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Apr 1998

Volume 103, Issue 4, pp. 1689-2236

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Temporal backward planar projection of acoustic transients

G. T. Clement, R. Liu, S. V. Letcher, and P. R. Stepanishen

J. Acoust. Soc. Am. Volume 103, Issue 4, pp. 1723-1726 (1998); (4 pages) | Cited 1 time

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Backward projection schemes use data in front of a transmitter to reconstruct a field at closer points. Existing techniques have concentrated propagating radial and temporal information along constant planar cross sections in front of a planar source. This approach requires a careful consideration of evanescent waves, as the transfer function used to backproject in space causes evanescent wave solutions to increase exponentially with the projected distance. Erroneous signals may result from exponentially increasing noise, experimental error or roundoff error. A method is presented that is designed to work with imaging methods that record three-dimensional spatial data at constant times. Several widely used optical methods are of this type. Our algorithm projects the field backward in time via linear wave theory. The approach is similar to previously reported methods but is designed to work with time-constant data and avoids problems associated with evanescent waves. © 1998 Acoustical Society of America.
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43.20.Bi Mathematical theory of wave propagation

Bounds and approximations for elastodynamic wave speeds in tetragonal media

Q. H. Zuo and K. D. Hjelmstad

J. Acoust. Soc. Am. Volume 103, Issue 4, pp. 1727-1733 (1998); (7 pages)

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This paper presents an analytical study of elastodynamic waves propagating along an arbitrary direction in anisotropic materials with tetragonal symmetry. Upper and lower bounds are developed on the wave speeds through an additive decomposition of the acoustic tensor into an associated hexagonal counterpart and a rank-one modification, the eigenproperties of which can be determined analytically. The bounds are obtained by applying the minimax property of eigenvalues. Linear approximations of the wave speeds are obtained from a first-order expansion of the eigenvalues of the acoustic tensor, with respect to a tetragonality index, about the value of that index for which tetragonal symmetry degenerates to hexagonal symmetry. A numerical example shows that the linear approximations agree remarkably well with the exact values of the wave speeds. © 1998 Acoustical Society of America.
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43.20.Bi Mathematical theory of wave propagation
43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves
43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants

Moving frame technique for planar acoustic holography

Hyu-Sang Kwon and Yang-Hann Kim

J. Acoust. Soc. Am. Volume 103, Issue 4, pp. 1734-1741 (1998); (8 pages) | Cited 11 times

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Acoustic holography is one of the best methods to visualize sound fields. The quality of the visualized sound is primarily determined by the size of the hologram, its microphone spacing, and the number of microphones. This paper describes a way to virtually increase the hologram size and the spatial resolution of the holograph. For a stationary sound field, the method continuously sweeps the sound field by a line array of microphones. For moving sound sources, radiating sound is measured by using a line array of microphones fixed in space. In both cases, the measured signals have Doppler effects. The theoretical formulation has been systematically addressed by employing a moving coordinate which has relative motion between the measurement coordinate and the hologram coordinate. Simulations and experiments support the proposed theory. The drawback is that the method is only applicable to discrete frequencies. © 1998 Acoustical Society of America.
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43.20.Fn Scattering of acoustic waves
43.35.Sx Acoustooptical effects, optoacoustics, acoustical visualization, acoustical microscopy, and acoustical holography

Acoustic bullets/transient Bessel beams: Near to far field transition via an impulse response approach

Peter R. Stepanishen

J. Acoust. Soc. Am. Volume 103, Issue 4, pp. 1742-1751 (1998); (10 pages) | Cited 8 times

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Acoustic transient Bessel beams (TBB) are a new class of waves which maintain their peak amplitude and general shape as they propagate in free space from an infinite planar aperture. The on axis and far field space-time properties of acoustic TBB waves generated by a finite spatial aperture are investigated using impulse response methods. The on-axis transition from the near field to the far field is investigated and several analogies to the acoustic field generated from a circular piston source are observed. In particular, the importance of an edge generated wave in determining the transition for the TBB field is clearly noted. Space-time properties of the far field are also investigated as a function of polar angle using impulse response methods. Numerical results are presented to illustrate the general characteristics of the on-axis and far field impulse response for a finite aperture. © 1998 Acoustical Society of America.
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43.20.Fn Scattering of acoustic waves

On coupled modes theory of two-dimensional wave motion in elastic waveguides with slowly varying parameters in curvilinear orthogonal coordinates

V. B. Galanenko

J. Acoust. Soc. Am. Volume 103, Issue 4, pp. 1752-1762 (1998); (11 pages) | Cited 1 time

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Coupled modes theory, as applied to 2-D wave propagation in range-dependent isotropic elastic waveguides in curvilinear orthogonal coordinates, is proposed. The model consists of one or more curvilinear layers with interfaces and outer boundaries departing slowly from the coordinate surfaces. The material parameters are supposed to be slowly dependent on the longitudinal coordinate. Four-dimensional vector-valued functions with the displacements, rotation, and divergence as the components are shown to be a convenient form of wave field description to extend the coupled modes theory from liquid to elastic waveguides. For this case, the cross section operator is defined and the generalized bi-orthogonality property of its eigenfunctions is established. Using the generalized bi-orthogonality, the coupling equations are derived. Wave propagation in a tube which narrows slowly to a conic rod and in a disk of radially dependent thickness are considered as the examples. The differences between the results obtained by the coupled modes theory and those the multiple-scales theory leads to are discussed. The theory modification for dealing with a cutoff phenomenon and the general algorithm of computation of the wave field excited by a point source are considered. © 1998 Acoustical Society of America.
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43.20.Mv Waveguides, wave propagation in tubes and ducts
43.20.Ks Standing waves, resonance, normal modes

An alternative formulation for predicting sound radiation from a vibrating object

Sean F. Wu and Qiang Hu

J. Acoust. Soc. Am. Volume 103, Issue 4, pp. 1763-1774 (1998); (12 pages) | Cited 2 times

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An alternative formulation is derived for predicting acoustic radiation from a vibrating object in an unbounded fluid medium. The radiated acoustic pressure is shown to be expressible as a surface integral of the particle velocity, which is determinable by using a nonintrusive laser velocimeter. This approach is in contrast with the Kirchhoff integral formulation which requires the knowledge of both the normal component of the surface velocity and the surface acoustic pressure prior to predicting the radiated acoustic pressure. Solutions thus obtained are unique. Moreover, the efficiency of numerical computations is high because the surface integration can be readily implemented numerically by using standard Gaussian quadratures. This alternative formulation may be desirable to analyze the acoustic and vibration responses of a lightweight, a flexible, or a structure under an adverse environment for which a nonintrusive laser measurement technique must be used. Validations of this alternative formulation are demonstrated both analytically and numerically for vibrating spheres and right circular cylinders. © 1998 Acoustical Society of America.
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43.20.Tb Interaction of vibrating structures with surrounding medium
43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
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