885095940

3:30

4:15

7PA10. Directions of degenerate plane-wave propagation in orthorbombic media. Michael Schocnberg (Schlumberger Cambridge Res., Madingley Rd., Cambridge CB3 OEL, England) and Klaus Helbig (Rijksuniversiteit Utrecht, Ven»ng Meinesz Laboratorium. POB 80.021, 3508 TA Utrecht, The Netherlands)

At each direction of propagation in an anisotropic elastic medium, there are three possible piane waves, each with its characteristic phase slowness. Points at which one or morę of the sheets of the slowness surfacc are in contact are “degenerate” and specify directions for which the characteristic equation has repeated roots. For an orthorhomic medium, one with three mutually orthogonal mirror symmetry planes (and no further symmetry, for the purposes of this discussion), the degener-atc directions are isolated. For degenerate directions that lie in any of the symmetry planes, the characteristic cubic equation in three vari-ables, i.e., the squares of the three components of the slowness vector, is factorable, and the problem rcduces to solving for the intersection of a straight linę and a eonie. The problem is much morę complicatcd out of the symmetry planes as the characteristic equation is not factorable. However, from the fact that in a degenerate direction, the Christoffcl equations' 3x3 matrix of coefficients, whose eigenvalues and eigenvec-tors give the slownesses and polarizations of the three waves, is rank one or less, one finds three linear equations on the squares of the three components of the repeated slowness vector. If the squares of the components are all positive, there is a single degenerate direction, not lying in any symmetry piane, in each symmetric octant, and explicit expres-sions for all relevant quantities are readily derived; if not, there is no degenerate direction that does not lie in a symmetry pbne.

3:45

7PA11. Acoustic wave propagation in a temporal and spatially varying tubę. Charles Thompson and Tam Le (Dept. of Elec. Eng., Lab. for Adv. Comput., Univ. of Lowcll, Lowell, MA 01854)

Acoustic wave propagation in a temporal and spatially varying tubę is investigated. The method of multiple scales is used to determine the dispersion of wave packets. This primary objective is to ascenain the effect of variations in tubę shape on the State transition probabilities uscd in hidden Markov models of speech.

4:00

7PAI2. An approximate numerical solution for the generał radiation problem by combining the method of wave superposition and tbe singular value decomposition. John B. Fahnline and Gary H. Koopmann (Ctr. for Acoustics and Vibration, Penn State Univ., 157 Hammond Bldg., University Park, PA 16802)

In the method of wave superposition, the field due to an arbitrarily shaped radiator is written in terms of the sum of the fields due to a finitc number of simple sources enclosed within the radbtor. The strengths of the sources are determined by requiring that the sum of their individual fields reproduce the radiator’s normal surface velocity at a finite number of locations either exactly or in the least square sense. Through the singular value decomposition (SVD), the dipole matri*, which relates the source strengths and normal surface velocities. can be written as a product of two unitary matrices and a real, diagonal matrix. Each of the unitary matrices represents a set of mutually orthogonal modę vectors, while the diagonal matrix represents the singular values associated with these modes. This decomposition is shown to contain the first jV terms of the exact multipole expansion for the solution of the associated boundary value problem.

7PA13. Acoustic radiation from a chaotic yiscous layer. Charles Thompson and Arun Mulpur (Dept. of Elec. Eng., Lab. for Adv. Comput., Univ. of Lowell, Lowell, MA 01854)

The Stokes boundary layer has been shown to exhibit linear insta-bility with inereasing amplitudę of acoustic excitation. Special consid-eration is given to the amplitudę rangę above which these disturbances bifurcate from linear stability. It is found that oscilbtory modubtion present in the basic-state results in successive period-doubling bifurca-tions for three-dimensional vortical disturbances. The acoustic radiation from these unstable vortical disturbances will be addressed.

4:30

7PA14. Application of direct integnd-equation method in acoustic-ware diffraction. L. C. Huang (Codę 1945, David Taylor Res. Ctr., Bethesda, MD 20084-5000), C. J. Huang, and A. T. Chwang (Dept. of Mech. Eng., The Univ. of Iowa, Iowa City, IA 52242)

The direct integral-equation method (DIEM) is applied to study the difTracted acoustic field of a point source at an arbitrary location relative to a ring aperture in a soft baffle. The velocity potential at an arbitrary field point is expressed in terms of a surfacc-source distribution with complex densities. A set of eight real Fredholm integral equations of the second kind is used to determine the surfacc-source densities. These equations are transformed into discrete forms by applying the Gauss-Legendre quadrature formula in the radia] direction and the best possible numerical integration formula in the angular direction. In com-parison to the boundary-element method, the DIEM is morę efficient, accurate, and flexible. The advantages of DIEM bccome apparent, cs-pecially when the parameters in a given problem vary within a large rangę. The numerical result of source strengths on the baffle surface in the far field agrees very well with the asymptotic solution. The effect of different parameters on the diffracted acoustic field is systematically studied and compared. These parameters include the location of the acoustic source, the wave number, the size of the ring aperture, as well as the thickness of the baffle. The numerical results show that the baffle thickncss and the size of the ring aperture havc relatively little influence on the diffracted acoustic field within the tested rangę. However, the wave number has a signifkant effect on the diffracted pressure field.

4:45

7PAI5. A flow-powered very low-frequency underwater tonę source.

S. A. Elder (U. S. Naval Acad., Annapolis, MD 21402-5026) and S. Yoshikawa (Naval Res. Lab., Washington, DC 20375-5000)

Previous studies of underwater flow excited cavity resonance in streamlined towed models have shown that large amplitudę acoustic oscillations can be achieved at frequencies under 40 Hz for towing speeds in the rangę of 5-15 kn. The present invcstigation aims to de-vclop an understanding of the phenomenon that could permit its utili-zation as a nonpowered low-frequency underwater tonę source. A res-onant cavity was constructed in the form of a rectangular box with a vertical slot cut in the side, allowing uncomplicated prediction of wali yibration and radiation. The box was then mounted in a fiberglass fair-ing to produce a uniform turbulcnt boundary layer at the location of the slot. Before towing, Identification of those yibration modes that provoke flow into and out of the cavity was performed in the laboratory, using modal analysis. Early tow tank runs are showing that tonal radiation seems to occur at expected rangę of speeds and frequencics, though the levcl of the sound is less than desired. Further “voicing” of the device is underway (sharpening the edge of the slot, raising the Q of the resona-tor by using morę resilient mounting, etc.).

1973

J. Acoust. Soc. Am., Vol. 89. No. 4, Pt. 2, April 1991

121st Meeting: Acoustical Sodety of America

1973