Numerical Investigation of Localized Mode Transitions in Nonlinear Oscillator Systems with Nonreciprocal Coupling Spring under Impulsive Excitation

Intrinsic localized modes (ILMs) in nonlinear oscillatory systems offer promising applications in energy harvesting, vibration isolation, and noise control due to their asymmetric energy localization. However, their sensitivity to impulsive disturbances poses a challenge to practical implementation. This study explores the role of nonreciprocal coupling in enhancing ILM robustness against impulse-induced transitions. A two-degree-of-freedom nonlinear oscillator system, coupled by a nonreciprocal spring, is modeled and analyzed numerically. The system is initialized in distinct ILM states and subjected to impulses of varying magnitude and duration. Results reveal that while high-amplitude impulses can destabilize ILMs, low-amplitude impulses may induce controlled, unidirectional transitions within specific frequency bands. The transition bandwidth is tunable via coupling stiffness. These findings demonstrate that nonreciprocal coupling not only improves ILM stability but also enables controllable behavior under disturbances, offering potential for passive impact noise suppression and resilient vibration isolation in engineered systems.