Vibration localization in dual-span, axially moving beams, Part I: Formulation and results

An investigation of the vibration localization phenomenon in dual-span, axially moving beams is presented. The effects of a tension difference among the spans, also referred to as disorder, on the natural modes of free vibration are studied in terms of inter-span coupling and transport speed. The equations governing the transverse vibration of the two-span, axially moving beam are derived through Hamilton’s principle, and solution methods are developed. Results demonstrate that normal mode localization indeed occurs for both stationary and translating disordered two-span beams, especially for small inter-span coupling.