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

H. Leckar, R. Sampaio, E. Cataldo


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.


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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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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


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