Representation Solutions of Damped Wave Equation of a String and a Rectangular Membrane Subject to a Restorative Force Using Maple

M. A. Ben Yzeed; A. F.  Abuaisha

doi:10.59743/kkfvc392

Authors

M. A. Ben Yzeed Physics Department, Faculty of Education, Alasmarya Islamic University, Zliten, Libya
A. F. Abuaisha Physics Department, Faculty of Education, Alasmarya Islamic University, Zliten, Libya.

DOI:

https://doi.org/10.59743/kkfvc392

Keywords:

Hyperbolic partial differential equations, vibrations, damped wave equation, Fourier series, Maple program

Abstract

This paper aims to obtain the representation of solutions of vibrating problem described by damped wave equation in terms of Fourier series which helps to understand thoroughly these solutions. The motion of an elastic fixed ends string and a stretched elastic rectangular membrane which are subjected to a restorative force proportional to velocity has been investigated. The role of the initial displacement has been discussed and the numerical solutions are then given by using Maple program [6]. Furthermore, For the sake of illustrations, the vibrations obtained by using the initial displacement in one and two dimensions have been plotted, respectively

References

Arfken G. B., Mathematical Methods for Physics, Fifth Edition. University of Virginia. 2001.

Asmar H. N., Partial Differential Equations with Fourier Series and Boundary Value Problems, Second Edition, University of Missouri. 2006.

Doma S. B., I. H. El-Sirafy, M. M. El-Borai and A. H. El-Sharif, Perturbation Treatment for the Vibrations of a Rectangular Membrane Subject to a Restorative Force, Alexandria Journal of Mathematics, Vol 2- No 1-2011.

Doma S. B., EL-Sirafy I. H., EL-Borai M. M. and EL-Sharif A. H. Perturbation Treatment for the Vibrations of a Circular Membrane Subject to a Restorative Force. Alexandria Journal of Mathematics. Vol 1- No 40-2010.

Kreyszig E., Advanced Engineering Mathematics, Tenth Edition, John Wiley & Sons, INC., New York, USA. 2011.

Microsoft, Maple 18 –User Manual, Waterloo, Canada, 2014.

Olver P. J., Introduction to Partial Differential Equations, Springer International Publishing, Switzerland. 2014.

Oneil P., Beginning Partial Differential Equations, Third Edition. John Wiley & Sons, INC. New York, USA. 2014