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Acceleration waves in constrained thermoelastic materials
Bibliography: pages 242-249.
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2015
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| _version_ | 1867613157388713984 |
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| access_status_str | Open Access |
| author | Bleach, Gordon Phillip |
| author2 | Reddy, Daya |
| author_browse | Bleach, Gordon Phillip Reddy, Daya |
| author_facet | Reddy, Daya Bleach, Gordon Phillip |
| author_sort | Bleach, Gordon Phillip |
| collection | Thesis |
| description | Bibliography: pages 242-249. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/15850 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:41.113Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/15850 Acceleration waves in constrained thermoelastic materials Bleach, Gordon Phillip Reddy, Daya Acceleration waves - Mathematical models Bibliography: pages 242-249. We study the propagation and growth of acceleration waves in isotropic thermoelastic media subject to a broad class of thermomechanical constraints. The work is based on an existing thermodynamic theory of constrained thermoelastic materials presented by Reddy (1984) for both definite and non- conductors, but we differ by adopting a new definition of a constrained non-conductor and by investigating the consequences of isotropy. The set of constraints considered is not arbitrary but is large enough to include most constraints commonly found in practice. We also extend Reddy's (1984) work by including consideration of sets of constraints for which a set of vectors associated with the constraints is linearly dependent. These vectors play a significant role in the propagation conditions and in the growth equations described below. Propagation conditions (of Fresnel-Hadamard type) are derived for both homothermal and homentropic waves, and solutions for longitudinal and transverse principal waves are discussed. The derivations involve the determination of jumps in the time derivative of constraint multipliers which are required in the solution of the corresponding growth equations, and it is found that these multipliers cannot be separately determined if the set of constraint vectors mentioned above is linearly dependent. This difficulty forces us to restrict the constraint set for which the growth equations for homothermal and homentropic waves can be derived. The growth of plane, cylindrical and spherical waves is considered and solutions are discussed, concentrating on the influence of the constraints on the results. 2015-12-20T15:34:06Z 2015-12-20T15:34:06Z 1989 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/15850 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Acceleration waves - Mathematical models Bleach, Gordon Phillip Acceleration waves in constrained thermoelastic materials |
| thesis_degree_str | Doctoral |
| title | Acceleration waves in constrained thermoelastic materials |
| title_full | Acceleration waves in constrained thermoelastic materials |
| title_fullStr | Acceleration waves in constrained thermoelastic materials |
| title_full_unstemmed | Acceleration waves in constrained thermoelastic materials |
| title_short | Acceleration waves in constrained thermoelastic materials |
| title_sort | acceleration waves in constrained thermoelastic materials |
| topic | Acceleration waves - Mathematical models |
| url | http://hdl.handle.net/11427/15850 |
| work_keys_str_mv | AT bleachgordonphillip accelerationwavesinconstrainedthermoelasticmaterials |