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mode-conversion coefficients, and it will be shown that the spatial wave-number spectrum of the local field is instrumental in setting up an acoustic far field in the surrounding fluid. An important mathematic issue is the proper description of evanescent fields; this analysis will be based on results obtained previously in connection with acoustic waveguides.

shells. The generally good agreement between the observable-based ray-acoustic algorithm and the reference solution provides further confir-mation of the utility of the physically incisive ray acoustic parametrization for this canonical problem. Some preliminary results are presented for applying the ray-3COustic scheme to a rigidly batfled hemi-sphere. [Work supported by ONR and DTRC.]

2:35

5SA4. Surface variational principle analysis of the response of an eccentrically łoaded submerged disk in a baffle. Jerry H. Ginsberg and P. T. Chu (School of Mech. Eng., Georgia Inst. of Technol., Atlanta, GA 30332)

As an initial step in the extension of the surface variational principle (SVP) to an assumed modę analysis of vibratory displacement and surface pressure on submerged axi$ymmetric structures subjected to arbitrary nonsymmetric loading, the present study considers a harmonie point force applied at an arbitrary location of an elastic piąte supported by an infinite, rigid baflle. Fourier series cxpansions of the azimuthal dependence of pressure and displacement are shown to be uncoupled, with each harmonie being govemed by equations that are similar in form to thosc for the analogous axisymmetric problem [J. H. Ginsberg, P. T. Chen, and A. D. Pierce, J. Acoust. Soc. Am. 88, 548-559 (1990)). Recursion relations using coefficients developed in the course of solving the axisymrnetric problem are shown to substantially expedite the eval-uation of the additional azimuthal harmonics. Results for a foree lo-cated at r—a/2 when ka = 3.35, where a is the radius of the piąte, are presented in terms of the radial variation associated with each harmonie, as well as overa!l surface distributions. It is shown that m — 0 to m = 4 azimuthal harmonics are comparable in magnitude, and that other harmonics are insignificant. In addition, radiated power is evalu-ated as a function of m. [Work supported by ONR, Codę 1132-SA.)

2:50

5SA5. Waves on fluid-Ioaded thin elastic plates: Analytical study based on fuli elastodynamic equations. Allan D. Pierce and Martin G. Manley (Graduate Próg. in Acoust. and Dept. of Mech. Eng., Penn State Univ., 157 Hammond Hldg., University Park, PA 16802)

An elastic, infinite piąte of finite thickness with fluid loading on one side and vacuum on the other is eonsidered. Displacement of the platc surface is dcrived from the fuli elastodynamic equations, rather than from a piąte model. Following Crighton’s parametrization scheme, analytical expressions of the dispersion and polarization relations of the bending wavc are derived. Systematic expansions of the dispersion and polarization relations are developed using a symbolic manipulation Computer program. [Work of ADP is supported by ONR and by the William E. Leonhard endowment to Penn State Univ.; work of MGM is supported by the PSU Appl. Res. Lab. Exploratory and Foundational Res. Próg.)

3:05

5SA6. Numerical implementation of ray-acoustic algorithm for sound wave scattering by submerged elastic spherical shells. J. M. Ho, X. J.

Gao, and L. B. Felsen (Elec. Eng. Dept., Weber Res. Inst., Polytech. Univ., Farmingdale, NY 11735)

The rigorously derived ray-acoustic algorithm for source-excited fluid-Ioaded thin elastic spherical shells [J. M. Ho and L. B. Felsen, J. Acoust. Soc. Am. 88, 2389-2414 (1990)] is implemented numerically

for far-field planc-wavc and point-source ^cattering, and compared

with reference Solutions based on exact spherical harmonie expansions. These comparisons permit an assessment of the rangę of applicability of thin-shell theory, and they indicate when and how [cf. S. P. Kargl and P. L. Marston, J. Acoust. Soc. Am. 85, 1014-1028 (1989)] the algorithm should be modified phcnomenologically to accommodate thick

1933 J. Acoust. Soc. Am., Vol. 89, No. 4, Pt. 2, April 1991

3:20

5SA7. Finlte-element analysis of airfoil vibration using variable thickness piąte elements. Paul J. Zoccola and Yun-Fan Hwang (Flow Noise Branch, David Taylor Res. Ctr., Bethesda, MD 20084)

A NASTRAN finite-element model has been developed for calcu-lating the modę shapes and frequencies of a cantilever beam with airfoil cross section. This model uses QUAD4 elements and takes advantage of the feature allowing a different thickness at each node on the element. This feature is particularly attractive for modeling the trailing edge (wedge) section of the airfoil. Numerical results are compared with those from a model of the same bcam using solid (HEXA1) elements and with an experimental modal analysis. For bending modes, the results from the QUAD4 and HEXA1 models agreed well with experi-mental results but the HEXA1 model required a much greater number of nodes and much morę Computer time. For torsional modes, however, a discrepancy exists in the calculated modli frequencies between the QUAD4 and HEXA1 models. Reasons for this discrepancy are dis-cussed. The chordwise modal behavior of the airfoil and its influence on the vibroacoustic response are also diseussed.

3:35

5SA8. Wave propagation below the ring frequency on fluid-Ioaded cylindrical shells. Steven L. Mcans (Graduate Próg. in Acoust., Penn State Univ._t P.O. Box 30, State College, PA 16804)

Williams, Houston, and Bucaro [J. Acoust. Soc. Am. 87, 513-522 (1990)] have published experimental and theoretical hclical wave spectra for a point-drwen, fluid-Ioaded shell. A previous attempt (qualita-tively successful) by Kouzoupis [J. Acoust. Soc. Am. Suppl. I 87, SI63 (1990)] to explain these spectra in terms of the wave theory of struc-tural acouslics was based on a model that neglected fluid loading in first approximation, but which included it as a correction in a somewhat sirnple manner. The present paper reexamines the problem with a wave theory of shells that takes fluid loading into account at the outset. The wave theory interprets the helical spectra as a plot within the wave-number piane (k_x vs k_y) for fixed angular frequency o>, derived from a dispersion relation F(k_x,k_y,co)=0, whose form has nothing to do with the manner of excitation. The morę completc analysis produces curves that have shapes that rescmble a figurę 8, when o) is less than the ring frequency, but a simplified analysis that takes the shell to be arbitrarily thin produces two hyperbolas. The top and the bottom of the eight are sensitive to the shell thickness, and an asymptotic theory is described that shows just how this feature varies with thickness. [Work supported by ONR and by the William E. Leonhard endowment to Penn. State Univ. The aut hor acknowledgcs the advice of A. D. Pierce.)

3:50

5SA9. A structural modeling of torsional ship motions. M. Cengiz Dokmeci (Dept. of Naval Architecture, Istanbul Tcchnical Univ., P. K. 9. Taksim, Istanbul 80191, Turkey)

This study is concerned with a structural modeling for torsional motions of thin-walled girders of ships by beam idcaiization on the basis of łhree-dimensional theory of clastodynamics. In the modeling, (1) the fundamenta! equations of clastodynamics are exprcssed in a unified vari-ational form that is expressed by means of Hamilton’s principle through Friedrichs’s transformation [M. C. Dokmeci, IEEE Trans. UFFC-37, 369-385 (1990)]. Next, (2) a series representation in the aerial coor-dinates of cross section is introduced for the displacement field. Mind-

121st Meeting: Acoustical Society of America 1933