On (Non) Applicability of a Mode-Truncation of a Damped Traveling String

  • Rajab Ali Malookani Department of Mathematics & Statistics, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah , Pakistan
  •  Sajid Hussain Sandilo Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology , Nawabshah , Pakistan
  •  Abdul Hanan  Shaikh Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah, Pakistan

Abstract

This study investigates a linear homogeneous initial-boundary value problem for a traveling string under linear viscous damping. The string is assumed to be traveling with constant speed, while it is fixed at both ends. Physically, this problem represents the vertical (lateral) vibrations of damped axially moving materials. The axial belt speed is taken to be positive, constant and small in comparison with a wave speed, and the damping is also considered relatively small. A two timescale perturbation method together with the characteristic coordinate’s method will be employed to establish the approximateanalytic solutions. The damped amplitude-response of the system will be computed under specific initial conditions. The obtained results are compared with the finite difference numerical technique for justification. It turned out that the introduced damping has a significant effect on the amplitude-response. Additionally, it is proven that the mode-truncation is applicable for the damped axially traveling string system on a timescale of order ε -1

Published
Apr 1, 2019
How to Cite
ALI MALOOKANI, Rajab; SANDILO,  Sajid Hussain; SHAIKH,  Abdul Hanan . On (Non) Applicability of a Mode-Truncation of a Damped Traveling String. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 38, n. 2, p. 471-478, apr. 2019. ISSN 2413-7219. Available at: <http://publications.muet.edu.pk/index.php/muetrj/article/view/978>. Date accessed: 20 oct. 2019.
Section
Articles
This is an open Access Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License