The Equations of Motion for Extensible Strings
The main purpose of this chapter is to give a derivation, which is mathematically precise, physically natural, and conceptually simple, of the quasilinear system of partial differential equations governing the large motion of nonlinearly elastic and viscoelastic strings. A part of this treatment is a careful study the Principle of Virtual Power and the equivalent Impulse-Momentum Law, which are physically and mathematically important generalizations of the governing equations. These formulations form the foundation of the treatment of concrete problems, which is begun in this chapter for very simple problems and is pursued in greater depth in Chaps. III and VI. These formulations also serve as models for those for more complicated bodies, such as rods, shells, and three-dimensional bodies, which we study later.
KeywordsConstitutive Equation Jump Condition Transverse Motion Longitudinal Motion Constitutive Function
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