Calculation of kinetic energy of a thin elastic 3-dimensional toroidal shell in MatLab

Abstract

The dynamics of a thin elastic 3-dimensional toroidal shell are considered. The motion of such a toroidal shell is considered in polar coordinates under certain assumptions. Understanding the behavior of these shells is crucial for various engineering applications (f.e., some subatomic particles and even magnetic fields). The unique properties of torus make them valuable in designing various structures, like toroidal shells themselves and resonators. The kinetic energy of such a system is calculated. Computer modeling of energy calculation in the given statement with changing shell parameters, choice of dimensions, and varying physical parameters was carried out in the form of an MatLab application (23.2.0.2365128 (R2023b)). Kapton-polyimide film was considered as a sample.

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