Volume 54 | Number 6 | Year 2018 | Article Id. IJMTT-V54P559 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P559
The present paper encompasses the analytical solution for axisymmetric one dimensional thermomechanical response of an annular disk. The basic equations have been written in the form of a vectormatrix differential equation in the Laplace transform domain and solved by eigenvalue approach. The solutions for displacement, temperature, radial and hoop stresses are obtained in closed form in the Laplace transform domain. Numerical inversions for these field variables in the space-time domain have been made and presented in graphical form.
[1] H.W.Lord, Y.Shulman, “A Generalized Dynamical Theory of Thermoelasticity”, J.Mech.Phys.Solids, vol.15, pp.299-309, 1967.
[2] A.E.Green, K.A.Lindsay, “Thermoelasticity”, J.Elasticity, vol.2, pp.1-7, 1972.
[3] A.E.Green, N.Laws, “On The Entropy Production Inequality”, Arch.Rat.Mech.Anal, vol.45, pp.45-47, 1972.
[4] A.E.Green, P.M.Nagdhi, “A Re-examination of The Basic Postulates of Thermodynamics”, Proc.R.Soc. London A, vol.432, pp.171-194, 1991.
[5] A.E.Green, P.M.Nagdhi, “Thermoelasticity without Energy Dissipation”, J.Elasticity, vol.31, pp. 189-208, 1993.
[6] R.B.Hetnarski, J.Ignaczak, “Generalized Thermoelasticity”, J.Thermal Stresses, vol.22, pp.451-476, 2004.
[7] D.S.Chandrasekharaiah,” Hyperbolic Thermoelasticity: A review of Recent Literature”, Appl.Mech.Review, vol.51, pp.705-729, 1998.
[8] M.Anwar, H.Sherief, “State Space Approach to Generalized Thermoelasticity”, J.Thermal Stresses, vol.11, pp.353-365, 1988.
[9] N.C.Das, A.Lahiri, “Thermoelastic Interactions Due to Prescribed Pressure Inside a Spherical Cavity in an Unbounded Medium”, Int. J. Pure and Appl.Math., vol.31, pp.19-32, 2001.
[10 ]H.Sherief, “On Uniqueness and Stability in Generalized Thermoelasticity”, Quarterly of Appl.Math., vol.45, pp.773-778, 1987.
[11] J. Ignaczak , “Uniqueness in Generalized Thermoelasticity”, J.Thermal Stresses, vol.2, pp.171-175, 1979.
[12] H. M. Youssef, “Theory of Two-Temperature Generalized Thermoelasticity”, IMA J.Appl.Math, vol.71, pp.383-390, 2006.
[13] S.Banik, M.Kanoria, “Effects of Three-Phase-Lag on Two-Temperature Generalized Thermoelasticity for Infinite Medium with Spherical Cavity”, Appl. Math. Mech-Engl.Ed., vol.33, pp.483-498, 2012.
[14] R.Quintanilla, R. Racke, “A Note on Stability in Three-Phase Lag Heat Conduction, International “, J. Heat and Mass Transfer, vol. 51, pp.24-29, 2008.
[15] R. Kumar, S. Mukhopadhyay, “Analysis of The effects of Phase-lags on Propagation of Harmonic Plane Waves in Thermoelastic Media”, Comp. Methods in Science and Technology, vol.16, pp.19-28, 2010.
[16] R. Kumar, S. Mukhopadhyay, “Effects of Three-Phase Lags on Generalized Thermoelasticity for an Infinite Medium with a Cylindrical Cavity”, J.Thermal stresses, vol.32, pp.1149-1165, 2009.
[17] A. Bagri, M. R. Eslami, “Generalized Coupled Thermoelasticity of Disks Based on The Lord-Shulman Model”, J.Thermal Stresses, vol.27, pp.691-704, 2004.
[18] H.Taheri, S.J.Fariborz, M.R.Eslami, “Thermoelastic Analysis of an Annulus Using the Green-Nagdhi Model”, J.Thermal Stresses, vol.28, pp.911-927, 2005.
[19] A. Kar, M.Kanoria, “ Analysis of Thermoelastic Response in a Fiber Reinforced Thin Annular Disc with Three-Phase-Lag Effect”, European J.of Pure and Applied Math, vol.4, pp.304-321, 2011
[20] A.Lahiri, N.C.Das, S.Sarkar and M.Das, “Matrix Method of solution of Coupled Differential Equations and Its Applications in Generalized Thermoelasticity”, Bull. Calcutta Mathematical Society, vol.101, pp.571-590, 2009.
[21] V.Zakian, “ Inversion of Laplace Transforms”, Electronic Letters, vol.5, pp.120-121, 1969.
N.Gangopadhyaya, N.C.Das, "Eigenvalue Approach to Generalized Thermoelastic Interactions in an Annular Disk," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 6, pp. 485-499, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P559