Memory feedback signals in nonlinear coupled pitch-roll ship motions under narrow-band stochastic excitations

Initiating from the complexity of ship sailing environment and the nonlinear coupling hysteresis effect of its motion, we focus on the memory feedback shake-reducing strategy turning from the delay generally considered to exhibit undesired effects, and introduce it into the nonlinear coupled pitch-roll ship motions under loads incorporating stochastic disturbances to control the ship shaking and optimize the frequency band distribution of the stable navigation associated with the saturation. This paper then reports the deterministic equilibrium solutions of the roll and pitch response via the perturbation analysis of the third-order scale and successively explains the stability closely related to the saturation and bifurcations. Instead of just formula deduction, visually depict the distinction of equilibrium points and the determination conditions, and the effective shake-reducing frequency band coupled with the drift modulated by the memory feedback signals, and then integrate the moment method and stochastic It (o) over cap law to compute the steady-state moment and the mean square scale checked by numerical simulations. Set basic samples of the equation parameters for dual scenarios, and then track time histories of ship rolling and pitching as well as the marginal and joint probability evolutions to illustrate the resonance behavior and modes transition with the energy penetration in complementary ways. The results of our investigation present a new insight into the stability schemes of ship sailing issues.