Roll instabilities that are caused by nonlinear interaction mechanisms must be modeled properly for the design and safe operation of seagoing vessels. Two different mechanisms that cause roll instabilities in ships are described. Equations of motion for a parametric wave excitation mechanism are given. An approximate solution based on the method of multiple scales is presented. Different simulations using the Large Amplitude Motions Program (LAMP) code are conducted to determine linear parameters of the heave, pitch, and roll response. A methodology for nonlinear system identification that combines the method of multiple scales and higher-order statistics is proposed.
It has been well documented that nonlinear resonance conditions between heave, pitch, and roll motions could lead to large roll responses. These roll motions can impede onboard operations and even cause capsizing. To reduce or prevent the effects of these motions, one needs prediction and control schemes. Such schemes can only be effective if the relevant mechanisms are correctly modeled. Because these mechanisms are primarily nonlinear, such models need to accurately describe the nonlinear resonances between the heave, pitch, and roll motions. Consequently, any system identification process must be able to quantify such resonances. In this work, we outline a methodology for the system identification of a roll instability in a series S60–70 ship. In Section II, we discuss how roll instabilities can result from either autoparametric resonances or parametric resonances. We present the governing equation for the parametric mechanism and an approximate solution based on the method of multiple scales. In Section III, we discuss the numerical simulations conducted, using the LAMP program developed by the Scientific Applications International Corporation (SAIC), to study the parametric mechanism. In Section IV, we identify the linear parameters governing this system. Finally, we propose a methodology, combining the method of multiple scales and higher-order spectra, for identification of the nonlinear system parameters.
