Abstract
In this study, linear vibrations of axially moving beam simply supported between the guides are examined and natural frequencies are calculated numerically. The vibrations of axially tensioned Euler-Bernoulli beam are investigated under clamped-clamped end conditions. Governing differential equations of motion are derived using Hamilton’s Principle for two regions of the beam. The boundaries at the outer ends of the beam are assumed immovable. Non-dimensional equations of motion are derived and the solutions of the linear problem are obtained. Assuming a weakly non-linear system, linear equations are obtained using the Method of Multiple Scales. First seven natural frequencies are calculated numerically based on the flexural rigidity, axial velocity and locations of the intermediate support.
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