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Structural Engineering and Mechanics Volume 39, Number 4, August25 2011 , pages 449-463 DOI: https://doi.org/10.12989/sem.2011.39.4.449 |
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Free vibration analysis of moderately-thick and thick toroidal shells |
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X.H. Wang and D. Redekop
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| Abstract | ||
| A free vibration analysis is made of a moderately-thick toroidal shell based on a shear deformation (Timoshenko-Mindlin) shell theory. This work represents an extension of earlier work by the authors which was based on a thin (Kirchoff-Love) shell theory. The analysis uses a modal approach in the circumferential direction, and numerical results are found using the differential quadrature method (DQM). The analysis is first developed for a shell of revolution of arbitrary meridian, and then specialized to a complete circular toroidal shell. A second analysis, based on the three-dimensional theory of elasticity, is presented to cover thick shells. The shear deformation theory is validated by comparing calculated results with previously published results for fifteen cases, found using thin shell theory, moderately-thick shell theory, and the theory of elasticity. Consistent agreement is observed in the comparison of different results. New frequency results are then given for moderately-thick and thick toroidal shells, considered to be completely free. The results indicate the usefulness of the shear deformation theory in determining natural frequencies for toroidal shells. | ||
| Key Words | ||
| vibration; toroidal shells; shear deformation theory; theory of elasticity; differential quadrature method | ||
| Address | ||
| X.H. Wang: Department of Civil Engineering, Shantou University, 243 Da Xue Road, Shantou, P.R. China D. Redekop: Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada K1N 6N5 | ||