International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

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 Volume 7, Issue 7 (July 2020), Pages: 48-55

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 Original Research Paper

 Title: On effects of viscous damping of harmonically varying axially moving string

 Author(s): Sanaullah Dehraj *, Rajab A. Malookani, Sajad H. Sandilo

 Affiliation(s):

 Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Sciences and Technology, Nawabshah, Pakistan

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0001-8453-3389

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2020.07.006

 Abstract:

In this study, the stability of an axially moving string under the influence of viscous damping in terms of transverse vibrations has been examined. Mathematically, an axially moving string can be expressed as a linear-homogenous partial differential equation with the initial and boundary conditions. The axial speed of string is taken to be time-varying, sinusoidal, and small compared to wave velocity. In order to approximate the exact solutions of the initial-boundary value problem, a Fourier-expansion method, together with the two timescales perturbation method, has been used. General resonance case and the detuning case have been studied in detail. The total energy of an infinite-dimensional coupled system has been obtained. Under certain values of the damping parameter, this total mechanical energy is either obtained to be bound or unbound. In addition, it turned out that there is a possibility of mode-truncation depending on the certain values of the damping parameter. 

 © 2020 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Axially moving string, Viscous damping, Perturbation method, Internal resonance

 Article History: Received 12 December 2019, Received in revised form 29 March 2020, Accepted 30 March 2020

 Acknowledgment:

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The authors declare that they have no conflict of interest.

 Citation:

 Dehraj S, Malookani RA, and Sandilo SH (2020). On effects of viscous damping of harmonically varying axially moving string. International Journal of Advanced and Applied Sciences, 7(7): 48-55

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 Figures

 Fig. 1

 Tables

 Table 1 Table 2 

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