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

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.