Vibration of the Hollow Sphere in an Acoustic Medium

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DISCUSSIONand Bhatia and Nachbar [3]. All three papers deal with finite deformations in centrally loaded circular membranes; the first treats a linear elastic membrane loaded through a central circular plug, the second considers the load as a concentrated central force, and the last analyzes an elastic-plastic membrane loaded through a hemispherical indenter.For moderate rotations of the membrane, the solutions given in the three papers just cited and the authors' paper should show close agreement for the traction-free region of the membrane. Have the authors carried out any comparisons between their results and those given in references [1][2][3]?

Section: Viscoelasticitymentioning

confidence: 56%

“…Have the authors carried out any comparisons between their results and those given in references [1][2][3]?…”

Section: Discussionmentioning

confidence: 99%

Discussion: “Transient Interaction of Spherical Acoustic Waves and a Spherical Elastic Shell” (Huang, H., Lu, Y. P., and Wang, Y. F., 1971, ASME J. Appl. Mech., 38, pp. 71–74)

Berger

1971

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“…The book presents a development of the phenomenological theory of viscoelastic materials, with the physical processes giving rise to the time-dependent behavior receiving only brief mention at isolated points. The mathematical aspects of the theoiy are emphasized but, for the most part, only insofar as 2 The authors' paper, which gives some valuable insight into a technically interesting problem, is similar to an earlier paper by Mann-Nachbar [l], 3 in that solutions are developed in terms of an integral transform in time and a series expansion of Legendre and Bessel functions in space. As noted in [1] the series representing the pressure of the fluid and the radial acceleration of the shell do not, in general, converge uniformly.…”

Section: Viscoelasticitymentioning

confidence: 64%

“…Considering that the sphere is rapidly loaded by the acoustic wave, a model of the shell based on the hollow sphere solution of linear elasticity might give a more accurate prediction of strain [2]. It appears that the authors' solution could be extended to the more exact case.…”

Section: Viscoelasticitymentioning

confidence: 99%

Discussion: “Indentation of a Circular Membrane” (Yang, W. H., and Hsu, K.-H., 1971, ASME J. Appl. Mech., 38, pp. 227–230)

Jahsman

1971

pressures near the slot are again observed and the explanation no doubt lies in the flow curvature in the entrained flow, which is greater for the larger values of t/y c . The effect was first reported by George [4].The law-of-the-wall for wall jets is established in the present paper. The same conclusion is reached by Guitton, [5], for wall jets over logarithmic spirals when the curvature is small. This, and other work, is mentioned in the review paper by Newman [6].The inaccuracy of the von Karman momentum equation as a means of determining skin friction is well known, and was discussed very fully by Button [7].

“…Again, results were limited to elastic shell material. Finally, Berger [5] considered vibrations of a submerged hollow sphere and specialized the results to the spherically symmetric problem. A numerical example for a finite-duration step pressure pulse is presented including graphs of sphere displacement and pressure in the surrounding acoustic fluid as a function of time.…”

Section: Introductionmentioning

confidence: 99%

Transient Response of Viscoplastic and Viscoelastic Shells Submerged in Fluid Media

Duffey¹

1976

The transient fluid-shell interaction problem is investigated for thin shells constructed of other than linearly elastic materials. Specifically, solutions are developed in terms of elementary functions for the transient responses of impulsively loaded, fluid-surrounded spherical shells constructed of either viscoplastic or viscoelastic materials. In all cases the fluid medium surrounding the shell is taken as inviscid and compressible and only spherically symmetric shell motions and radiation of sound into the surrounding medium are considered. It is found that the influence of material strain hardening and strain-rate sensitivity can be significant in reducing fluid-shell displacement responses. Further, limited investigations for viscoelastic materials indicate that for higher loss materials, displacement response of the shell is significantly altered by the inclusion of the viscoelastic behavior.