Forced Plane Vibration of a Moving Threadline.
IOWA UNIV IOWA CITY DEPT OF MECHANICS AND HYDRAULICS
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The plane response of a moving threadline under forced excitation is studied experimentally and theoretically. Instabilities in the first mode vibration are produced for a variety of initial conditions. The axial velocity of instability is observed to be dependent on one dimensionless coefficient, labeled Tr. Tr is found from a dimensional analysis, and also appears in the non-dimensionalization of the basic equations of motion for a moving threadline. Analytically, a system of ordinary differential equations are developed from the basic partial differential equations, by applying a weighted residual method. The ordinary system is solved numerically, and the solutions are periodic for a range of axial velocity. The velocity where periodic solutions break down is found to be dependent on Tr, verifying the experimental results. Author