Vibration analysis of an elastic toroidal tank considering nonlinearity of sloshing

Abstract

The vibration of an elastic toroidal tank induced by nonlinear sloshing is analyzed. A computationally efficient semi-analytical method is presented for sloshing in a toroidal tank with circular meridional cross-section, for which it is customary to resort to numerical methods. This method expresses the solution in term of polar coordinates defined in the meridional cross-section such that their origin is at the intersection of the straight lines that are tangent to the tank at the contact points of the static liquid surface with the tank wall. Numerical results illustrate that the difference between the linear and nonlinear responses of the stress in the tank shell is small although the nonlinearity augments the sloshing motion. To examine the physical reason for this counterintuitive trend, response analysis is conducted for the case where an upper part of the tank is open. The examination shows that the closed circular cross-section of the tank suppresses flexible modes with circumferential wave numbers 2 and 3.

Keywords

• vibration of continuous system
• sloshing
• nonlinear vibration
• semi-analytical method
• toroidal tank