THE JOURNAL OF KMUTNB

Volume 31, No. 04, Month OCTOBER, Year 2021, Pages 661 - 674

Axisymmetric and antisymmetric free vibrations of inflated toroidal membrane

Komkorn Chaidachatorn, Weeraphan Jiammeepreecha, Sittisak Jamnam

Abstract Download PDF

This paper presents the axisymmetric and antisymmetric free vibrations analysis of inflated toroidal membrane. The geometry of the inflated toroidal membrane can be computed from differential geometry. The energy functional of inflated toroidal membrane is written in terms of displacements from the principle of virtual work. Natural frequencies and corresponding axisymmetric and antisymmetric mode shapes can be obtained by finite element method. The effects of thickness and internal pressure under constant prestress parameter, cross-sectional radius, internal pressure, and elastic modulus on the axisymmetric and antisymmetric free vibrations of the inflated toroidal membrane are presented in this paper. The results indicate that the mode of the vibration of the inflated toroidal membrane consists of axisymmetric and antisymmetric mode shapes.

Keywords

Axisymmetric Free Vibration; Antisymmetric Free Vibration; Inflated Toroidal Membrane; Differential Geometry; Natural Frequency

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