Microstructured continua and scaling for wave motion
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| Title | Microstructured continua and scaling for wave motion |
| Authors | |
| Abstract | This paper deals with wave motion in microstructured solids. A short introduction explains how the basic mathematical models for description of microstructure(s) of solids are derived. Based on the Mindlin-type micromorphic theory, the governing equations for wave motion in such solids are presented in one-dimensional setting. The focus of the paper is in explaining the importance of internal scales in microstructured solids. It is shown that the proper scaling permits to construct the mathematical models which involve hierarchies of wave operators. Depending on the scale parameter (the ratio of an internal scale over the wave length), the various operators govern the wave propagation. The main case analysed here consists of the second-order operators but the first-order operators which are characteristic to evolution equations, are also briefly explained. |
| Publisher | Accademia Peloritana dei Pericolanti |
| Date | 2013-01-29 |
| Source | 0365-0359 |
| Rights | Articles and conference papers published in Atti della Accademia Peloritana dei Pericolanti – Classe di Scienze Fisiche, Matematiche e Naturali are distributed under the terms and conditions of a Creative Commons Attribution 3.0 Unported License (effective since 2009, Vol. 87). Correspondingly, authors who publish with this journal agree to the following terms:Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work´s authorship and initial publication in this journal.Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal´s published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access). |