Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied.
Free Vibration Analysis of an Inflated Toroidal Shell
Contributed by the Technical Committee on Vibration and Sound for publication in the Journal of Vibration and Acoustics. Manuscript received April 2001; revised January 2002. Associate Editor: J. Wickert.
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Jha, A. K., Inman, D. J., and Plaut, R. H. (June 12, 2002). "Free Vibration Analysis of an Inflated Toroidal Shell ." ASME. J. Vib. Acoust. July 2002; 124(3): 387–396. https://doi.org/10.1115/1.1467650
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