Nonlinear analysis of heavy-lift barge roll motion

Two types of nonlinearity pertinent to heavy-lift barge roll motion were treated: quadratic damping and nonlinear roll restoring moment. The Ritz method based on variational calculus was applied to solve the nonlinear equation of motion. Extensive large amplitude roll motion wave tank data on a series of seven barge configurations was reanalyzed using this method. A comparison study of roll responses was conducted for three key barge design parameters: draft, length-beam ratio, and roll period. Quadratic (φ|φ|) damping was used to represent effects of wave impact, deck edge immersion, and bilge emergence. Nonlinear restoring moments were introduced by modifying GM to account for deck cargo immersion and green water on deck at large angles of roll. Characteristic features of the nonlinear responses included shift of the natural frequency with increasing roll angle and localized instabilities in roll angle and phase angle.