Publication

Transverse waves in nonlinearly elastic solids and the Milne-Pinney equation

Destrade, Michel
Thumbnail Image
Files
Thumbnail Image
Journal article
Adobe PDF, 221.73 KB
Repository DOI
Publication Date
2011-08-17
Keywords
Nonlinear elastodynamics, Exact solutions, Milne-Pinney equation, Ermakov equation
Type
Article
Downloads
Show all metadata
Citation
Destrade, M., Saccomandi, G. (2011) 'Transverse waves in nonlinearly elastic solids and the Milne-Pinney equation'. Mathematics and Mechanics of Solids, Special Issue in Honour of M.M. Carroll [invited contribution], 16 :586-593.
Abstract
We establish a connection between the general equations of nonlinear elastodynamics and the nonlinear ordinary differential equation of Pinney [Proc Amer Math Soc 1950; 1: 681]. As a starting point, we use the exact travelling wave solutions of nonlinear elasticity discovered by Carroll [Acta Mechanica 1967; 3: 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.
Funder
|~|
Publisher
SAGE Journals
Publisher DOI
http://dx.doi.org/10.1177/1081286510387704
Rights
Attribution-NonCommercial-NoDerivs 3.0 Ireland
cbn
Collections
Mathematics (Scholarly Articles)