Sindhu Jamali,Khalid H. Malak,Sanaullah Dehraj,Sajad H. Sandilo,Zubair A. Kalhoro,




axially moving string,viscous damping,straightforward expansion method,


In this paper, a mathematical model for an externally damped axially moving string is studied. This mathematical model is a second order partial differential equation which is a wave-like equation. The String is assumed to be externally damped by the viscous medium such as oil, and there is no restriction on the parametric values of the damping parameter. From a physical point of view, a string is represented as a chain moving in oil in the  positive horizontal direction between pair of pulleys. The axial speed of the string is assumed to be constant, positive and small compared to wave-velocity. To approximate the exact solutions of the initial-boundary value problem, the straightforward expansion method has been used to obtain valid approximations. It will be shown that if the damping parameter is neglected then the method breaks down as expected, and if damping is present in the system then the amplitudes of the oscillations are damped out and, solutions are valid and uniform.


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