An Exact Solution for Classic Coupled Magneto-Thermo-Elasticity in Cylindrical Coordinates

Subject Areas : Engineering

M  Jabbari ¹ (Postgraduate School, South Tehran Branch, Islamic Azad University)
H  Dehbani ² (Sama technical and vocational training college, Islamic Azad University, Varamin Branch)

Received: 2011-11-08 Accepted : 2012-01-07 Published : 2012-03-30

Keywords: Hollow cylinder, Exact solution, Coupled magneto –thermo-elasticity,

Abstract :

In this paper, the classic coupled Magneto-thermo-elasticity model of hollow and solid cylinders under radial-symmetric loading condition (r, t) is considered. A full analytical and the direct method based on Fourier Hankel series and Laplace transform is used, and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body force, the heat source and magnetic field vector are considered in the most general forms, where no limiting assumption is used. This generality allows to simulate a variety of applicable problems. The results are presented for thermal and mechanical shock, separately, and compare the effect of magnetic field on temperature and displacement.

References:

[1] Hetnarski R. B., 1964, Solution of the coupled problem of thermoelasticity in the form of series of functions, Archiwum Mechaniki Stosowanej 16:919-941.

[2] Hetnarsk R.B., Ignaczak J., 1993, Generalized Thermoelasticity: Closed-Form Solutions, Journal of Thermal Stresses 16: 473–498.

[3] Hetnarsk R.B., Ignaczak J., 1994, Generalized Thermoelasticity: Re­sponse of Semi-Space to a Short Laser Pulse, Journal of Thermal Stresses 17:377–396.

[4] Georgiadis H. G., Lykotrafitis G., 2005, Rayleigh Waves Generated by a Thermal Source: A Three-dimensional Transiant thermoelasticity Solution, Journal of Applied Mechanics 72:129-138.

[5] Wagner P., 1994, Fundamental Matrix of the System of Dynamic Linear Thermoelasticity, Journal of Thermal Stresses 17:549-565.

[6] Lee Z.Y., 2009, Magneto thermoelastic analysis of multilayered conical shells subjected to magnetic and vapor fields, International Journal of Thermal Sciences 48:50-72.

[7] Dai H.L., Fu Y.M., 2007, Magneto thermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads, International Journal of Pressure Vessels and Piping 84:132-138.

[8] Wang X., Dong K., 2006, Magneto thermodynamic stress and perturbation of magnetic field vector in a non-homogeneous thermoelastic cylinder, European Journal of Mechanics - A/Solids 25:98-109.

[9] Dai H.L., X. Wang, 2006, The dynamic response and perturbation of magnetic field vector of orthotropic cylinders under various shock loads, International Journal of Pressure Vessels and Piping 83:55-62.

[10] Misra S. C., Samanta S. C., Chakrabarti A. K., 1992, Transient magneto thermoelastic waves in a viscoelastic half-space produced by ramp-type heating of its surface, Computers & Structures 43:951-957.

[11] Massalas C. V., 1991, A note on magneto thermoelastic interactions, International Journal Engineering Science 29:1217-1229.

[12] Misra J. C., Samanta S. C., Chakrabarti A. K., Misra Subhas C., 1991, Magneto thermoelastic interaction in an infinite elastic continuum with a cylindrical hole subjected to ramp-type heating, International Journal Engineering Science 29: 1505-1514.

[13] Roy Choudhuri S. K., Chatterjee Roy G., 1990, Temperature-rate dependent magneto thermoelastic waves in a finitely conducting elastic half-space, Journal Computers & Mathematics with Applications 19:85-93.

[14] H. S., Narasimhan R., 1987, Magneto thermoelastic stress waves in a circular cylinder, International Journal of Engineering Science, 25: 413-425.

[15] Gargi Chatterjee(Roy), Roychoudhuri S. K., 1985, The coupled magneto thermoelastic problem in elastic half-space with two relaxation times, International Journal Engineering Science 23: 975-986.

[16] Maruszewsk B., 1981, Dynamical magneto thermoelastic problem in cicular cylinders-I: Basic equations, International Journal Engineering Science 19:1233-1240.

[17] Ezzat M. A., El-Karamany A. S., 2003, Magneto thermoelasticity with two relaxation times in conducting medium with variable electrical and thermal conductivity, Journal Applied Mathematics and Computation 142:449-467.

[18] Chen W.Q., Lee K.Y., 2003, Alternative state space formulations magnetoelectric thermoelasticity with transverse isotropy and the application to bending analysis of nonhomogeneous plates, Journal Solids & Structures 40: 5689-5705.

[19] Tianhu H., Yapeng S., Xiaogeng T., 2004, A two-dimensional generalized thermal shock problem for a half-space in electromagneto-thermoelasticit, International Journal Engineering. Science 42:809-823.

[20] Sharma J.N., Pal M., 2004, Rayleigh-Lamb waves in magneto thermoelastic homogeneous isotropic plate, International Journal Engineering Science 42:137-155.

[21] Abd-Alla A.M., Hammad H.A.H., Abo-Dahab S.M., 2004, Magneto-thermo-viscoelastic interactions in an unbounded body with a spherical cavity subjected to a periodic loading, Journal Applied Mathematics and Computation 155:235-248.

[22] Jabbari M., Dehbani H., Eslami MR., 2010, An Exact Solution for Classic Coupled Thermo elasticity in Spherical Coordinates, Journal of Pressure Vessel, ASME, Transaction 132: 031201-11.

[23] Jabbari M., Dehbani H., Eslami MR., 2011, An Exact Solution for Classic Coupled Thermo elasticity in Cylindrical Coordinates, Journal of Pressure Vessel, ASME, Transaction 133: 051204-10.

[24] Jabbari M., Dehbani H., 2009, An Exact Solution for Classic Coupled Thermoporoelasticity in Cylindrical Coordinates, Journal of Solid Mechanics 1: 343-357.

[25] Jabbari M., Dehbani H., 2010, An Exact Solution for Classic Coupled Thermoporoelasticity in Ax symmetric Cylinder, Journal of Solid Mechanics 2: 129-143.

[26] Jabbari M., Dehbani H., 2010, An Exact Solution for Lord-Shulman Generalized Coupled Thermo poroelasticity in Spherical Coordinates, Journal of Solid Mechanics 2: 214-230.

[27] Jabbari M., Dehbani H., 2011, An Exact Solution for Lord-Shulman Generalized Coupled Thermoporoelasticity in Cylindrical Coordinates, Published in 9th international congress on thermal, Budapest, Hungry.

[28] Jabbari M., Dehbani H., 2012, An Exact Solution for Quasi-Static Poro-Thermoelasticity in Spherical Coordinates, Iranian journal of mechanical engineering transactions of the ISME 12: 86-108.

[29] Necati Ozisik M., 1980, Heat conduction, Wiley & Sons.

[30] Hetnarski R. B., Eslami M. R., 2009, Thermal Stresses Advanced Theory and Applications, Springer, New York..

[31] Berezovski A., Engelbrecht J., Maugin G. A., 2003, Numerical Simulation of Two-Dimensional Wave Propagation in Functionally Graded Materials, Eur. J. Mech. A/Solids 22: 257–265.

[32] Berezovski A., Maugin G. A., 2003, Simulation of Wave and Front Propagation in Thermoelastic Materials With Phase Transformation, Comput. Mater. Sci 28: 478–485.

[33] Berezovski A., Maugin G. A., 2001, Simulation of Thermoelastic Wave Propagation by Means of a Composite Wave- Propagation Algorithm, J.Comput. Phys 168: 249–264.

[34] Engelbrecht J., Berezovski A., Saluperea A., 2007, Nonlinear Deformation Waves in Solids and Dispersion, Wave Motion 44: 493–500.

[35] Angel Y. C., Achenbach J. D., 1985, Reflection and Transmission of Elastic Waves by a Periodic Array of Cracks: Oblique Incidence, Wave Motion 7: 375–397.