| To date, vibration localization in the large class of systems modeled by multi-span axially moving materials has not been examined. These systems are common in many engineering applications, such as band saw blades, power transmission, belts and chains, and magnetic and paper tapes.; An investigation of the vibration localization phenomenon in two-span, axially moving beams is presented. The effects of tension disorder, interspan coupling, and transport speed on the confinement of the natural modes of free vibration are studied. The equations governing the transverse vibration of the two-span, axially moving beam are derived through Hamilton's principle and solution methods are developed. Numerical results demonstrate that normal mode localization indeed occurs for both stationary and translating disordered two-span beams, especially for small interspan coupling. The occurrence of localization is characterized by a peak deflection much greater in one span than in the other. In the stationary disordered case, localization becomes more pronounced as interspan coupling decreases, i.e., as the span axial tension increases. For an axially translating beam with identical spans, the two loci in each pair of natural frequencies may exhibit a single or double crossing (depending on the value of tension) when plotted against the axial transport speed. These crossings become veerings when the beam is disordered, and localization is strongest at those speeds where the eigenvalue veerings occur.; A perturbation approach, which provides additional insights into the sensitivity of the system to disorder, is also utilized. Analytical expressions are obtained in the limiting cases of weak and strong interspan coupling. Findings show that the sensitivity of the system to disorder primarily depends upon disorder and interspan coupling strengths.; Finally, an investigation of the localization phenomenon is performed for a more complete model of a band/wheel system. The effects of tension disorder on the confinement of the natural modes of free vibration are investigated both theoretically and experimentally. It is shown that results obtained with the simple interspan coupling model are in qualitative agreement with those of the more complex model, thereby confirming the usefulness of the model featuring a simple coupling mechanism. Analytical predictions from the simple model are also very nicely validated by the experimental results. |
