Sunny Kumar Aasoori,Rajab A. Malookani,Sajad H.Sandilo,Sanaullah Dehraj,A.H.Sheikh,




Transverse vibrations,asymptotic approximations,structural damping,perturbation method.,


In this paper the transversal vibrations of axially moving string under structural damping are studied. The focus on the possibility of truncation method has been discussed. Governing equations of motion is modeled as second order linear homogeneous partial differential equation with constant coefficients.  The string is taken to be fixed at both ends. To construct the asymptotic approximations, the Fourier expansion method in conjunction with the two timescales perturbation method is employed. Amplitude-response of individual mode is computed under the effect of various structural damping parameter values. It is obtained that the response of individual-mode decays as the time increases. Furthermore, to investigate the applicability of truncation method, the method of characteristic coordinates and two timescales perturbation method are used in conjunction with each other. The amplitude-response subject to the specific initial conditions under the effect of various structural damping parameter values is computed. It turned out that amplitude-response decay as the time increases. Energy of the system is also computed and found to be decaying as the time progresses. From the amplitude-response of the system and individual mode amplitude-response, it is found out that the mode-truncation is allowed in the structural damping case.


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