Friday, February 8, 2013

1302.1675 (Michel Destrade et al.)

Transverse Waves in Nonlinearly Elastic Solids and the Milne-Pinney (or
Ermakov) Equation

Michel Destrade, Giuseppe Saccomandi
We establish a connection between the general equations of nonlinear elastodynamics and the nonlinear ordinary differential equation of Pinney [Proc. Amer. Math. Soc. 1 (1950) 681]. As a starting point, we use the exact travelling wave solutions of nonlinear elasticity discovered by Carroll [Acta Mechanica 3 (1967) 167]. The connection provides a method for finding new exact and approximate dynamic solutions for neo-Hookean and Mooney-Rivlin solids, and for the general third- and fourth-order elasticity models of incompressible solids.
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