Ultraharmonics and subharmonics in the rolling motion of a ship: Steady-state solution1

Co-simulation of ship motions and sloshing in tanks

“…This is due to the effects of, mainly, nonlinear roll damping and nonlinear roll restoring (e.g. Francescutto, 2011, 2013;Bulian et al, 2012;Cardo et al, 1981Cardo et al, , 1982Francescutto and Contento, 1999b;Francescutto and Naito, 2004;Hashimoto et al, 2012;Himeno, 1981;Holden and Fossen, 2012;Kawahara et al, 2009;de Kat and Paulling, 1989;Matusiak, 2007;el Moctar et al, 2012;Neves et al, 2009;Sadat-Hosseini et al, 2010;Sinibaldi and Bulian, 2014;Tzamtzis, 2004). In addition, the sloshing flow inside the tank is also expected to behave nonlinearly as the motions (particularly roll, sway and yaw) increase as a consequence of the increase in the wave forcing.…”

The nonlinear dynamics of ship motions: a field overview and some recent developments

“…Records of subharmonic responses were also presented, verifying that the roll motion may undergo a period-doubling bifurcation. Analytical investigations on subharmonic rolling were performed later by the Trieste group (Cardo et al . 1981).…”

Approximate analytical response curve for a parametrically excited highly nonlinear 1-DOF system with an application to ship roll motion prediction

“…The analysis of roll motion in beam sea can usually be carried out, in an approximate way, taking into account the exact shape of the restoring arm curve, up to desired order without great di culty from a numerical point of view and without too cumbersome calculations from an analytical point of view [8,26,28]. Thus, the bases of the nonlinear modelling of roll motion in beam sea is, for certain main aspects, quite well developed and understood.…”