Propagation of disturbances in a flexible extensible filament under longitudinal accelerated motions in a fluid
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We seek a solution of the linearized equation of motion of a flexible extensible filament in a fluid in the form of an expansion in eigenfunctions of a boundary-value problem. For a uniformly accelerated motion and for motion accelerated according to a hyperbolic tangent law we find the exact solutions. For other forms of accelerated motion we propose a numerical solution of the initial inhomogeneous problem. We carry out an analysis of the solutions obtained. It is found that the first peak of the tension depends only weakly on the resistance of the fluid, but strongly on the acceleration parameters. The natural vibrations damp out more rapidly both as the resistance increases and as the acceleration increases.
KeywordsExact Solution Resistance Increase Hyperbolic Tangent Natural Vibration Accelerate Motion
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