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TECHNICAL PAPERS

Free Vibration Analysis of an Inflated Toroidal Shell

[+] Author and Article Information
Akhilesh K. Jha, Daniel J. Inman

Center for Intelligent Material Systems and Structures, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0105

Raymond H. Plaut

Charles E. Via, Jr. Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0105

J. Vib. Acoust 124(3), 387-396 (Jun 12, 2002) (10 pages) doi:10.1115/1.1467650 History: Received April 01, 2001; Revised January 01, 2002; Online June 12, 2002
Copyright © 2002 by ASME
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References

Malone, P. K., and Crawford, L., 1993, “Developing an Inflatable Solar Array,” 7th AIAA/USU Conference on Small Satellites, LPA-93-GW-008, P1J93.
Dornheim,  M. A., 1999, “Inflatable Structures Taking to Flight,” Aviat. Week Space Technol., January, pp. 60–62.
Kordes, E. E., 1960, “Vibration Analysis of Toroidal Shells of Circular Cross Section,” Ph.D. Dissertation, Engineering, Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA.
McGill, D. J. M., 1966, “Axisymmetric Free Oscillations of Thick Toroidal Shells,” Ph.D. Dissertation, Department of Mechanics and Aerospace Engineering, University of Kansas, Lawrence, KS.
Kosawada,  T., Suzuki,  K., and Takahashi,  S., 1985, “Free Vibration of Toroidal Shells,” Bull. JSME, 28(243), pp. 2041–2047.
Fang,  Z., 1992, “Free Vibration of Fluid-Filled Toroidal Shells,” J. Sound Vib., 155(2), pp. 343–352.
Leung,  A. Y. T., and Kwok,  N. T. C., 1994, “Free Vibration Analysis of a Toroidal Shell,” Thin-Walled Struct., 18, pp. 317–332.
Jordan, P. F., 1966, “Vibration and Buckling of Pressurized Torus Shells,” 4th Aerospace Science Meeting, Los Angeles, California, AIAA Paper No. 66–445.
Saigal,  S., Yang,  T. Y., Kim,  H. W., and Soedel,  W., 1986, “Free Vibration of a Tire as a Toroidal Membrane,” J. Sound Vib., 107(1), pp. 71–82.
Plaut,  R. H., Goh,  J. K. S., Kigudde,  M., and Hammerand,  D. C., 2000, “Shell Analysis of an Inflatable Arch Subjected to Snow and Wind Loading,” Int. J. Solids Struct., 37, pp. 4275–4288.
Liepins,  A. A., 1965, “Free Vibrations of Prestressed Toroidal Membrane,” AIAA J., 3(10), pp. 1924–1933.
Lewis, J. A., 2000, “Finite Element Modeling and Active Control of an Inflated Torus Using Piezoelectric Devices,” MS Thesis, Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA.
Sanders, J. L., 1959, “An Improved First Approximation Theory for Thin Shells,” NASA Report 24, June, Washington, D.C.
Budiansky,  B., 1968, “Notes on Nonlinear Shell Theory,” ASME J. Appl. Mech., 35, No. 2, June, pp. 393–401.
Soedel, W., 1986, Vibrations of Shells and Plates, Marcel Dekker, New York.
Leissa, A. W., 1973, Vibration of Shells, NASA SP-288, Washington, D.C.

Figures

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Geometry of the torus (not to scale): (a) side view (b) section A-A
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Initial stresses, stress and moment resultants, and loads
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Symmetrically and antisymmetrically deformed cross-sections of the torus. Solid lines are the deformed cross-sections and dotted lines are the undeformed cross-sections and axes.
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Mode shapes of the inflated torus
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Mode shapes of the inflated torus
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The first five natural frequencies vs. the aspect ratio of (a) symmetric modes and (b) antisymmetric modes corresponding to n=0
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The first five natural frequencies vs. the aspect ratio of (a) symmetric modes and (b) antisymmetric modes corresponding to n=4
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Effect of the internal pressure on the first ten natural frequencies of the inflated torus
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Effect of the thickness on the first ten natural frequencies of the inflated torus

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