Effect of Rotation in Case of 2-D Problems of the Generalized Thermoelasticity with Thermal Relaxation

• Autorzy: Othman M. I. A.
• Języki publikacji: EN

Abstrakty

EN

The mode of two-dimensional equations of generalized thermo-elasticity with one relaxation time under the effect of rotation is studied using the theory of thermo-elasticity recently proposed by Lord-Shulman. The normal mode analysis is used to obtain the exact expressions for the temperature distributions, the displacement components and thermal stresses. The resulting formulation is applied to two different concrete problems. The first concerns to the case of a heated punch moving across the surface of a semi-infinite thermo-elastic half-space subjected to appropriate boundary conditions. The second deals with a thick plate subjected to a time-dependent heat source on each face. Numerical results are given and illustrated graphically for each problem. Comparisons are made with the results predicted by the coupled theory and with the theory of generalized thermo-elasticity with one relaxation time in the absence of rotation.

Słowa kluczowe

EN

rotation; thermal relaxation; thermo-elasticity; normal mode

PL

relaksacja termiczna; drgania własne

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2005
• Tom: Vol. 9, nr 2
• Strony: 115--130
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Othman M. I. A.

• Department of Mathematics, Faculty of Education, P.O. Box 2801, Salalah 211, Sultanate of Oman,

Bibliografia

• [1] Nowinski, J: Theory of Thermo-elasticity with Applications, (1978), Sijthoff & Noordhoff International Publishers, Alphenaan de Rijn, 826.
• [2] Biot, M: Thermo-elasticity and Irreversible Thermo-dynamics, J. Appl. Phys., (1956), 27, 240-253.
• [3] Lord, H and Shulman, Y: A Generalized Dynamical Theory of Thermoelasticity, J. Mech. Phys. Solid, (1967), 15, 299-309.
• [4] Dhaliwal, R and Sherief, HH: Generalized Thermoelasticity for An isotropic Media, Quart. Appl. Math., (1980), 33, 1-8.
• [5] Sherief, HH and Dhaliwal, R: Generalized One-dimensional Thermal-shock Problem for Small Times, J. Thermal Stresses, (1981), 4, 407.
• [6] Sherief, HH: Fundamental Solutions of the Generalized Thermoelastic Problem for Short Times, J. Thermal Stresses, (1986), 9, 151-164.
• [7] Sherief, HH and Ezzat, M: Solution of the Generalized Problem of Thermo-elasticity in the Form of Series of Functions, J. Thermal Stresses, (1994), 17, 75-95.
• [8] Muller, I: The Coldness, A Universal Function in Thermo-elastic Solids, Arch. Rat. Mech. Anal., (1971), 41, 319.
• [9] Green, AE and Laws, N: On the Entropy Production Inequality, Arch. Rat. Mech. Anal., (1972), 45, 47.
• [10] Green, AE and Lindsay, KA: Thermoelasticity, J. Elast., (1972), 2, 1.
• [11] Suhubi, ES: Themoelastic Solids, in: Continuum Physics II, Chapter 2, (1975), ed. Eringen, AC, Academic, Press, New York.
• [12] Erbay, S and Suhubi, ES: Longitudinal Wave Propagation in a Generalized Elastic Cylinder, J. Therm. Stresses, (1986), 9, 279.
• [13] Ignaczak, J: A Strong Discontinuity Wave in Thermoelasticity with Relaxation Times, J. Therm. Stresses, (1985), 8, 25-40.
• [14] Ignaczak, J: Decomposition Theorem for Thermoelasticity with FiniteWave Speeds, J. Therm. Stresses, (1978), 1, 41.
• [15] Dhaliwal, R and Rokne: Thermal Shock Problem in Generalized Thermoelastic, J. Therm. Stresses, (1989), 12, 259-278.
• [16] Ezzat, MA: Fundamental Solution in Thermo-elasticity with two Relaxation Times for Cylindrical Regions, Int. J. Engng. Sci., (1995), 33, 2011-2020.
• [17] Othman, MIA: Lord-Shulman Theory Under the Dependence of the Modulus of Elasticity on the Reference Temperature in Two-dimensional Generalized Thermo-elasticity, J. Therm. Stresses, (2002), 25, 1027-1045.
• [18] Schoenberg M and Censor, D: Elastic Waves in Rotating Media, Quart. of Appl. Math., (1973), 31, 115-125.
• [19] Sherief, HH and Anwar, MA: Two-Dimensional Problem of Moving Heated Punch in Generalized Thermo-elasticity, J. Therm. Stresses, (1986), 9, 325-343.
• [20] Sherief, HH and Anwar, MA: Generalized Thermoelasticity Problem For a Plate Subjected to Moving Heat Sources on Both Sides, J. Therm. Stresses, (1992), 15, 489-505.
• [21] Nowacki, W: Dynamic Problems of Thermoelasticity, (1975), Noordhoof International, The Netherlands.
• [22] Ezzat, MA and Othman, MIA: Electromagneto-thermoelasticity Plane Waves with Two Relaxation Times in a Medium of Perfect Conductivity, Int. J. Engng. Sci., (2000), 38, 107-120.
• [23] Othman, MIA: Electrohydrodynamic Stability in a Horizontal Viscoelastic Fluid Layer in the Presence of a Vertical Temperature Gradient, Int. J. Engng. Sci., (2001), 39, 1217-1232.
• [24] Othman, MIA and Ezzat, MA: Electromagneto-hydrodynamic Instability in a Horizontal Viscoelastic Fluid Layer with One Relaxation Time, Acta Mech., (2001), 50, 1-2, 1-9.
• [25] Othman, MIA and Zaki, SA: The Effect of Thermal Relaxation Time on a Electrohydrodynamic Viscoelastic Fluid Layer Heated from Below, Can. J. Phys., (2003), 81, 779-787.