Chaotic threshold control in a giant magnetostrictive actuator via nonlinear damping

Irregular vibrations in giant magnetostrictive actuators, arising from parametric variations, can significantly degrade the actuation accuracy and system stability. This study investigates chaotic threshold control in a giant magnetostrictive actuator through nonlinear damping, including the incorporation of fractional-order damping effects. Analytical conditions for the onset of Smale horseshoe chaos are derived using the Melnikov method. In particular, the first-order Melnikov analysis reveals that the integral associated with the prestress function vanishes, suggesting an analytical independence of the chaos threshold from the prestress coefficient C 0 . However, comprehensive numerical simulations, including bifurcation diagrams, Poincaré maps, and basins of attraction, demonstrate that variations in C 0 substantially shift the chaotic threshold and alter the global stability boundaries, highlighting inherent limitations of first-order analytical predictions. The influences of excitation force, linear damping, nonlinear stiffness, and control parameters on the system dynamics are further examined numerically. The results show that nonlinear damping with a fractional order P < 1 . 0 facilitates the emergence of chaotic responses and shrinks the basins of attraction for stable orbits, whereas higher-order damping ( P ≥ 2 . 0 ) effectively suppresses chaos, expands the safe basins, and stabilizes the system behavior. These findings emphasize the critical role of nonlinear damping in chaos control and underscore the necessity of numerical validation for the reliable design and control of giant magnetostrictive actuator systems.