Cancellation and resonance of damped two-span continuous bridges under successive moving loads based on modal characteristics

Abstract

This study presents an analytical investigation of the dynamic response of a damped twospan continuous bridge subjected to successive moving loads, with particular emphasis on the role of bridge damping in internal and external cancellation phenomena and resonance conditions. The formulation is developed by exploiting the symmetric and antisymmetric modal characteristics of an equal-span bridge system, enabling analytical derivation of free-vibration response in a two-span continuous bridge. A parametric study is conducted to quantify the effects of damping ratio, number of loads, and spacing of loads. The results demonstrate that bridge damping introduces a leaking effect that prevents complete vibration cancellation in damped systems, such that only minimum response levels can be achieved under cancellation conditions for both antisymmetric and symmetric modes. For small bridge damping ratios, cancellation and resonance conditions, as well as the optimal length ratios, remain essentially unaffected, indicating negligible influence of damping on critical speed parameters. Internal cancellation is shown to depend primarily on mode order, whereas external cancellation is governed by load number and spacing. Increasing bridge damping suppresses the occurrence of external cancellation, while increasing load number or spacing promotes it. The findings provide theoretical insight into vibration mitigation and dynamic design considerations for multi-span bridges under successive moving loads.