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May 1990

Volume 87, Issue S1, pp. S1-S164

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back to top Session TT. Physical Acoustics VI and Underwater Acoustics VIII: Wave Propagation in Random and Quasiperiodic Media
Invited Papers
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Probing porous media with superfluid acoustics (A)

David Linton

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S112-S112 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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Those properties of porous media that can be deduced from experiments using measurements of superfluid 1st, 2nd, 4th, and 3rd sound are discussed; the transferability of these results to other transport experiments, especially the acoustic properties of porous media saturated with Newtonian fluids, is also explored. Many of the relevant geometrical parameters are those that arise in a canonical electrical conductivity problem in which the porous solid is insulating, the pore fluid is conducting, and there is an additional surface conductivity lining the walls of the pore space. The most important geometrical parameters are the three‐dimensional tortuosity of the pore space, α2 the two‐dimensional tortuosity of the pore/grain interface, α2, and ʌ, which is a well‐defined measure of dynamically connected pore sizes.
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Sound propagation in superfluid helium as a probe of the microscopic geometry of a porous solid (A)

S. R. Baker

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S112-S112 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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Liquid helium is unique among substances on Earth in that when it is cooled to extremely low temperatures it has the ability to flow without friction through the tiniest of channels. More than any other, this property of liquid helium at low temperatures, or superfluid helium, as it is known, makes sound propagation in it a superior probe of the microscopic geometry of a porous solid. It will be shown how the three Blot parameters that characterize the microscopic geometry of a porous solid may be extracted from speed and attenuation measurements of the propagating sound modes in superfluid helium contained within it. The results of experiments in which such measurements were made for a variety of porous solid samples will be described. [Work supported by ONR, NRL‐USRD, and the Naval Postgraduate School.]
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Molecular dynamics of viscous flows (A)

Jayanth R. Banavar, Wen‐Jong Ma, Joel Koplik, and Jorge Willemsen

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S112-S112 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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Molecular dynamics techniques are used to study the microscopic aspects of several slow viscous flows past a solid wall, where both fluid and wall have a molecular structure. Systems of several thousand molecules are found to exhibit reasonable continuum behavior, albeit with significant thermal fluctuations. In Couette and Poiseuille flow of liquids it is found that the no‐slip boundary condition arises naturally as a consequence of molecular roughness, and that the velocity and stress fields agree with the solutions of the Stokes equations. At lower densities slip appears, which can be incorporated into a flow‐independent slip‐length boundary condition. An immiscible two‐fluid system is stimulated by a species‐dependent intermolecular interaction. The local velocity field near a moving contact line shows a breakdown of the no‐slip condition and, up to substantial statistical fluctuations, is consistent with earlier predictions of Dussan. [Work supported by NSF.]
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Direct and inverse problems for pulse reflection from random media (A)

George C. Papanicolaou

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S112-S112 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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The reflection of pulsed acoustic waves from a layered random half‐space is studied. A theorem that determines the local power spectral density of the reflected signal on the surface is given. From the structure of this power spectral density, slowly varying properties of the medium can be inferred. Extensive numerical computations that delineate the scope of the theory are presented.
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Acoustic.wave propagation in quasiperiodic, incommensurate, and random systems (A)

Jian Ping Lu and Joseph L Birman

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S113-S113 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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Acoustic‐wave propagation in one‐dimensional systems with quasiperiodic, incommensurate, and random modulation is studied [J.P. Lu and J.L. Bitman, Phys. Rev. B 38, 8067 (1988)]. In the short‐wavelength limit it was found that if the initial pulse is narrow (with a spatial extension of a few lattice spacings), the pulse is localized in a quasiperiodic system, as in the case of a random system. This indicates that at short length scale a quasiperiodic system is similar to a random system. On the other hand, if the initial injected wave has a wavelength much larger than the lattice spacing, it is found that there is resonance for quasiperiodic and incommensurate systems when the wave vector satisfies the Bragg conditions. In this case the propagation appears to be diffusive rather than propagative; namely, the total energy of the initial wave does not propagate along the chain as it does otherwise, but is homogeneously distributed over the region of space where the wave front passed. The problem is solved analytically in the long‐wavelength limit in terms of two‐mode‐coupling theory and the Fourier spectrum of the quasiperiodic systems. Analytical results are in full agreement with numerical simulations.
Contributed Papers
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Finite‐difference modeling of acoustic waveforms in a fluid‐filled borehole surrounded by a Biot porous media (A)

Sergio Kostek and Alvin Bayliss

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S113-S113 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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Analytical techniques are very efficient in dealing with either homogeneous or layered fluid‐saturated poroelastic media. Inhomogeneities in the material properties or complicated interfacial boundaries make the problem analytically intractable, forcing then the use of numerical techniques such as finite‐difference, finite element, etc. An explicit finite‐difference time domain modeling scheme that is able to handle fluid, elastic, and fluid‐saturated poroelastic complex media is presented. In particular, an axisymmetric version of the code is used to model acoustic wave propagation in fluid‐filled boreholes surrounded by a Biot type of medium. The effects of borehole rugosity, mudcake, and vertical layering are investigated. Comparisons with analytical solutions in simple cases are also made, showing good agreement between the different methods. Absorbing boundary conditions for application in the porous regions were also developed and proved to be effective in avoiding spurious reflections.
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Forced response and acoustical radiation for beams with periodic and quasiperiodic attachments (A)

Ten‐Bin Yuang and Anna L. Pate

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S113-S113 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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A uniform Bernouli‐Euler beam with multiple, concentrated mass/stiffness/damping attachments is investigated with the transfer matrix method. The method is similar to that of Y. K. Lin and T. J. McDaniel [Trans. ASME, J. Eng. Ind. (Nov. 1969)]. The response of the beam to a point force as well as the associated acoustical radiation are calculated. Specifically, the effect of periodic and quasiperiodic attachments on the beam response is of interest. Numerical results are compared with the results of experimental studies of both vibrations and nearfield and farfield acoustical radiation of the beam. [Work supported by ONR.]
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Experiments on linear and nonlinear wave propagation in random and quasiperiodic media (A)

Mark J. McKenna, P. S. Spoor, R. L. Stanley, Elaine Dimasi, and J. D. Maynard

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S113-S113 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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Since the development of Anderson localization and the discovery of aluminum alloy quasicrystals, there has been considerable experimental and theoretical interest in wave propagation in random and quasiperiodic systems. More recently, there has been interest in the nonlinear properties of such systems. Having completed some experimental research on the linear behavior of waves in a one‐dimensional random system and a two‐dimensional quasiperiodic system, the nonlinear properties of such systems are now being studied. Two systems, one having a local nonlinear interaction (surface waves in a superfluid film) and the other having a global nonlinear interaction (transverse waves in a stretched string), will be described. [Work supported by NSF DMR 8701682 and the Office of Naval Research.]
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Linear and nonlinear acoustic propagation in a periodic waveguide (A)

Charles E. Bradley

J. Acoust. Soc. Am. Volume 87, Issue S1, pp. S113-S113 (1990); (1 page)

Online Publication Date: 13 Aug 2005

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The effect of periodic nonuniformity of a waveguide on the propagation of both infinitesimal and finite‐amplitude waves is investigated theoretically and experimentally. Analytic expressions for a dispersion relation, the impedance function, and the Bloch wavefunction are derived for the case of linear, plane wave mode propagation in a rectangular wave‐guide that is periodically loaded with rigidly terminated side branches. Experiments have been done in a 25.4‐mm × 38.1‐mm × 6‐m air‐filled aluminum waveguide with 38.l‐mm‐deep side branches at 0.l‐m intervals. Measurements verify the predicted passband/stopband structure of the dispersion relation and the forward and backward traveling wave composition of the Bloch wavefunction. In the case of finite‐amplitude excitation, the compound wave composition of the fundamental Bloch wave results in a bidirectional excitation of the second harmonic. Preliminary measurements show that second harmonic behavior is qualitatively similar to that for an ordinary dispersive medium in that parametric upconversion is effectively blocked. Possible application in the amplification of traveling waves is discussed. [Work supported by U.S. Office of Naval Research.]
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