Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-26T09:31:56.875Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of Phase-Lag on Thick Circular Plate with Heat Sources in Modified Couple Stress Thermoelastic Medium

Published online by Cambridge University Press:  12 May 2016

R. Kumar  and
S. Devi
R. Kumar*
Affiliation:
Department of MathematicsKurukshtra UniversityKurukshtra, India
S. Devi
Affiliation:
Department of Mathematics & StatisticsHimachal Pradesh UniversityShimla, India
*
*Corresponding author (rajneesh_kuk@rediffmail.com)
Get access

Abstract

The main objective of the present paper is to analyze the effects of phase-lag on thick circular plate with heat sources in modified couple stress thermoelastic medium. The mathematical formulation is prepared for three-phase-lag heat conduction model subjected to prescribed normal heat flux along with stress free boundary. Laplace and Hankel transforms are used to deal the problem. The displacements, stresses and temperature change are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. The results obtained numerically for these quantities are presented graphically. Some particular cases are also discussed in the present problem.

Keywords

Modified couple stress theoryThermoelasticityHeat sourcesLaplace and Hankel transforms
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 6 , December 2016 , pp. 665 - 671
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Voigt, W., “Theoretische Studien uber die Elasticitatsverhaltnisse der Krystalle,” Abh. Ges. Wiss. Göttingen, 34, (1887).Google Scholar
2. Cosserat, E. and Cosserat, F., “Theory of Deformable Bodies,” Hermann et Fils, Paris (1909).Google Scholar
3. Yang, F., Chong, A. C. M., Lam, D. C. C. and Tong, P., “Couple Stress Based Strain Gradient Theory for Elasticity,” International Journal of Solids and Structures, 39, pp. 2731–2743 (2002).CrossRefGoogle Scholar
4. Ma, H. M., Gao, X. L. and Reddy, J. N., “A Microstructure-Dependent Timoshenko Beam Model Based on a Modified Couple Stress Theory,” Journal of the Mechanics and Physics of Solids, 56, pp. 3379–3391 (2008).CrossRefGoogle Scholar
5. Chen, W., Li, L. and Xu, M., “A Modified Couple Stress Model for Bending Analysis of Composite Laminated Beams with First Order Shear Deformation,” Composite Structures, 93, pp. 2723–2732 (2011).CrossRefGoogle Scholar
6. Simsek, M. and Reddy, J. N., “Bending and Vibration of Functionally Graded Microbeams Using a New Higher Order Beam Theory and the Modified Couple Stress Theory,” International Journal of Engineering Science, 64, pp. 37–53 (2013).CrossRefGoogle Scholar
7. Yaghoub, T. B., Fahimeh, M. and Hamed, R., “Free Vibration Analysis of Size-Dependent Shear Deformable Functionally Graded Cylindrical Shell on the Basis of Modified Couple Stress Theory,” Composite Structures, 120, pp. 65–78 (2015).Google Scholar
8. Darijani, H. and Shahdadi, A. H., “A New Shear Deformation Model with Modified Couple Stress Theory for Microplates,” Acta Mechanica, 226, pp. 2773–2788 (2015).CrossRefGoogle Scholar
9. Roychoudhuri, S. K., “On a Thermoelastic Three-Phase-Lag Model,” Journal of Thermal Stresses, 30, pp. 231–238 (2007).Google Scholar
10. Quintanilla, R. and Racke, R. A., “Note on Stability in Three-Phase-Lag Heat Conduction,” International Journal of Heat Mass Transfer, 51, pp. 24–29 (2008).CrossRefGoogle Scholar
11. Kumar, R., Chawla, V. and Abbas, I. A., “Effect of Viscosity on Wave Propagation in Anisotropic Thermoelastic Medium with Three-Phase-Lag Model,” Theoretical and Applied Mechanics, 39, pp. 313–341 (2012).CrossRefGoogle Scholar
12. Kumar, R., Kaur, M. and Rajvanshi, S. C., “Reflection and Transmission Between Two Micropolar Thermoelastic Half-Spaces with Three-Phase-Lag Model,” Journal of Engineering Physics and Thermophysics, 87, pp. 290–302 (2014).CrossRefGoogle Scholar
13. Kumar, R. and Gupta, V., “Plane Wave Propagation in an Anisotropic Dual-Phase-Lag Thermoelastic Diffusion Medium,” Multidiscipline Modeling in Materials and Structures, 10, pp. 562–592 (2014).CrossRefGoogle Scholar
14. Kumar, R. and Gupta, V., “Dual-Phase-Lag Model of Wave Propagation at the Interface Between Elastic and Thermoelastic Diffusion Media,” Journal of Engineering Physics and Thermophysics, 88, pp. 247–259 (2015).Google Scholar
15. Tripathi, J. J., Kedar, G. D. and Deshmukh, K. C., “Dynamic Problem of Generalized Thermoelasicity for a Semi Infinite Cylinder with Heat Sources,” Journal of Thermoelasticity, 2, pp. 1–8 (2014).Google Scholar
16. Tripathi, J. J., Kedar, G. D. and Deshmukh, K. C., “Generalized Thermoelastic Diffusion Problem in a Thick Circular Plate with Axisymmetric Heat Supply,” Acta Mechanica, DOI: 10.1007/s00707-015-1305-7 (2015).CrossRefGoogle Scholar
17. Kumar, R. and Deswal, S., “Axi-Symmetric Problem in a Micropolar Generalized Thermoelastic Half-Space,” International Journal of Applied Mechanics and Engineering, 12, pp. 413–429 (2007).Google Scholar
18. Sherief, H. H. and Saleh, H., “A Half-Space Problem in the Theory of Generalized Thermoelastic Diffusion,” International Journal of Solids and Structures, 42, pp. 4484–4493 (2005).CrossRefGoogle Scholar