Acceleration waves in constrained thermoelastic materials

 

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dc.contributor.advisor Reddy, Daya en_ZA
dc.contributor.author Bleach, Gordon Phillip en_ZA
dc.date.accessioned 2015-12-20T15:34:06Z
dc.date.available 2015-12-20T15:34:06Z
dc.date.issued 1989 en_ZA
dc.identifier.citation Bleach, G. 1989. Acceleration waves in constrained thermoelastic materials. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/15850
dc.description Bibliography: pages 242-249. en_ZA
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Acceleration waves - Mathematical models en_ZA
dc.title Acceleration waves in constrained thermoelastic materials en_ZA
dc.type Doctoral Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Doctoral
dc.type.qualificationname PhD en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Bleach, G. P. (1989). <i>Acceleration waves in constrained thermoelastic materials</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/15850 en_ZA
dc.identifier.chicagocitation Bleach, Gordon Phillip. <i>"Acceleration waves in constrained thermoelastic materials."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1989. http://hdl.handle.net/11427/15850 en_ZA
dc.identifier.vancouvercitation Bleach GP. Acceleration waves in constrained thermoelastic materials. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1989 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/15850 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Bleach, Gordon Phillip AB - 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. DA - 1989 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1989 T1 - Acceleration waves in constrained thermoelastic materials TI - Acceleration waves in constrained thermoelastic materials UR - http://hdl.handle.net/11427/15850 ER - en_ZA


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