Solving Mathematical Models of String Vibrations with Radial Basis Function Networks

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Published Mar 14, 2026

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Alifia Nisa Maghfiroh
Department of Mathematics, Faculty of Science and Technology, Maulana Malik Ibrahim State Islamic University of Malang
Ari Kusumastuti
Department of Mathematics, Faculty of Science and Technology, Maulana Malik Ibrahim State Islamic University of Malang

Abstract

String vibration phenomena on suspension bridges describe oscillations due to external forces and gravity, which can affect the stability and safety of the structure. The mathematical model for this vibration problem is stated by Mckenna (1999) in the form of a second-order ordinary differential equation for deflection . This study aims to analyze the behavior of the  model and solve the model solution with Radial Basis Function (RBF) and compare it with the analytical solution. In RBF, the basis function is selected in the form of a 1st order multiquadratic function. Error analysis is carried out by calculating the difference between RBF and the analytical solution at a time interval  with parameters . The results show that the numerical solution of RBF to the exact solution produces a difference of  at time  for , and a difference of  at time  for . With this level of accuracy, the RBF method can be said to be quite effective in solving string vibration models, and has the potential to be applied to the stability analysis of engineering structures such as suspension bridges.

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How to Cite
MAGHFIROH, Alifia Nisa; KUSUMASTUTI, Ari. Solving Mathematical Models of String Vibrations with Radial Basis Function Networks. Proceedings of the International Conference on Green Technology, [S.l.], v. 15, n. 1, mar. 2026. ISSN 2580-7099. Available at: <https://conferences.uin-malang.ac.id/index.php/ICGT/article/view/3839>. Date accessed: 01 may 2026.
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Issue
Vol 15 No 1 (2025): Proceeding of 15th International Conference on Green Technology
Section
Pure and Applied Mathematics
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