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TECHNICAL BRIEFS

Free Vibration Analysis of Rotating Circular Cylindrical Shells on an Elastic Foundation

[+] Author and Article Information
T. Y. Ng, K. Y. Lam

Centre for Computational Mechanics, Department of Mechanical & Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

J. Vib. Acoust 122(1), 86-89 (Feb 01, 1999) (4 pages) doi:10.1115/1.568445 History: Received August 01, 1998; Revised February 01, 1999
Copyright © 2000 by ASME
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References

Raju,  K. K., and Rao,  G. V., 1993, “Vibrations of Initially Stressed Beams and Plates around Transition Values of Elastic Foundation Stiffness,” J. Sound Vib., 161, pp. 378–384.
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Qin,  Q. H., 1993, “Nonlinear Analysis of Reissner Plates on an Elastic Foundation by the BEM,” Int. J. Solids Struct., 30, pp. 3101–3111.
Qin,  Q. H., 1995, “Hybrid-Trefftz Finite Element Method for Reissner Plates on an Elastic Foundation,” Comput. Methods Appl. Mech. Eng., 122, pp. 379–392.
Guler,  K., and Celep,  Z., 1995, “Static and Dynamic Responses of a Circular Plate on a Tensionless Elastic Foundation,” J. Sound Vib., 183, pp. 185–195.
Omurtag,  M. H., Ozutok,  A., and Akoz,  A. Y., 1997, “Free Vibration Analysis of Kirchhoff Plates Resting on Elastic Foundation by Mixed Finite Element Formulation Based on Gateaux Differential,” Int. J. Numer. Methods Eng., 40, pp. 295–317.
Librescu,  L., and Lin,  W. Q., 1997, “Postbuckling and Vibration of Shear Deformable Flat and Curved Panels on a Non-Linear Elastic Foundation,” Int. J. Non-Linear Mech., 32, pp. 211–225.
Eslami,  M. R., and Ayatollahi,  M. R., 1993, “Modal Analysis of Shell of Revolution on Elastic Foundation,” Int. J. Pressure Vessels Piping, 56, pp. 351–568.
Paliwal,  D. N., Gupta,  R., and Jain,  A., 1993, “Stress Analysis of Ellipsoidal Shell on an Elastic Foundation,” Int. J. Pressure Vessels Piping, 56, pp. 229–242.
Paliwal,  D. N., 1994, “Large Deflection in a Shallow Spherical Shell on an Elastic Foundation Under a Concentrated Load at the Centre,” Int. J. Pressure Vessels Piping, 57, pp. 131–133.
Paliwal,  D. N., Pandey,  R. K., and Nath,  T., 1996, “Free Vibrations of Circular Cylindrical Shell on Winkler and Pasternak foundations,” Int. J. Pressure Vessels Piping, 69, pp. 79–89.
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Figures

Grahic Jump Location
Coordinate system of the rotating cylindrical shell
Grahic Jump Location
Bifurcations of the natural frequencies of a rotating cylindrical shell of L/R=6,h/R=0.02 and k=0. ‘–’, (m,n)=(1,1); ‘⋅ ⋅ ⋅’, (m,n)=(1,2); ‘–––’, (m,n)=(1,3); ‘⋅–⋅–⋅–’, (m,n)=(1,4).
Grahic Jump Location
Bifurcations of the natural frequencies for a simply-supported rotating cylindrical shell of ν=0.3 and geometric properties L/R=1 and R/h=100. (a) mode (1,1), (b) mode (1,2), (c) mode (1,3) ‘–’, k=0, ‘⋅ ⋅ ⋅⋯’, k=0.005, ‘[[dashed_line]]’, k=0.01.
Grahic Jump Location
Bifurcations of the natural frequencies for a simply-supported rotating cylindrical shell of ν=0.3 and geometric properties L/R=1 and R/h=100. (a) mode (2,1), (b) mode (2,2), (c) mode (2,3) ‘–’, k=0, ‘⋅ ⋅ ⋅’, k=0.005, ‘[[dashed_line]]’, k=0.01.
Grahic Jump Location
Bifurcations of the natural frequencies for a simply-supported rotating cylindrical shell of ν=0.3 and geometric properties L/R=1 and R/h=100. (a) mode (3,1), (b) mode (3,2), (c) mode (3,3) ‘–’, k=0, ‘⋅ ⋅ ⋅’, k=0.005, ‘[[dashed_line]]’, k=0.01.

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