The excitation threshold and the onset of subharmonic oscillations in nonlinear rolling

Article type: Research Article

Authors: Cardo, A.^a | Francescutto, A.^b | Nabergoj, R.^c

Affiliations: [a] Istituto di Architettura Navale, Trieste, Italy | [b] Istituto di Fisica, Trieste, Italy | [c] Istituto di Fisica, Udine, Italy

Abstract: The characteristic features of subharmonic oscillations in the nonlinear rolling of a ship are investigated. The mathematical model used for this purpose is given by a second order differential equation taking into account both the righting moment and the damping nonlinearities. The righting moment is expressed by a cubic polynomial, whereas the damping effects are nonlinear both in angle and angular velocity. Particular attention is devoted to subharmonics for the case of a ship in upright equilibrium position. It has been proved that a subharmonic oscillation with tuning factor 3 can be present only after the excitation intensity has exceeded a threshold level. The phenomenon can be particularly dangerous for ships whose righting moment shows a strong departure from the linearity. This occurs in particular for modern container ships.

DOI: 10.3233/ISP-1985-3237302

Journal: International Shipbuilding Progress, vol. 32, no. 373, pp. 210-214, 1985