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this device has been previously characterized experimentally by optical holographic techniques. These rcsults have indicatcd thal the poor high-frequcncy response of the bonę vibrator can be attributed lo case reso-nances in the higher modes of vibration. To further investigate both the out-of-plane and in-plane vibration of the bonę vibrator case, a finite element model was developed with the ANSYS system. The case modę shapes obtained previous!y by laser holography were used to verify the semiempirical FEM model. Once verified, this finite element model was used to analytically dctcrminc modifications to the bonę vibrator that would improve its high-frequency response. This was accomplished by varying design specifications of the bonę vibrator including its dimen-sions, stiffnesses, and masses and observing its effect on the case modę shapes.

9:35

2SA3. Soize's theory of structural fuzzy: An examination of fundamental assumptions. Victor W. Sparrow (Graduate Próg. in Acoust., 157 Hammond Bldg., Penn State Univ._t University Park, PA 16802)

In 1986, C. Soize introduced a theory of scattering from structures that are known in gross aspects, but whosc details are either unknown or only imprecisely known. Soize called his method a theory of struc-tural fuzzy [Resh. Aćrosp. 1986-5, 23 and Resh. Aerosp. 1986-5, 49 (1986)], which he applied to scattering in the midfrequcncy rangę. In the theory, Soize described complex mechanical subsystems by fuzzy finite elements, clcments where the mass, ratę of dissipation, and modal density are formulated using uniform probability density distributions. In this presentation, Soize’s methods are outlined and the fundamental assumptions that underlay the theory are considered. Spccifically, the implications of the uniform probability distributions and other assumptions on the fuzzy finite elements will be reported. Other probabilistic descriptions for thcse constituent elements may be morę realistic. The-oretical limitations will also be summarized for the frequency ranges over which the fuzzy structure theory is predicted to be valid.

9:50

2SA4. Wave-number-frequency spectrum of turbułent wali pressure Auctuations. Carolyn Karangelen (Dept. of Mech. Eng., The Catholic Univ. of America, Washington, DC 22064)

The study of the properties of turbułent wali flows is important to understanding the structural excitations that might induce flow noise. Models of the forcing functions of the structural excitations have been based on generalized properties of the spectral features of these flows. This paper will highlight the characteristics of turbułent spectral energy in wave number space, and prescnt new experimental results. Discus-sion will address the wave number spectrum as a model for the forcing function of structural excitation. (Funded by ONR and IBM.]

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2SA5. Optical measurements of shear waves on a point-driven cylindrical shell excited radially. Dowon Lee, Hyun-Gwon Kil, Christian Glandier, Jacek Jarzynski, and Yves Berthelot (School of Mech. Eng., Georgia Inst. of Technol., Atlanta, GA 30332)

A differential laser Doppler velocimcter (LDV) [Ixe et al.. Proceed-ings of the 3rd International Congress on Intensity Techniques. Senlis, France, pp. 181-188 (1990)] has been used to measure in-plane motion associated with waves propagating on a thin cylindrical shell excited radially at a single frequency by a shaker. The endcaps of the shell approximate the case of a simply supported shell with axial constraints at both ends. The fiber optic technology used in the LDV system allows the optical probe head, located at a distance of about 30 cm from the shell, to bc scanned over the entire surface of the shell. Data were recorded along an array of 32 points circumferentially and 16 points axially, cnough to sample spatially both extensional (fast wavcs, Iow wave numbers) and flexural (slow waves, high wave numbers) waves. The data were analyzed with both a two-dimensional spatial FFT algo-rithm and a Prony algorithm. The analysis clearly reveals both type of waves separately. Theoretical predictions are obtained from the analysis of a point-driven infinite shell and from Forsberg’s original paper [AIAA J. 2 (12), 2150 (1964)]. Both theoretical and experimental results clearly show the presence of shear waves propagating on thc structure. (Work supported by ONR ]

10:20

2SA6. Coupling of piąte and shell modes at joints. I-Tai Lu, Henry L. Bertoni, and H. Y. Chen (Weber Res. Inst., Dept. of Elect. Eng., Polytechnic Univ., Route 110, Farmingdale, NY 11735)

For cylindrical and spherical shells without truncation or for flat plates with infinite latcral extent, fundamental shell or piąte modes propagate independently without coupling. However, at a joint of two or morę piąte or shell elements, these modes couple together. If a modę is incident at an oblique angle from one element, it will excite other modes propagating away from the junction in each element. The prop-agation direction and the excitation strength of each modę can be de-termined by the following boundary conditions: continuity of displace-ment at the joint, continuity of rotation about the axis of the joint, and vanishing net forcc and torque on the joint. These boundary conditions are derived from the assumption that the joint is massiess and has rigid cross scction but oflfers no rcsistance to extension along and twisting about the axis of the joint, and to bending transverse to the axis. To be consistent with thin plate/shell theory, it is necessary to account for the first cutoff modę in addition to the three propagating modes in each piąte or shell. Numerical examples will be discussed. [Work supported by ONR.]

10:35

2SA7. Alumer: A “rigid," acoustically transparent, composite materiał. Pieter S. Dubbclday and Forrest M. Egglcston (Naval Res. Lab., Underwater Sound Reference Detachment, P.O. Box 568337, Orlando, FL 32856-8337)

The elastic properties of foamed aluminum have been reported in an earlier presentation (J. Acoust. Soc. Am. Suppl. 1 88, S22 (1990)]. When the open-cell structure of this materiał is impregnated with a light elastomer, a composite materiał results that has a density and dilata-tional wave speed close to that of water. The Young’s modulus and bulk modulus of this “Alumer” materiał have been measured, as a function of frequency, for various combinations of foamed aluminum, characterized by relative density and porę size, and polyurethane. The aluminum matrix imparts stiffness to the materiał, for use as an acoustically transparent backing piąte or other structure. The elastomer may be chosen to give morę or less absorptive properties to the materiał. (Work supported by thc Office of Naval Research.]

10:50

2SA8. Model ing of impact response in moving chains. Sabih I. Hayek, Shyi-Ping Liu, K. W. Wang (Penn State Univ., University Park, PA 16802), and Francis H. K. Chen (General Motors Res. Labs, Warren, Ml 48090-9055)

A significant contributor to noise from chain drives can be traced to the impact of a roller chain on a sprocket. A model is developed to estimate thc impact impulsive load generated by an axially moving roller chain on a sprocket during the meshing process. Due to the dependence of the impulsive impact force on the velocity of the chain before impact, the impulsive load at each impact varies from impact to impact. The meshing proccss then produces nonperiodic and nonuni-form impulsive impact forces. The model is used to analyze the response of the roller chain after each impact. The chain response model is being

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

121st Meeting: Acoustical Society oł America

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