Purpose <p>This study investigates the suppression of oscillations in an unloaded chain suspended from a bridge crane and transported by a moving trolley. The objective is to develop robust input-shaping strategies that minimize residual vibrations while satisfying practical operating constraints.</p> Methods <p>A continuous vibration model based on Bessel functions was employed to represent the chain dynamics. Two input shapers, namely Zero-Vibration and Zero-Vibration-Derivative, were developed using smooth exponential input functions. The shapers were designed to eliminate the dominant vibration modes while satisfying limits on input acceleration and achieving a prescribed final trolley velocity. Extensive numerical simulations were conducted for different chain lengths and maneuvering conditions.</p> Results <p>The proposed shapers effectively suppressed residual oscillations in the dominant lower modes across a range of chain lengths. The Zero-Vibration-Derivative shaper demonstrated enhanced robustness to chain-length variations compared with the Zero-Vibration shaper, maintaining near-zero residual oscillations around the design condition. Although higher vibration modes were not directly targeted, their influence remained negligible. The analysis of the chain’s specific kinetic energy confirmed substantial energy reduction, indicating improved oscillation suppression and system stability.</p> Conclusion <p>The proposed exponential-based input shapers provide an effective and practical approach for vibration suppression in suspended chains transported by bridge cranes. The Zero-Vibration-Derivative shaper offers superior robustness, while both shapers significantly reduce residual oscillations and improve operational safety and precision. The developed methodology can be extended to address higher vibration modes and other flexible transportation systems.</p>