Study On Nonlinear And Random Rolling Behaviors Leading To The Capsize Of Ship

Nonlinear rolling motion and capsizing of ships in random beam seas areinvestigated combining the Melnikov function and modern theory of stochasticdynamics. The main content and achievements in this thesis are as following:The expression of excitation moment of random beam seas is given in this paper.The differential equation of ships nonlinear rolling motion in random seas isestablished considering the nonlinear damping, nonlinear restoring moment andrandom characteristic of wave moment. The approximate solution to FPK equation isobtained. The joint probability density function and stationary mean out-crossing rateare investigated for ship nonlinear rolling subjected to additive white noise excitation.Melnikov function and phase space flux are applied to analyze highly nonlinear rolland capsizing of ships in the random seas. The variation of phase space flux withrespect to the characteristic wave period, significant wave height and damping ofships is studied. The expression of critical wave height of ships in random beam seasis presented in the paper. Considering a fish vessel of 30.7 long and 6.9m wide, the ISSC wave spectrumis used for determining the coefficients of wave, the Melnikov function iscomputed in the time domain. The relation between the phase space flux andMelnikov function is obtained and the influence of significant wave height onphase space flux is also shown. The curves of critical wave height are plotted overa range of characteristic wave period. The white noise is also adopted as theexcitation and the critical strength of white noise is given is this paper. Thevariation of Melnikov function and the rate of phase space flux with respected tothe external excitation and damping characteristic of biased ship in random beamseas are also analyzed. Numerical simulations show that phase space flux is growing continually alongwith significant wave height and the safe basin of ships is decreasing rapidly. Theclosed relations between the phase space flux and ship capsize are revealed. Thecritical curves that established by different significant wave height andcharacteristic wave period may be provided for the safe standard of ships.