Active Control of a Non-Linear Ship model with External and Parametric Excitation

The response of a ship model with non-linearly coupled pitch and roll modes under modulated external and parametric solved and studied. The active control is applied to reduce the vibration of the system . The method of multiple scale perturbation technique is applied to obtain the periodic response equation near the primary resonance in the presence of internal resonance of the system. The objective of this research is focused on the stability of this periodic solution, dynamical properties and chaotic response. The stability of the obtained numerical solution is studied using both frequency response equation and phase-plane methods. The effects of some parameters on the vibrating system are investigated and reported in this paper