In this paper an overview of the mathematical model for an inflated thin-film toroidal structure is provided. In particular, attention has been confined to determine the free vibrations of inflated circular toroidal members. The provided solution is based on an improved set of equations of motion for uniform membrane. From which the dependence of natural frequencies on material properties, dimension, mode of vibration, and the inner pressure can be investigated. The validity of the developed models was verified by comparing some of the computed results with those available for special cases. Numerical results for natural frequencies and mode shapes are provided for a specific thin-film inflated torus.
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