Eigenvalue approach to nanobeam in modified couple stress thermoelastic with three-phase-lag model induced by ramp type heating

• Autorzy: Kumar R. , Devi S.

Identyfikatory

DOI

10.15632/jtam-pl.55.3.1067

• Języki publikacji: EN

Abstrakty

EN

This article deals with the study of a thermoelastic nanobeam in a modified couple stress theory subjected to ramp-type heating. The mathematical model is prepared for the nanobeam in thermoelastic three-phase-lag. The Laplace transform and the eigenvalue approach are used to find the displacement component, lateral deflection, temperature change and axial stress of the thermoelastic beam. The general algorithm of the inverse Laplace transform is developed to compute results numerically. The comparison of three-phase-lag, dual-phaselag and GN-III (1993) models are represented, and their illustration is depicted graphically. This study finds the applications in engineering, medical science, sensors, etc.

Słowa kluczowe

EN

modified couple stress thermoelastic; eigenvalue approach; nanobeam

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2017
• Tom: Vol. 55 nr 3
• Strony: 1067--1079
• Opis fizyczny: Bibliogr. 31 poz., rys.

Twórcy

autor

Kumar R.

• Kurukshetra University, Department of Mathematics, Kurukshetra, India

autor

Devi S.

• Himachal Pradesh University, Department of Mathematics and Statistics, Shimla, India

Bibliografia

• 1. Abbas I.A., Kumar R., Rani L., 2015, Thermoelastic interaction in a thermally conducting cubic crystal subjected to ramp-type heating, Applied Mathematics and Computation, 254, 360-369
• 2. Abouelregal A.E., Zenkour A.M., 2014, Effect of phase lags on thermoelastic functionally graded microbeams subjected to ramp-type heating, Iranian Journal of Science and Technology: Transactions of Mechanical Engineering, 38, M2, 321-335
• 3. Asghari M., 2012, Geometrically nonlinear micro-plate formulation based on the modified couple stress theory, International Journal of Engineering Science, 51, 292-309
• 4. Cosserat E., Cosserat F., 1909, Theory of Deformable Bodies, Hermann et Fils, Paris
• 5. Chen W., Li L., Xu M., 2011, A modified couple stress model for bending analysis of composite laminated beams with first order shear deformation, Composite Structures, 93, 2723-2732
• 6. Chen W., Wang Y., 2016, A model of composite laminated Reddy plate of the global-local theory based on new modified couple-stress theory, Mechanics of Advanced Materials and Structures, 23, 6, 636-651
• 7. Darijani H., Shahdadi A.H., 2015, A new shear deformation model with modified couple stress theory for microplates, Acta Mechanica, 226, 2773-2788
• 8. Green A.E., Naghdi P.M., 1993, Thermoelasticity without energy dissipation, Journal of Elasticity, 31, 189-209
• 9. Hetnarski R.B., Ignaczak J., 1999, Generalized themoelasticity, Journal of Thermal Stresses, 22, 451-476
• 10. Kumar R., 2016, Response of thermoelastic beam due to thermal source in modified couple stress theory, Computational Methods in Science and Technology, 22, 2, 87-93
• 11. Kumar R., Chawla V., Abbas I.A., 2012, Effect of viscosity on wave propagation in anisotropic thermoelastic medium with three-phase-lag model, Theoretical and Applied Mechanics, 39, 4, 313-341
• 12. Kumar R., Devi S., 2015, Interaction due to Hall current and rotation in a modified couple stress elastic half-space due to ramp-type loading, Computational Methods in Science and Technology, 21, 4, 229-240, DOI:10.12921/cmst.2015.21.04.007.
• 13. Kumar R., Singh R., Chadha T.K., 2007, Eigenvalue approach to micropolar thermoelasticity without energy dissipation, Indian Journal of Mathematics, 49, 3, 355-369
• 14. Ma H.M., Gao X.L., Reddy J.N., 2008, A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids, 56, 3379-3391
• 15. Mohammad-Abadi M., Daneshmehr A.R., 2014, Size dependent buckling analysis of micro beams based on modified couple stress theory with high order theories and general boundary conditions, International Journal of Engineering Science, 74, 1-14
• 16. Quintanilla R., Racke R.A., 2008, Note on stability in three-phase-lag heat conduction, International Journal of Heat Mass Transfer, 51, 1/2, 24-29
• 17. Rao S.S., 2007, Vibration of Continuous Systems, John Wiley & Sons, Inc. Hoboken, New Jersey
• 18. Reddy J.N., Romanoff J., Loya J.A., 2016, Nonlinear finite element analysis of functionally graded circular plates with modified couple stress theory, European Journal of Mechanics – A/Solids, 56, 92-104
• 19. Rezazadeh G., Vahdat A.S., Tayefeh-Rezaei S., Cetinkaya C., 2012, Thermoelastic damping in a micro-beam resonator using modified couple stress theory, Acta Mechanica, 223, 6, 1137-1152
• 20. Roychoudhuri S.K., 2007, On a thermoelastic three-phase-lag model, Journal of Thermal Stresses, 30, 231-238
• 21. Simsek M., Reddy J.N., 2013, 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, 37-53
• 22. Sur A., Kanoria M., 2014, Vibration of a gold-nanobeam induced by ramp type laser pulse three-phase-lag model, International Journal of Applied Mathematics and Mechanics, 10, 5, 86-104
• 23. Tzou D.Y., 1995a, A unified field approach for heat conduction from micro to macroscales, ASME Journal of Heat Transfer, 117, 8-16
• 24. Tzou D.Y., 1995b, Experiments support for the lagging behaviour in heat propagation, Journal of Thermophysics and Heat Transfer, 9, 686-693
• 25. Tzou D.Y., 1997, Macro to Microscale Heat Transfer: the Lagging Behaviour, Series in Chemical ad Mechanical Engineering, Taylor & Francis, Washington, DC
• 26. Yaghoub T.B., Fahimeh M., Hamed R., 2015, Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory, Composite Structures, 120, 65-78
• 27. Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39, 2731-2743
• 28. Yong-Gang W., Wen-Hui L., Liu N., 2015, Nonlinear bending and post-buckling of extensible microscale beams based on modified couple stress theory, Applied Mathematical Modelling, 39, 117-127
• 29. Zang J., Fu Y., 2012, Pull-in analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory, Meccanica, 47, 1649-1658
• 30. Zenkour A.M., Abouelregal A.E., 2015, Effects of phase-lags in a thermoviscoelastic orthotropic continuum with a cylindrical hole and variable thermal conductivity, Archives of Mechanics, 67, 6, 457-475
• 31. Zenkour A.M., Abouelregal A.E., 2016, Effect of ramp-type heating on the vibration of functionally graded microbeams without energy dissipation, Mechanics of Advanced Materials and Structures, 23, 5, 529-537