The Finite Difference Scheme for the Suspended String Equation with the Nonlinear External Forces

Authors: Jaipong Kasemsuwan

Abstract:

This paper presents the finite difference scheme and the numerical simulation of suspended string. The vibration solutions when the various external forces are taken into account are obtained and compared with the solutions without external force. In addition, we also investigate how the external forces and their powers and coefficients affect the amplitude of vibration.

Keywords: Nonlinear external forces, Numerical simulation, Suspended string equation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335640

References:

[1] N. S. Koshlyakov, E. V. Gliner and M. M. Smirnov, Differential Equations of Mathematical Physics, Moscow, 1962 (in Russian). English Translation : North-Holland Publ. Co, 1964.
[2] J. Wongsawasdi and M. Yamaguchi, Global Solutions of IBVP to Nonlinear Equation of Suspended String, Tokyo Journal of Mathematics 30, No.2 (2007), 543-556.
[3] J. Wongsawasdi and M. Yamaguchi, Global Classical Solutions of IBVP to Nonlinear Equation of Suspended String, Tokyo Journal of Mathematics 31, No.2 (2008), 351-373.
[4] J. Kasemsuwan, P. Chitsakul and P. Chaisanit, Simulation of suspended string equation, The 3rd Thai-Japan International Academic Conference, 2010, 60-61.
[5] K. Subklay and J. Kasemsuwan, Numerical simulation of suspended string Vibration, The 8th Kasetsart University Kamphaeng Saen Campus Conference, 2011, 1486-1491.
[6] J. Kasemsuwan, Numerical Solution of the Damped Vibration of Suspended String, University of the Thai Chamber of Commerce Journal, 33, No.2 (2012), 77-90.
[7] J. Kasemsuwan, The Finite Difference Scheme for the Suspended String Equation with the Nonlinear Damping Term, International Conference on Applied Physics and Mathematics, 2012, 566-568.