Propagation of nonlinear, coupled thermoelastic waves in elastic media under volume force and heat supply /
انتشار الموجات المرنة الحرارية غير الخطية المتزاوحة فى الأوساط المرنة تحت تأثير قوة حجمية ومصدر حرارى حجمى
Wael Mahmoud Mohamed ; Supervised A. F. Ghaleb , A. A. Mosharafa , H.A.Z.Hassan
- Cairo : Wael Mahmoud Mohamed , 2016
- 127 P. : charts ; 25cm
Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics
Anumericalsolutionispresentedforfournonlinear, one-dimensionalboundary- value problems of thermoelasticity with variable volume force and heat supply inaslaborhalf-spaceofananisotropicelasticmaterial. Onesurfaceofthebody is subjected to a given periodic displacement and Robin thermal condition, while the other surface is kept xed and at zero temperature. The volume force and bulk heating simulate the eect of a beam of hot particles inltrating the medium and coming to rest in a layer adjacent to the boundary. Particular forms for the bulk force and heating functions are considered for deniteness, but other choices may be treated equally well. No phase transition is considered and the domain of the solution excludes any shock wave formation. The basic eld equations used in this thesis have been derived elsewhere (cf. [18]) on the basis of rigorous thermodynamics and are formulated in material coordinates, making them adequate for dealing with moving boundaries. As to the used numerical scheme, it nds its origin in [15,2325] and was readapted in [62]. This is a three-level, iterative nite-dierence scheme. It has been shown to exhibit unconditional stability for the case of only one dis- placement component in [62]. This result was extended in the present Thesis to include the case of three displacement components. Based on the obtained results, the used numerical method reproduces correctly the dierent aspects of the process of coupled thermo-mechanical wave propagation.
Elastic media Thermoelastic waves Volume force and heat