How to cite this paper
Kumar, R & Devi, S. (2023). The effects of two temperature and laser pulse on modified couple stress thermoelastic diffusion beam.Engineering Solid Mechanics, 11(2), 217-230.
References
Abouelregal, A.E. & Zenkour, A.M. (2017). Two-temperature thermoelastic surface waves in micropolar thermoelastic media via dual-phase-lag model. Advances in Aircraft and Spacecraft Science, 4(6), 711-727. DOI: 10.12989/aas.2017.4.6.711.
Abouelregal, A.E., Zenkour, A.M. (2019). A generalized thermoelastic medium subjected to pulsed laser heating via a two-temperature model. Journal of Theoretical and Applied Mechanics, 57(3), 631-639. DOI: 10.15632/jtam-pl/109713.
Abouelregal, A.E. (2020). Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory. Applied Mathematics and Mechanics, 41(12), 1805–1820. DOI:10.1007/s10483-020-2676-5.
Akbas, S.D. (2017). Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory. International Journal of Structural Stability and Dynamics, 17(3), 1750033(1-23).
Alzahrani, F.S. & Abbas, I.A. (2016). Generalized thermoelastic diffusion in a nanoscale beam using eigenvalue approach. Acta Mechanica, 227(4), 955-968.
Cauchy, A.L. (1851). Note surl’equilibreet les mouvements vibratoires des corps solides, Comptes Rendus, 32, 323-326.
Chen, P.J. & Gurtin, M.E. (1968). On a theory of heat conduction involving two temperatures. Z. Angew. Math.Phys., 19(4), 614-627.
Chen, P.J., Gurtin, M.E. & Williams, W.O. (1968). A note on non-simple heat conduction. Zeitschrift f¨ur angewandte Mathematik und Physik (ZAMP). 19(6), 969-970.
Chen, P.J., Gurtin, M.E. & Williams, W.O. (1969). On the thermodynamics of non-simple elastic materials with two temperatures. Zeitschrift f¨ur angewandte Mathematik und Physik (ZAMP), 20(1), 107-112.
Cosserat, E. & Cosserat, F. (1909). Theory of deformable bodies. A. Herman Et. Fils, Paris.
Ebrahimi, F., & Barati, M. R. (2018). Free vibration analysis of couple stress rotating nanobeams with surface effect under in-plane axial magnetic field. Journal of Vibration and Control, 24(21), 5097-5107.
El-Bary, A.A., Youssef, H.M. & Nasr, M.A.E. (2022). Hyperbolic two-temperature generalized thermoelastic infinite medium with cylindrical cavity subjected to the non-Gaussian laser beam. Journal of Umm Al-Qura University for Engineering and Architecture . https://doi.org/10.1007/s43995-022-00004-y.
Green, A.E., & Rivlin, R.S. (1964). Simple force and stress multipoles. Archives for Rational Mechanics and Analysis, 16(5), 325-353.
Hamidi, B.A., Hosseini, S.A., Hassannejad, R. & Khosravi, F. (2019). An exact solution on gold microbeam with thermoelastic damping via generalized Green-Naghdi and modified couple stress theories. Journal of Thermal Stresses, 43(2), 157-174.
Honig, G. & Hirdes, U. (1984). A method for the numerical inversion of the Laplace transform. Journal of Computational and Applied Mathematics, 10(1), 113-132.
Koiter, W.T. (1964). Couple-stresses in the theory of elasticity I & II. Proceedings of the Koninklijke Nederlandse Academie van, Wetenschappen-Amsterdam, 67B, 17-44.
Kumar, R. & Devi, S. (2017a). Thermoelastic beam in modified couple stress thermoelasticity induced by laser pulse. Computers and Concrete, 19(6), 707-716.
Kumar, R. & Devi, S. (2017b). Eigenvalue approach to nanoscale beam in modified couple stress thermoelastic diffusion. Engineering Solid Mechanics, 271-284.
Kumar, R., Devi, S. & Abo-Dahab, S.M. (2018). Stoneley Waves at the Boundary Surface of Modified Couple Stress Generalized Thermoelastic with Mass Diffusion. Journal of Applied Science and Engineering, 21(1),1-8.
Kumar, R. & Devi, S. (2019a). Analysis of thick circular plate due to heat sources in modified couple stress thermoelastic diffusion. Computational Methods in Science and Technology, 25(4), 167–176.
Kumar, R., Devi, S. & Sharma, V. (2019b). Resonance of nanoscale beam due to various sources in modified couple stress thermoelastic diffusion with phase lags. Mechanics and Mechanical Engineering, 23, 36–49.
Kumar, R. & Devi, S. (2021). Abo-Dahab SM. Propagation of Rayleigh waves in modified couple stress generalized thermoelastic with three-phase-lag model. Waves in Random and Complex Media, 31(2), 359-371.
Kumar, R. & Kumar R. (2021). Effect of two-temperature parameter on thermoelastic vibration in micro and nano beam resonator. European Journal of Mechanics -A/Solids, 89, 104310, DOI:10.1016/j.euromechsol.2021.104310.
Kutbi, M.A. & Zenkour, A. M. (2022). Modified couple stress model for thermoelastic microbeams due to temperature pulse heating. Journal of Computational Applied Mechanics, 53(1), 83-101.
Mindlin, R.D. & Tiersten, H.F. (1962). Effects of couple stresses in linear elasticity. Archives for Rational Mechanics and Analysis, 11(1), 415-448.
Othman, M.I.A. & Marin, M. (2017). Effect of thermal loading due to laser pulse on thermoelastic porous media under G-N theory. Results in Physics, 7, 3863-3872.
Othman, M.I. & Said, S.M. (2018). Effect of diffusion and internal heat source on a two-temperature thermoelastic medium with three-phase-lag model. Archives of thermodynamics, 39(2), 15–39. DOI: 10.1515/aoter-2018-0010.
Othman, M.I.A. & Abd-Elaziz, E.M. (2019). Influence of gravity in the thermo- elastic porous medium and microtemperatures under three theories. International Journal of Numerical Methods for Heat and Fluid Flow, 29(9), 3242-3262.
Othman, M.I.A. & Mondal, S. (2020). Memory-dependent derivative effect on wave propagation of micropolar thermoelastic medium under pulsed laser heating with three theories. International Journal of Numerical Methods for Heat & Fluid Flow, 30(3), 1025-1046. DOI 10.1108/HFF-05-2019-0402.
Park, S.K. & Gao, X.L. (2006). Bernoulli-Euler beam model based on a modified couple stress theory. Journal of Micromechanics and Microengineering, 16(11), 2355–2359.
Rao, S.S. (2007). Vibration of continuous systems. John Wiley & Sons, Inc. Hoboken, New Jersey.
Reddy, J.N. & Arbind, A. (2012). Bending relationships between the modified couple stress-based functionally graded Timoshenko beams and homogeneous Bernoulli-Euler beams. Annals of Solid and Structural Mechanics, 3(1-2), 15-26.
Said, S.M. (2022). Fractional derivative heat transfer for rotating modified couple stress magneto-thermoelastic medium with two temperatures. Waves in Random and Complex Media, 22(3), 1517-1534.
Sherief, H.H., Hamza, F.A. & Saleh, H.A. (2004). The theory of generalized thermoelastic diffusion. International Journal of Engineering Science, 42(5), 591-608.
Tang, D.W. & Araki, N. (2000). Non-fourier heat conduction behavior in finite mediums under pulse surface heating. Materials Science and Engineering A, 292(2), 173-178.
Toupin, R.A. (1962). Elastic materials with couple-stresses. Archives for Rational Mechanics and Analysis, 11(1), 385-414.
Voigt, W. (1887). Theoretische Studienüber die Elasticitätsverhältnisse der Krystalle. Abh. Kgl. Ges. Wiss. Göttingen, Math. Kl., 34, 3-51.
Wang, Y.G., Lin, W.H. & Liu, N. (2015). Nonlinear bending and postbuckling of extensible microscale beams based on modified couple stress theory. Applied Mathematical Modelling, 39(1), 117-127.
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(10), 2731-2743.
Zenkour, M. (2018). Refined two-temperature multi-phase-lags theory for thermomechanical response of microbeams using the modified couple stress analysis. Acta Mechanica, 229, 3671-3692.
Zenkour, A.M. & Abouelregal, A.E. (2020). Two-temperature theory for a heated semi-infinite solid by a pulsed laser radiation. Archives of Thermodynamics, 41(2), 85–101.
Abouelregal, A.E., Zenkour, A.M. (2019). A generalized thermoelastic medium subjected to pulsed laser heating via a two-temperature model. Journal of Theoretical and Applied Mechanics, 57(3), 631-639. DOI: 10.15632/jtam-pl/109713.
Abouelregal, A.E. (2020). Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory. Applied Mathematics and Mechanics, 41(12), 1805–1820. DOI:10.1007/s10483-020-2676-5.
Akbas, S.D. (2017). Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory. International Journal of Structural Stability and Dynamics, 17(3), 1750033(1-23).
Alzahrani, F.S. & Abbas, I.A. (2016). Generalized thermoelastic diffusion in a nanoscale beam using eigenvalue approach. Acta Mechanica, 227(4), 955-968.
Cauchy, A.L. (1851). Note surl’equilibreet les mouvements vibratoires des corps solides, Comptes Rendus, 32, 323-326.
Chen, P.J. & Gurtin, M.E. (1968). On a theory of heat conduction involving two temperatures. Z. Angew. Math.Phys., 19(4), 614-627.
Chen, P.J., Gurtin, M.E. & Williams, W.O. (1968). A note on non-simple heat conduction. Zeitschrift f¨ur angewandte Mathematik und Physik (ZAMP). 19(6), 969-970.
Chen, P.J., Gurtin, M.E. & Williams, W.O. (1969). On the thermodynamics of non-simple elastic materials with two temperatures. Zeitschrift f¨ur angewandte Mathematik und Physik (ZAMP), 20(1), 107-112.
Cosserat, E. & Cosserat, F. (1909). Theory of deformable bodies. A. Herman Et. Fils, Paris.
Ebrahimi, F., & Barati, M. R. (2018). Free vibration analysis of couple stress rotating nanobeams with surface effect under in-plane axial magnetic field. Journal of Vibration and Control, 24(21), 5097-5107.
El-Bary, A.A., Youssef, H.M. & Nasr, M.A.E. (2022). Hyperbolic two-temperature generalized thermoelastic infinite medium with cylindrical cavity subjected to the non-Gaussian laser beam. Journal of Umm Al-Qura University for Engineering and Architecture . https://doi.org/10.1007/s43995-022-00004-y.
Green, A.E., & Rivlin, R.S. (1964). Simple force and stress multipoles. Archives for Rational Mechanics and Analysis, 16(5), 325-353.
Hamidi, B.A., Hosseini, S.A., Hassannejad, R. & Khosravi, F. (2019). An exact solution on gold microbeam with thermoelastic damping via generalized Green-Naghdi and modified couple stress theories. Journal of Thermal Stresses, 43(2), 157-174.
Honig, G. & Hirdes, U. (1984). A method for the numerical inversion of the Laplace transform. Journal of Computational and Applied Mathematics, 10(1), 113-132.
Koiter, W.T. (1964). Couple-stresses in the theory of elasticity I & II. Proceedings of the Koninklijke Nederlandse Academie van, Wetenschappen-Amsterdam, 67B, 17-44.
Kumar, R. & Devi, S. (2017a). Thermoelastic beam in modified couple stress thermoelasticity induced by laser pulse. Computers and Concrete, 19(6), 707-716.
Kumar, R. & Devi, S. (2017b). Eigenvalue approach to nanoscale beam in modified couple stress thermoelastic diffusion. Engineering Solid Mechanics, 271-284.
Kumar, R., Devi, S. & Abo-Dahab, S.M. (2018). Stoneley Waves at the Boundary Surface of Modified Couple Stress Generalized Thermoelastic with Mass Diffusion. Journal of Applied Science and Engineering, 21(1),1-8.
Kumar, R. & Devi, S. (2019a). Analysis of thick circular plate due to heat sources in modified couple stress thermoelastic diffusion. Computational Methods in Science and Technology, 25(4), 167–176.
Kumar, R., Devi, S. & Sharma, V. (2019b). Resonance of nanoscale beam due to various sources in modified couple stress thermoelastic diffusion with phase lags. Mechanics and Mechanical Engineering, 23, 36–49.
Kumar, R. & Devi, S. (2021). Abo-Dahab SM. Propagation of Rayleigh waves in modified couple stress generalized thermoelastic with three-phase-lag model. Waves in Random and Complex Media, 31(2), 359-371.
Kumar, R. & Kumar R. (2021). Effect of two-temperature parameter on thermoelastic vibration in micro and nano beam resonator. European Journal of Mechanics -A/Solids, 89, 104310, DOI:10.1016/j.euromechsol.2021.104310.
Kutbi, M.A. & Zenkour, A. M. (2022). Modified couple stress model for thermoelastic microbeams due to temperature pulse heating. Journal of Computational Applied Mechanics, 53(1), 83-101.
Mindlin, R.D. & Tiersten, H.F. (1962). Effects of couple stresses in linear elasticity. Archives for Rational Mechanics and Analysis, 11(1), 415-448.
Othman, M.I.A. & Marin, M. (2017). Effect of thermal loading due to laser pulse on thermoelastic porous media under G-N theory. Results in Physics, 7, 3863-3872.
Othman, M.I. & Said, S.M. (2018). Effect of diffusion and internal heat source on a two-temperature thermoelastic medium with three-phase-lag model. Archives of thermodynamics, 39(2), 15–39. DOI: 10.1515/aoter-2018-0010.
Othman, M.I.A. & Abd-Elaziz, E.M. (2019). Influence of gravity in the thermo- elastic porous medium and microtemperatures under three theories. International Journal of Numerical Methods for Heat and Fluid Flow, 29(9), 3242-3262.
Othman, M.I.A. & Mondal, S. (2020). Memory-dependent derivative effect on wave propagation of micropolar thermoelastic medium under pulsed laser heating with three theories. International Journal of Numerical Methods for Heat & Fluid Flow, 30(3), 1025-1046. DOI 10.1108/HFF-05-2019-0402.
Park, S.K. & Gao, X.L. (2006). Bernoulli-Euler beam model based on a modified couple stress theory. Journal of Micromechanics and Microengineering, 16(11), 2355–2359.
Rao, S.S. (2007). Vibration of continuous systems. John Wiley & Sons, Inc. Hoboken, New Jersey.
Reddy, J.N. & Arbind, A. (2012). Bending relationships between the modified couple stress-based functionally graded Timoshenko beams and homogeneous Bernoulli-Euler beams. Annals of Solid and Structural Mechanics, 3(1-2), 15-26.
Said, S.M. (2022). Fractional derivative heat transfer for rotating modified couple stress magneto-thermoelastic medium with two temperatures. Waves in Random and Complex Media, 22(3), 1517-1534.
Sherief, H.H., Hamza, F.A. & Saleh, H.A. (2004). The theory of generalized thermoelastic diffusion. International Journal of Engineering Science, 42(5), 591-608.
Tang, D.W. & Araki, N. (2000). Non-fourier heat conduction behavior in finite mediums under pulse surface heating. Materials Science and Engineering A, 292(2), 173-178.
Toupin, R.A. (1962). Elastic materials with couple-stresses. Archives for Rational Mechanics and Analysis, 11(1), 385-414.
Voigt, W. (1887). Theoretische Studienüber die Elasticitätsverhältnisse der Krystalle. Abh. Kgl. Ges. Wiss. Göttingen, Math. Kl., 34, 3-51.
Wang, Y.G., Lin, W.H. & Liu, N. (2015). Nonlinear bending and postbuckling of extensible microscale beams based on modified couple stress theory. Applied Mathematical Modelling, 39(1), 117-127.
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(10), 2731-2743.
Zenkour, M. (2018). Refined two-temperature multi-phase-lags theory for thermomechanical response of microbeams using the modified couple stress analysis. Acta Mechanica, 229, 3671-3692.
Zenkour, A.M. & Abouelregal, A.E. (2020). Two-temperature theory for a heated semi-infinite solid by a pulsed laser radiation. Archives of Thermodynamics, 41(2), 85–101.