Wave Propagation at an Interface of Elastic and Microstretch Thermoelastic Solids with Microtemperatures

Journal of Solid Mechanics

مقاله 2، دوره 5، شماره 3، آذر 2013، صفحه 226-244   

نوع مقاله: Research Paper

نویسندگان

R Kumar¹؛ M Kaur^{* 2}؛ S.C Rajvanshi³

¹Department of Mathematics, Kurukshetra University

²Department of Applied Sciences, Guru Nanak Dev Engineering College, Ludhiana

³Department of Applied Sciences, Gurukul Vidyapeeth Institute of Engineering and Technology

چکیده

In the present paper, the problem of reflection and transmission of waves at an interface of elastic and microstretch thermoelastic solids with microtemperatureshas been studied. The amplitude ratios of various reflected and transmitted waves are functions of angle of incidence and frequency of incident wave. The expressions of amplitude ratios have been computed numerically for a particular model. The variations of amplitude ratios with angle of incidence are shown graphically to depict the effect of microrotation. Some particular cases of interest have been also deduced.

کلیدواژه‌ها

Microstretch؛ Microtemperatures؛ Wave propagation؛ Amplitude ratios؛ Elastic solid

مراجع

[1] Eringen A.C., 1966, Mechanics of micromorphic materials, Proceedings of the 2nd International Congress of Applied Mechanics, Springer, Berlin, 131-138.

[2] Eringen A.C., 1968, Mechanics of Micromorphic Continua, Mechanics of Generalized Continua, IUTAM Symposium, Freudenstadt-Stuttgart, Springer, Berlin, 18-35.

[3] Eringen A.C., 1971, Micropolar Elastic Solids with Stretch, Ari Kitabevi Matbassi 24:1-18.

[4] Eringen A.C., 1990, Theory of thermo-microstretch elastic solids, International Journal of Engineering Science 28: 1291-1301.

[5] Grot R.A., 1969, Thermodynamics of a continuum with microstructure, International Journal of Engineering Science 7: 801–814.

[6] Riha P., 1976, On the microcontinuum model of heat conduction in materials with inner structure, International Journal of Engineering Science 14: 529-535.

[7] Iesan D., Quintanilla R., 2000, On a theory of thermoelasticity with microtemperatures, Journal of Thermal Stresses 23:199–215.

[8] Ciarletta M., Scalia A., 2004, Some results in linear theory of thermomicrostretch elastic solids, Meccanica 39:191-206.

[9] Iesan D., Quintanilla R., 2005, Thermal stresses in microstretch elastic plates, International Journal of Engineering Science 43: 885-907.

[10] Othman M.I.A, Lofty K.H., Farouk R.M., 2010, Generalized thermo-microstretch elastic medium with temperature dependent properties for different theories, Engineering Analysis with Boundary Elements 43 :229-237.

[11] Passarella F., Tibullo V., 2010, Some results in linear theory of thermoelasticity backward in time for microstretch materials, Journal of Thermal Stresses 33:559-576.

[12] Marin M., 2010, A partition of energy in thermoelasticity of microstretch bodies, Nonlinear Analysis-Real World Applications 11(4): 2436-2447.

[13] Marin M., 2010, Lagrange identity method for microstretch thermoelastic materials, Journal of Mathematical Analysis and Applications 363:275-286.

[14] Kumar S., Sharma J.N., Sharma Y.D., 2011, Generalized thermoelastic waves in microstretch plates loaded with fluid of varying temperature, International Journal of Applied Mechanics 3:563-586.

[15] Othman M.I.A., Lofty K.H., 2010, On the plane waves of generalized thermomicrostretch elastic half space under three theories, International Communications in Heat and Mass Transfer 37:192-200.

[16] Othman M.I.A., Lofty K.H., 2011, Effect of rotation on plane waves in generalized thermo-microstretch elastic solid with one relaxation time, Multidiscipline Modelling in Materials and Structures 7:43-62.

[17] Kumar R., Rupender, 2008, Reflection at free surface of magneto-thermo-microstretch elastic solid, Bulletin of Polish Academy of Sciences 56:263-271.

[18] Kumar R., Rupender, 2012, Propagation of plane waves at imperfect boundary of elastic and elctro-microstretch generalized thermoelastic solids, Applied Mathematics and Mechanics 30:1445-1454.

[19] Shaw S., Mukhopadhayay B., 2012, Electromagnetic effects on rayleigh surface wave propagation in a homogeneous isotropic thermo-microstretch elastic half-space, Journal of Engineering Physics and Thermophysics 85 :229-238.
[20] Iesan D., 2001, On a theory of micromorphic elastic solids with microtemperatures, Journal of Thermal Stresses 24: 737-752.

[21] Iesan D., Quintanilla R., 2009, On thermoelastic bodies with inner structure and microtemperatures, Journal of Mathematical Analysis and Applications 354:12-23.

[22] Casas P.S., Quintanilla R., 2005, Exponential stability in thermoelasticity with microtemperatures, International Journal of Engineering Science 43:33-47.

[23] Scalia A., Svanadze M., 2006, On the representation of solutions of the theory of thermoelasticity with microtemperatures, Journal of Thermal Stresses 29: 849-863.

[24] Iesan D., 2006, Thermoelasticity of bodies with microstructure and microtemperatures, International Journal of Solids and Structures 43: 3414-3427.

[25] Aouadi M., 2008, Some theorems in the isotropic theory of microstretch thermoelasticity with microtemperatures, Journal of Thermal Stresses 31:649-662.
[26] Scalia A., Svanadze M., Tracinà R., 2010, Basic theorems in the equilibrium theory of thermoelasticity with microtemperatures peratures, Journal of Thermal Stresses 33:721-753.

[27] Quintanilla R., 2011, On growth and continous dependence in thermoelasticity with microtemperatures, Journal of Thermal Stresses 34:911-922.

[28] Steeb H., Singh J., Tomar S.K., 2013, Time harmonic waves in thermoelastic material with microtemperatures, Mechanics Research Communications 48:8-18.

[29] Chirita S., Ciarletta M., Apice C.D., 2013, On the theory of thermoelasticity with microtemperatures, Journal of Mathematical Analysis and Applications 397:349-361.

[30] Iesan D., 2007, Thermoelasticity of bodies with microstructure and microtemperatures, International Journal of Solids and Structures 44:8648-8662.

[31] Bullen K.E., 1963, An Introduction of the Theory of Seismology, Cambridge University Press, Cambridge.

[32] Eringen A.C., 1984, Plane waves in non local micropolar elasticity, International Journal of Engineering Science 22: 1113-1121.

[33] Dhaliwal R.S., Singh A.,1980, Dynamic Coupled Thermoelasticity, Hindustan Publication Corporation, New Delhi, India .