Validation of the D’Alembert’s Equation for the Vibrating String Problem

Authors

  • H. Leckar
  • R. Sampaio
  • E. Cataldo

DOI:

https://doi.org/10.5540/tema.2006.07.01.0075

Abstract

The aim of this work is to discuss the dynamics of an one spacedimension structure without flexural stiffness. We model the behavior of a very light string and we present the problem, considering large deformations, considering that each particle has only vertical motion. We discuss the kind of constitutive equations needed in such motion. Using a perturbation method, we show that the D’Alembert’s equation can be seen as a first approximation for a general model and, then, its limitations become clear.

References

[1] S.S. Antman, The equations for large vibrations of string, American Mathematical Monthly, 87 (1980), 359 - 370.

S.S. Antman, “Non-Linear Problems in Elasticity”, Springer, Applied Mathematical Sciences 107 , Berlin, 1991.

J.E. Bolwell, The flexible string’s neglected term, Journal of Sound and Vibrations, 206 (1997), 618-623.

J.B. Keller, Large amplitude motion of a string, American Journal of Physics, 27 (1959), 584-586.

H.F. Leckar and R. Sampaio, “Mathematical Aspects of Mechanical Vibrations”, Notes in portuguese, 49 Brazilian Seminar of Analysis, UNICAMP, Campinas, 1999.

R. Sampaio, “Topics in Wave Propagation”, Notes in Portuguese, III School of Applied Mathematics, LNCC- CNPq, Rio de Janeiro, 1982.

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Published

2006-06-01

How to Cite

Leckar, H., Sampaio, R., & Cataldo, E. (2006). Validation of the D’Alembert’s Equation for the Vibrating String Problem. Trends in Computational and Applied Mathematics, 7(1), 75–84. https://doi.org/10.5540/tema.2006.07.01.0075

Issue

Vol. 7 No. 1 (2006)

Section

Original Article

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