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Jun 1979

Volume 65, Issue S1, pp. S2-S142

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back to top Session H. Physical Acoustics II and Underwater Acoustics II: Waves in Layered Media
Invited Papers
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Waves in periodically layered media (A)

G. Herrmann

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S19-S19 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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Waves in linearly elastic media of infinite extent, composed of alternating layers of two different materials with perfectly bonded interfaces, exhibit some special features which are due to periodicity and impedance discontinuities at each interface. Floquet's theory permits an analysis of such waves which naturally separates into problems of anti‐plane and plane strain. The recently developed dispersion relations for such waves will be discussed, placing emphasis on the special features, such as existence of stopping bands, transition points, conical points, and asymptotic behavior. More. recent work on the applicability of Floquet‐type solutions in anti‐plane strain to layered semi‐infinite media with traction‐free surfaces parallel to the layers and to layered plates will also be discussed. A new class of surface is shown to exist which are dispersive, are restricted to a limited frequency range in some cases, and which can be propagating or evanescent. Finally. attempts to mathematically, model waves in periodically layered media by means of approximate theories will be mentioned, in particular the class of “effective dispersion” theories, which contain both the dispersive and the filtering properties.
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Wave propagation in single and multiple visoelastic layers (A)

Walter Madigosky

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S19-S20 (1979); (2 pages)

Online Publication Date: 11 Aug 2005

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This paper summarizes recent progress in wave propagation in fluid, elastic, and viscoelastic layers. This work finds application in underwater acoustics, NDT, geophysics, SAW devices, medical acoustics, etc. The role of absorption in viscoelastic layers can be accounted for by introducing complex propagation constants into elastic theories. This necessitates the need for four independent material constants, one of which (the shear loss) is difficult to obtain experimentally. This difficulty has been overcome by introducing a physical model relating the shear to longitudinal absorption. In the case of inhomogeneous layers (frequently encountered in practice) a theory which predicts effective material constants, including dynamic effects, is introduced. These constants can then be used in computer codes to calculate the transmission (T), reflection (R), and absorption coefficients for single and multiple layered configurations. The effect of finite thickness and fluid loading on the acoustic properties has recently been clarified by the application of the resonance theory which readily allows the interpretation of resonances in T and R. Resonance widths and amplitudes are modified by the presence of absorption loss, and the interaction between resonances accounts for an apparent violation of the coincidence rule in viscoelastic layers.
Contributed Papers
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Generation of ultrasonic leaky waves at liquid‐solid interfaces (A)

Laszlo Adler

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S20-S20 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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Recent experimental investigations by M. A. Breazeale, L. Adler, and G. W. Scott [J. Appl. Phys. 48, 530–537 1977)] have verified the theory of Bertoni and Tamir [Appl. Phys. 2, 157–172 (1973)]. Excitation of leaky Rayleigh waves takes place at the liquid‐solid interface when a Gaussian ultrasonic beam is incident at or near the Rayleigh angle to the interface. Now we should like to report two additional examples of leaky wave generation: (1) When a thin (less than a wavelength) ceramic layer is added to a metal surface, leaky waves are generated. The velocity and amplitude distribution of these waves will be discussed. (2) For interfaces such as water‐Plexiglas no real solution of the leaky Rayleigh velocity exists since the sound velocity in the water is larger than the shear velocity in Plexiglas. By studying the reflection of an incident Gaussian beam from water‐Plexiglas interfaces we have observed leaky waves near the longitudinal critical angle. Similar observations were made at water‐sediment interfaces. [M. A. Breazeale and L. Bjørnø, Proc. Ultrasonics Int., 1977, pp. 440–444]. [Research supported in part by the Office of Naval Research.]
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Attenuation of Stoneley waves on boundaries between thin bonded glass substrates (A)

R. O. Claus and R. L. Renfro

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S20-S20 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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Variations in the attenuation of Stoneley waves on the glued boundaries between several thin aluminized front surface mirrors and flat 7070 Pyrex glass samples are reported [R. Stoneley, Proc. R. Soc. London Ser. A 106, 416–428 (1924)]. The Pyrex samples were ground using successively finer grades of carborundum abrasive. Nine megahertz surface acoustic waves (SAW) generated on the mirror surface were converted to Stoneley waves on the 2.54 cm by 0.635 cm mirror glass/ground glass sample boundary and then back from Stoneley to SAW on the opposite side of the sample. Stoneley wave attenuation was determined for each pair by optically measuring incident and transmitted SAW amplitudes via fixed input beam differential interferometry [C. H. Palmer, J. Acoust. Soc. Am. 53, 948–949 (1973)]. Preliminary results indicate a correlation between measure Stoneley wave attenuation and adhesive bond and interface quality. [Work supported by NSF under Grants ENG‐78‐05773 and ENG‐78‐11040.]
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Existence of Stoneley waves on boundaries between acoustically similar solids (A)

R. L Renfro and R. O. Claus

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S20-S20 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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Stoneley waves exist on the boundaries between a limited range of isotropic and anisotropic solids and have been directly and indirectly detected on several pairs at ultrasonic frequencies [D. A. Lee and D. M. Corbly, IEEE Trans. Sonics Ultrason. SU‐24, 206 (1977); R. O. Claus and C. H. Palmer, Appl. Phys. Lett. 31, 547 (1977)]. Of particular importance to current optical measurements are those waves that exist between pairs of transparent glass substrates for which Weichert's condition, μ1/μ2 ≈ ρ1/ρ2 ≈ 1, is nearly satisfied. We study the range of possible existence for these pairs and indicate that the existence region in the (μ1/μ2), (ρ1/ρ2) plane defined by Scholte [Proc. Ned. Akad. Weten. 45, 20, 159, 380, 439, 516, (1942)] degenerates to a single point when the media obey Weichert's equality. Experimental implication of the theoretical results is discussed. [Work supported by NSF under Grants ENG‐78‐05773 and ENG‐78‐11040.]
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Acoustical behavior of an elastomer‐coated submerged steel plate with one unconstrained surface (A)

Anthony J. Rudgers and Martin D. Ring

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S20-S20 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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The results of a computer evaluation of the theoretical equations that describe the acoustic field either radiated or reflected by a 5‐cm‐thick steel plate, to which is bonded an elastomer coating, are reported. The equations that describe the acoustical behavior of the coated plate were derived by applying Timoshenko‐Mindlin thick‐plate theory to both the plate and the coating layer. The coated plate has water on one side and is unconstrained on the other. The computations treat elastomeric coating layers of various thicknesses. Two different elastomeric coating materials are also considered, a relatively soft, low‐loss nitrile rubber and a stiffer high‐loss neoprene. The computations demonstrate that the presence of an elastomeric coating, whatever the elastic properties of the coating material might be, does not significantly affect the acoustical characteristics of the steel plate, even when the coating thickness becomes equal to the thickness of the plate. The reason why elastomer‐coated plates exhibit this behavior is discussed.
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Torsional waves in a bimetallic rod with laminated, periodic structure (A)

R. K. Kaul, W. Muller, and R. P. Shaw

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S20-S21 (1979); (2 pages)

Online Publication Date: 11 Aug 2005

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Torsional waves are studied for an elastic traction free circular cylinder with an axial periodic structure and a cylindrical core and concentric casing (of differing materials) radially. Pochhammer type solutions are obtained first and the dispersion spectrum is found in terms of an interfacial coupling coefficient, Q. As Q approaches zero, or infinity, the problem reduces to a core and casing with traction free surfaces and a core with a displacement free outer boundary and casing with displacement free inner boundary and traction free outer boundary, respectively. The actual spectrum is bounded by these two cases; furthermore, invariant points exist in the spectrum which do not depend on the material properties. The frequency equation is solved explicitly for long wavelengths using McMahon type expansions and various features of the spectrum at long wavelengths and high frequencies, asymptotic results for slopes and curvatures, are discussed. Next, the propagation of Floquet waves is examined; at the end of each Brillouin zone, the frequency equation uncouples and the presence of passing and stopping bands and conical points is exhibited. [Work supported by ONR.]
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Viscoelastic effects in resonant sound scattering from layered cylindrical shells (A)

G. C. Gaunaurd and H. Überall

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S21-S21 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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We consider a layered cylindrical structure consisting of an inner elastic shell supporting an outer viscoelastic layer. The structure is immersed in an outer fluid and it contains a dissimilar fluid in its interior. We study the scattering of sound waves normally incident on the structure utilizing the recently developed resonance theory of sound scattering. The role of the viscoelastic properties of the outer layer in the damping of the scattering resonances is investigated, as well as their effect on the partial wave scattering amplitudes, making up the monostatic cross section of the structure. For the purpose of this investigation, we have isolated the resonances from the composite partial‐wave contributions, and we have quantitatively shown to what extent their strength can be effectively reduced, for all modes, by increasing the viscous level of the outer layer. [H. Überall is also at Catholic University, Washington, DC, and was additionally supported by Code 421 of ONR.]
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Minimum reflectance of inhomogeneous layers; normally incident, monochromatic sound waves (A)

K. P. Scharnhorst

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S21-S21 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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We discuss the problem of determining the minimum reflectance achievable with a given inhomogeneous layer thickness, substrate input impedance and range of allowed material parameters for normally incident, monochromatic sound waves. The density and dilitation modulus are permitted to vary independently. Real and complex moduli are considered. In the case of real parameters, analytic solutions for the switching curves and sublayer thicknesses of the multilayer system are presented. The resulting sublayer sequences will be discussed. The sequences are periodic and we show that for certain combinations of parameters the reduced unit cell thickness is approximately equal to 2π radians. General results concerning the parametrization of sublayers in the case of complex moduli will be discussed. Examples of particular solutions will be presented.
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On the formation of parametric acoustic arrays in layered media (A)

F. H. Fenlon and D. L. Yeager

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S21-S21 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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The interaction of directive finite‐amplitude waves in a liquid layer embedded in two isotropic homogeneous “liquid‐like” (i.e., low shear moduli) half‐spaces of arbitrary impedance is reviewed in this paper via analytical solutions of the second‐order acoustic wave equation. Necessary conditions for mode‐locking in the layer are deduced in terms of the boundary‐induced dispersion characteristics of the composite medium and the angle of intersection of the primary waves. On the basis of these results, the potential utility of parametric acoustic arrays for directive “low‐frequency” penetration of typical geophysical strata is then briefly addressed.
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Diffraction at a caustic—A correction to ray theory (A)

A. A. Hudimac

J. Acoust. Soc. Am. Volume 65, Issue S1, pp. S21-S21 (1979); (1 page)

Online Publication Date: 11 Aug 2005

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It had been shown that the errors of a ray theoretic solution could be corrected by the radiation from a volume distribution of simple sources having the phase of the ray theoretic solution at that point, and a strength proportional to the Laplacian of the ray theoretic amplitude. On the boundary between an ensonified region and a shadow zone, the correcting distribution is a surface distribution of simple sources and/or dipoles. This correction remains valid even in the case of a caustic. Previous calculations have been extended for a particular example of a caustic, and the evanescent field has been calculated. The comparison between this approximate result and the known result obtained by a wave theoretic method is good.
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