Vibration localization in band-wheel systems: Theory and experiment

An investigation of the localization phenomenon in band-wheel systems is presented. The effects of tension disorder, inter-span coupling and translation speed on the confinement of the natural modes of free vibration are investigated both theoretically and experimentally. Two models of the band-wheel system dynamics are discussed; a simple model proposed by the authors [1] and a more complete model originally proposed by Wang and Mote [9]. The results obtained using the simple inter-span coupling model reveal phenomena (i.e., eigenvalue crossings and veerings and associated mode localization) that are qualitatively similar to those featured by the more complex model of inter-span coupling, thereby confirming the usefulness of the simple coupling model. The analytical predictions of the two models are validated by an experiment. A very good agreement between the experimental results and the theoretical ones for the simple model is observed. While both the experimental observations and the theoretical predictions show that a beating phenomenon takes place for ordered stationary and axially moving beams, beating is destroyed (indicating the occurrence of localization) when any small tension disorder is introduced, especially for small inter-span coupling (i.e., when localization is strongest).