Some remarks on one-dimensional models of wave motion in elastic rods

Le Matematiche. 1991;46(1):303-310


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Journal Title: Le Matematiche

ISSN: 0373-3505 (Print); 2037-5298 (Online)

Publisher: Universit√† degli Studi di Catania

Society/Institution: University of Catania

LCC Subject Category: Science: Mathematics

Country of publisher: Italy

Language of fulltext: Italian, French, English

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Paolo Podio-Guidugli


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Time From Submission to Publication: 53 weeks


Abstract | Full Text

<span style="font-family: DejaVu Sans,sans-serif;">An exact derivation from three-dimensional elasticity of a model equation for the longitudinal vibrations of a cylindrical elastic rod is presented, based on the results of [1]. Similarities and differences are discussed with the model of [2], whose study strongly motivated the work leading to [1] and opened the way to the present discussion. A difference is that the model of è2+ is not exact, being obtained through a line of reasoning that involves truncated expansions in the radius of the cross section; a similarity is that the resulting equations share the mathematically relevant properties, and describe the same physical phenomenology (in particular, they support traveling wave solutions of the solitary type).</span>