On the mathematical and geometrical structure of the determining equations for shear waves in nonlinear isotropic incompressible elastodynamics

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Abstract

Using the theory of $1+1$ hyperbolic systems we put in perspective the mathematical and geometrical structure of the celebrated circularly polarized waves solutions for isotropic hyperelastic materials determined by Carroll in Acta Mechanica 3 (1967) 167--181. We show that a natural generalization of this class of solutions yields an infinite family of emph{linear} solutions for the equations of isotropic elastodynamics. Moreover, we determine a huge class of hyperbolic partial differential equations having the same property of the shear wave system. Restricting the attention to the usual first order asymptotic approximation of the equations determining transverse waves we provide the complete integration of this system using generalized symmetries.

Autore Pugliese

Tutti gli autori

  • G. Saccomandi , R. Vitolo

Titolo volume/Rivista

JOURNAL OF MATHEMATICAL PHYSICS

Anno di pubblicazione

2014

ISSN

0022-2488

ISBN

Non Disponibile

Numero di citazioni Wos

6

Ultimo Aggiornamento Citazioni

28/04/2018

Numero di citazioni Scopus

6

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile