Chaotic behavior and vibration suppression of a ship model via NDF controller

It is essential to investigate the nonlinear phenomena associated with rolling ships to enhance marine operations, reliability, and stability under challenging circumstances. Ship design, operating protocols, and control strategies are improved by comprehending and anticipating these patterns of behavior. A dynamic analysis of the nonlinear rolling ship model under a parametric force is presented in this work. The nonlinear derivative feedback (NDF) control is used to enhance stability and lessen unwanted vibrations, particularly in the resonance zone. To obtain the approximate solutions (AS), the multiple-scales process (MSP) develops and solves the differential formula regarding the nonlinear rolling ship to the proper order. The correctness of the AS is verified by comparing it to the calculated numerical solutions (NS) using the fourth-order Runge–Kutta process (RK-4). Solvability requirements and resonance examples are explored to acquire the modulation formulas. MATLAB programming is used to display the frequency responses and time histories of the obtained solutions graphically. Furthermore, the temporal histories of the obtained solutions are analyzed graphically both with and without control. Stability analysis and steady-state results are also investigated using resonance curves. To determine the crucial factors that result in significant fluctuations in the structure’s behavior, the nonlinear dynamics of the model are further examined using bifurcation analysis, as represented by bifurcation diagrams. Periodic as well as chaotic oscillations are studied using the Poincaré diagram, which sheds light on the long-term equilibrium of the structure and the genesis of chaotic processes. These findings facilitate a better understanding and mitigation of dynamic disruptions in flexible structures across diverse operating environments. The dynamical analysis of the rolling ship model plays a vital role in enhancing ship stability, safety, and performance. It aids in the design of anti-roll systems, ensures cargo security, and informs safe operational guidelines under varying sea conditions. Additionally, it supports simulation-based crew training and helps predict critical transitions to chaotic motion, reducing the risk of capsizing and improving overall maritime safety.