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May 1989

Volume 85, Issue S1, pp. S1-S156

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back to top Session VV. Structural Acoustics and Vibration VI: Wave Propagation in Structures
Contributed Papers
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Energy flow associated with fundamental elastic wave types on inhomogeneous cylindrical shells (A)

Allen D. Pierce

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S117-S117 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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The basic shell dynamic equations for an inhomogeneous cylindrical shell (slowly varying radius, thickness, and material properties) result from Hamilton's principle. The version adopted here is one which yields the Donnell equations in the limiting case of a homogeneous thin shell, although the same technique applies for more sophisticated shell theories. There are three wave types that result from the theory that can be identified in the high‐frequency limit as compressional (longitudinal), in‐plane shear, and flexural. The propagation of these waves is directionally dependent, frequency dependent, and dispersive. The general ray acoustics formulation developed in previous papers by the author, by Felsen and Lu, and by Norris is extended to include the proper invariants for propagation along ray tubes. The energy density and energy flux vectors for each of the three wave types are derived with the aid of Hamilton's principle and a Poynting's theorem expressing conservation of wave energy is obtained for each wave type. This identification allows the discussion of the energy transfer when waves are partially reflected and converted to other wave types at ribs or at abrupt transitions of shell radius. [Work supported by ONR and by the William E. Leonhard endowment to Pennsylvania State University.]
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Surface waves in layered structures with application to vocal‐fold vibration (A)

Richard S. McGowan

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S117-S117 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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The initiation of surface waves over a layered structure, including an air channel, a thin elastic layer, an inviscid waterlike fluid, and an impedance boundary, is discussed. This structure is a rudimentary picture of the vocal folds near the edges. The initiation of surface waves at the interface between the air and elastic layer is similar to the problems of initiation of wind waves over water and the flutter of panels. Early linear analyses of surface wave initiation considered Kelvin‐Helmholtz instability, a static instability, and the use of Jeffreys' sheltering coefficient as a destabilizing mechanism for a dynamic instability. Both static and dynamic instabilities are possible in vocal‐fold vibration. However, the dynamic type of instability is the mechanism that usually is operable in a layered structure model of vocal‐fold vibration, although Jeffreys' sheltering coefficient does not provide the correct term for negative damping. This is confirmed by the lumped element two‐mass model, a very successful model for simulating some aspects of vocal‐fold vibration [K. Ishizaka and J. L. Flanagan, Bell Syst. Tech. J. 51, 1233 (1968)]. The two‐mass model also illustrates how to incorporate dynamic pressure loss into the layered structure approach to account for the negative stiffness. The layered structure approach has the advantage of allowing for testing of the effects of changing the mechanical properties of various histological layers on the initiation of the surface wave. [Work supported by NIH grants HD‐1994, NS‐13870, and NS‐13617 to Haskins Laboratories.]
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Analysis of kinetic energy repartition for in‐plane beam structures (A)

J. B. Piaud, T. Loyau, and I. Nicolas

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S117-S117 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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In this paper, kinetic energy repartition for in‐plane beam structures is analyzed using three different methods: the statistical energy analysis, the energy influence coefficient method (based on the modal approach), and the exact method (based on the wave approach). The two last methods allow the definition of a linear relation between the average kinetic energy of each beam and the excitations applied to all the structure. Therefore the contribution of each excitation to the kinetic energy of each beam can be shown. In the structure, the beam angle at a junction can take any value. A junction model with three degrees of freedom is developed to account for longitudinal and flexural motions. A comparison between the three methods is performed. The analysis results are presented for different angles, different types of junctions, and supports.
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Critical frequencies of ribbed plates (A)

G. Maidanik, J. Dickey, and J. Ertel

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S117-S117 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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The vibrational and radiative properties of panels are often cast in terms of the relationship between the two sets of properties. The relationship is expressed in terms of the radiation efficiencies of these panels. Often interest lies in the dependence of the radiation efficiency on frequency; the radiation efficiency is, therefore, usually displayed as a function of frequency. If the panel is basically a plate responding in flexure it is customary to ascertain the radiation efficiency as a function of the normalized frequency (ω/ωc), where ω is the frequency variable and ωc is defined as the frequency at which the phase velocity of the free waves, in a specified direction, on the unloaded uniform plate matches the speed of sound in the irradiated fluid. The critical frequency may have directional properties. However, if the uniform plate is isotropic, the critical frequency is independent of direction. When the plate is nonuniform; e.g., because the plate is ribbed and/or finite, the “free waves and their phase velocity” on the unloaded nonuniform plate may not correspond to those on the unloaded uniform plate. Even if these free waves admit to the definition of the critical frequency ωg this critical frequency may not be equal to ωc. If there is merit in displaying the radiation efficiency as a function of the normalized frequency, which critical frequency need be used in the normalization? The paper is a brief attempt to answer this question. The definition of the critical frequencies and their use in normalizing the frequency for displaying the radiation efficiencies of regularly ribbed plates are cited as examples.
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Propagation of elastic waves on thin‐walled circular cylinders (A)

Hyun‐Gwon Kil, Allan D. Pierce, and Jerry H. Ginsberg

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S118-S118 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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This paper examines the nature of elastic waves propagating in a thin‐walled circular cylinder from the viewpoint that the cylinder's geometry is a source of anisotropy. A point‐excited circular cylinder is regarded as a two‐dimensional anisotropic medium extending over an infinite domain formed from the stretched angular coordinate. Correspondingly, the displacement field is represented as a superposition of waves propagating out from localized sources into an unbounded medium. The excitation of waves by various types of point force is analyzed using Lighthill's theory. This leads to an expression for the farfield response of the point‐excited unbounded medium, which can be expressed in a simple asymptotic form at frequencies somewhat higher than the ring frequency. Thus, in this frequency range, the farfield response of a point‐excited circular cylinder can be easily obtained using the corresponding asymptotic farfield response of an unbounded medium. Using these results, it is shown that the wave motion in a thin‐walled circular cylinder at moderate frequencies may be interpreted in terms of the wave motion in a thin plate. [Work supported by ONR.]
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Theory and measurements of transient ultrasonic waves in a viscoelastic plate (A)

Richard L. Weaver, Wolfgang Sachse, and Lin Niu

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S118-S118 (1989); (1 page)

Online Publication Date: 13 Aug 2005

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The nearfield responses of a thick viscoelastic plate are computed for epicenter, off‐epicenter receiver locations to a point step load acting normal to the surface. Analysis of these responses shows that the ray arrival behavior of a transient ultrasonic signal propagated through a thick viscoelastic plate can be analyzed to recover the plate material's dispersion and attenuation. Such measurements form the basis of the point‐source/point‐receiver measurement technique. Signal processing algorithms are demonstrated with synthetic and real signals obtained via this technique in elastic and viscoelastic materials.
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Forced vibrations of stiffened cylindrical elastic panels (A)

Zahit Mecitoglu and M. C. Dökmeci

J. Acoust. Soc. Am. Volume 85, Issue S1, pp. S118-S118 (1989); (1 page) | Cited 2 times

Online Publication Date: 13 Aug 2005

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The objective of this paper is to investigate the forced response of a stiffened circular cylindrical panel within the frame of Love's first approximation theory of elastic shells. The effects of stiffeners are taken into account by the orthotropic material approach, including the eccentricity of stiffeners. The variational equation of motion for the forced vibrations of thin elastic shells with clamped edges is derived from Hamilton's principle. The stiffened elastic panel is discretized by the Semiloof elements. Then, with the help of the variational equation, the matrix equation is obtained to determine the frequencies and mode shapes of the stiffened circular cylindrical elastic panel. Two types of stiffened shell panels are considered for forced‐response analysis: the stiffened models by the stiffeners with rectangular cross section and with profile shape cross section. The influence of the spacings and dimensions of stiffeners on the forced response of the stiffened circular cylindrical panel is examined. The numerical results are plotted with respect to the parameters, and they are compared with certain earlier results. Further needs of research are pointed out.
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