Vibration Control for a Coupled Pitch- roll Ship Model Via a Negative Cubic Velocity Feedback Control

AbstractOne of the most essential ship reactions to waves is roll motion. Due to the intricacy of ship wave interactions and their sensitivity, predicting such a reaction is extremely challenging. Because vibration motion is an undesirable occurrence, it must be removed, decreased, or controlled. A coupled Pitchroll ship model with negative cubic velocity feedback control subjected to parametric excitations is premeditated and solved in this paper. The method of multiple time scales is applied to scrutinize the response of the two modes of the system neighbouring the simultaneous sub-harmonic, and internal resonance situation. Besides, the steady-state solution is determined through the RungKutta Method (RKM) of fourth order. Stability of the steady state solution near this resonance case is discussed and studied applying Lyapunov’s first indirect method and RouthHurwitz criterion. The influences of the different parameters on the steady state solution are reconnoitred and discussed. The controller effects on the stability are clarified. Simulation results are accomplished with the help of MATLAB and Maple software programs.