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Two-dimensional motion in a Bell-constrained plate

Sandiford, KJ; Rogerson, GA; Murphy, JG

Authors

KJ Sandiford

GA Rogerson

JG Murphy



Abstract

The so-called Bell constraint has been used for several years in plasticity theory and has additionally been the subject to several investigations within an elastic context. In this paper the effects of the Bell constraint on the propagation of harmonic waves in a finitely deformed elastic plate are considered. Strong ellipticity conditions are first derived for the unbounded case, and are shown to be dependent on the scalar multiplier associated with the Bell constraint. The dispersion relation, associated with harmonic wave propagation in a plate composed of such a material with zero incremental surface traction, is derived in respect of an arbitrary strain energy function. Asymptotic expansions are then obtained for high and low wave number. These expansions, which give phase speed as a function of wave number, harmonic number and pre-stress, are shown to give excellent agreement with numerical solutions.

Citation

Sandiford, K., Rogerson, G., & Murphy, J. (2006). Two-dimensional motion in a Bell-constrained plate. International Journal of Engineering Science, 44(5-6), 379-394. https://doi.org/10.1016/j.ijengsci.2005.12.006

Journal Article Type Article
Publication Date Mar 1, 2006
Deposit Date Aug 23, 2007
Journal International Journal of Engineering Science
Print ISSN 0020-7225
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 44
Issue 5-6
Pages 379-394
DOI https://doi.org/10.1016/j.ijengsci.2005.12.006
Publisher URL http://dx.doi.org/10.1016/j.ijengsci.2005.12.006