical Society of America.
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43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves

Multimode radiation from an unflanged, semi-infinite circular duct

Phillip Joseph and Christopher L. Morfey

J. Acoust. Soc. Am. Volume 105, Issue 5, pp. 2590-2600 (1999); (11 pages) | Cited 6 times

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Theoretical expressions for sound radiation from a single incident duct mode, arriving at the open end of a semi-infinite circular unflanged duct with rigid walls, are used to obtain numerical results for (1) the single-mode sound power transmission coefficient, and (2) the multimode far-field directivity factor. For the multimode calculations the modes are assumed incoherent, and a weighting model is adopted which includes, as special cases, equal power per mode (above cutoff), and excitation by incoherent monopoles or axial dipoles uniformly distributed over a duct cross section. High-frequency asymptotic features of the results are explored in detail and analytical approximations are given. The findings have practical application to sound power measurement from tall exhaust stacks. © 1999 Acoustical Society of America.
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43.20.Mv Waveguides, wave propagation in tubes and ducts
43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods

Dispersion of longitudinal waves propagating in liquid-filled cylindrical shells

Hegeon Kwun, Keith A. Bartels, and Christopher Dynes

J. Acoust. Soc. Am. Volume 105, Issue 5, pp. 2601-2611 (1999); (11 pages) | Cited 3 times

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The dispersion of the first two longitudinal wave modes, L(0,1) and L(0,2), was experimentally investigated for a cylindrical shell (such as a pipe or tube) that was completely filled with a liquid. It was observed that the presence of a liquid inside the cylinder dramatically alters the dispersion curve for the L(0,2) mode by dividing (or branching) the curve into approximately equally spaced regions separated by cutoff-type behavior. This branching was attributed to coupling between the unperturbed L(0,2) mode in the shell and the unperturbed longitudinal modes in a liquid cylinder with rigid boundaries, LL(0,2N), where N is an integer. The physical mechanism for the mode coupling was determined to be radial resonances in the combined liquid/pipe system. In time domain, the liquid effects on the dispersion are manifested as a long-duration signal or a series of short-duration pulses, depending on the pulse length of the transmitted signal relative to the reciprocal of the frequency interval between branching. © 1999 Acoustical Society of America.
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43.40.At Experimental and theoretical studies of vibrating systems
43.20.Mv Waveguides, wave propagation in tubes and ducts

Comparison of acoustic fields radiated from piezoceramic and piezocomposite focused radiators

D. Cathignol, O. A. Sapozhnikov, and Y. Theillère

J. Acoust. Soc. Am. Volume 105, Issue 5, pp. 2612-2617 (1999); (6 pages) | Cited 5 times

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The acoustic field radiated from piezoelectric transducers is usually predicted supposing that the transducer vibrates in thickness mode. However, different reports have shown that not only thickness vibrations were excited, but also plate waves. These waves are responsible for discrepancy between the experimental acoustic fields and those predicted by the Rayleigh integral. It could be supposed that the plate waves are strongly attenuated in piezocomposite materials, as mechanical cross-talk between neighboring elements of the composite structure is fairly weak. A similar effect could be achieved in piezoceramic material by employing a heavy backing, which partially damps the plate waves. These opportunities of plate wave damping are investigated in the present paper. Three transducers are studied, which have identical geometrical characteristics, but are made from different materials. The plate waves in these transducers are indirectly compared by measuring corresponding ultrasound fields and comparing them with theoretically predicted field. It is shown that plate wave patterns are strongly material dependent and that it is only for piezocomposite sources (even when highly focused) that Rayleigh integral modeling can accurately predict the pressure field distribution. © 1999 Acoustical Society of America.
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43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
43.20.Bi Mathematical theory of wave propagation
43.20.Px Transient radiation and scattering
43.38.Fx Piezoelectric and ferroelectric transducers

Extension of the angular spectrum approach to curved radiators

Ping Wu and Tadeusz Stepinski

J. Acoust. Soc. Am. Volume 105, Issue 5, pp. 2618-2627 (1999); (10 pages) | Cited 5 times

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The angular spectrum approach (ASA) is conventionally applied to the evaluation of acoustic fields from planar radiators because it is usually based on the 2-D Fourier transform (or the zero-order Hankel transform in the axisymmetrical case) which is implemented only in a plane. The present paper is intended to extend the ASA to more general cases where radiators have curved surfaces. For this purpose, two approaches are developed. The first one is the extended ASA and is derived in a general way. From this approach, the angular spectrum of a curved radiator is given by a double integral that does not take the 2-D Fourier transform form, and thus cannot be implemented using 2-D fast Fourier transform (FFT) but by numerical integration. The second approach is the indirect ASA that gives the angular spectrum via 2-D Fourier transforming an initial field pre-calculated in a plane. The method for calculating the initial field is proposed based on the method developed by Ocheltree and Frizzell for planar sources. An example is given of a linear array with a cylindrically concave surface, and in this case, the angular spectrum (the double integral) from the extended ASA reduces to a single integral. The angular spectra of the array are calculated using both approaches and compared. The comparison has shown that the angular spectra obtained from both approaches are in excellent agreement. The accuracy and efficiency of the two approaches are studied in the numerical implementation. In this example, the extended ASA has been shown to be more efficient and more accurate than the latter approach. Both approaches can be applied to arbitrarily curved transducers. In the general case where the double integral cannot be reduced to a single integral, the latter approach can be more efficient. © 1999 Acoustical Society of America.
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43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
43.20.Bi Mathematical theory of wave propagation
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