Nonlinear Free Vibration Analysis of a Toroidal Pressure Vessel under Constrained Volume Condition

This paper focussed on the large displacement nonlinear free vibration of a toroidal pressure vessel in free space under constrained volume condition. Three states of the toroidal pressure vessel surface comprising the initial unstrained surface, reference surface, and vibrating surface were considered in the energy functional of the toroidal pressure vessel system based on the principle of virtual work. For the reference surface, it was assumed that the toroidal pressure vessel has a circular cross-section and is subjected to uniform internal pressure. Nonlinear numerical solutions were obtained utilizing the FEM and a modified direct iteration technique, and compared with those generated by ABAQUS. More importantly, this study showed that the fundamental nonlinear natural frequency of a toroidal pressure vessel under the constrained volume condition was lower than that of the published results for an inflated toroidal membrane and shell.