How to cite this paper
Kumar, R & Devi, S. (2017). Eigenvalue approach to nanoscale beam in modified couple stress thermo-elastic diffusion.Engineering Solid Mechanics, 5(4), 271-284.
Refrences
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.
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.
Alzahrani, F. S., & Abbas, I. A. (2016). Generalized thermoelastic diffusion in a nanoscale beam using eigenvalue approach. Acta Mechanica, 227(4), 955-968.
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.
Choudhary, S., & Deswal, S. (2010). Mechanical loads on a generalized thermoelastic medium with diffusion. Meccanica, 45(3), 401-413.
Cosserat, E. & Cosserat, F. (1909). Theory of Deformable Bodies, Hermann et Fils, Paris.
Das, N. C., Lahiri, A., & Giri, R. R. (1997). Eigenvalue approach to generalized thermoelasticity. Indian Journal of Pure and Applied Mathematics, 28, 1573-1594.
Green, A. E., & Naghdi, P. M. (1993). Thermoelasticity without energy dissipation. Journal of Elasticity, 31(3), 189-208.
Honig, G., & Hirdes, U. (1984). A method for the numerical inversion of Laplace transforms. Journal of Computational and Applied Mathematics, 10(1), 113-132.
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.
Kumar, R., & Kansal, T. (2008). Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate. International Journal of Solids and Structures, 45(22), 5890-5913.
Kumar, R., Singh, R. & Chadha, T. K. (2007). Eigenvalue approach to Micropolar thermoelasticity without energy dissipation. Indian Journal of Mathematics, 49(3), 355-369.
Mindlin, R. D., & Tiersten, H. F. (1962). Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and Analysis, 11(1), 415-448.
Nowacki, W. (1974). Dynamical Problems of Thermo diffusion in Solids I. Bulletin of Polish Academy of Science and Technology, 22, 55-64.
Rao, S. S. (2007). Vibration of continuous systems. John Wiley & Sons.
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.
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.
Samaei, A. T., Aliha, M. R. M., & Mirsayar, M. M. (2015). Frequency analysis of a graphene sheet embedded in an elastic medium with consideration of small scale. Materials Physics and Mechanics, 22(2), 125-135.
Sarkar, N., & Lahiri, A. (2012). Eigenvalue approach to two-temperature magneto-thermoelasticity. Vietnam Journal of Mathematics, 40(1), 13-30.
Sengupta, P. R. & Ghosh, B. (1974a). Effect of couple stresses on surface waves in elastic media. Gerlands Beitr. Geophysik, Leipzig, 83, 309-318.
Sengupta, P. R., & Ghosh, B. (1974b). Effect of couple-stresses on the propagation of waves in an elastic layer. Pure and Applied Geophysics, 112(2), 331-338.
Shaat, M., Mahmoud, F. F., Gao, X. L., & Faheem, A. F. (2014). Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects. International Journal of Mechanical Sciences, 79, 31-37.
Sherief, H. H., & Saleh, H. A. (2005). A half-space problem in the theory of generalized thermoelastic diffusion. International Journal of Solids and Structures, 42(15), 4484-4493.
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.
Şimşek, 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.
Toupin, R. A. (1962). Elastic materials with couple-stresses. Archive for Rational Mechanics and Analysis, 11(1), 385-414.
Voigt, W. (1887). Theoretische Studien uber die Elasticitatsverhaltnisse der Krystalle Abh. Ges. Wiss. p, 34.
Wang, Y. G., Lin, W. H., & Liu, N. (2015). Nonlinear bending and post-buckling of extensible microscale beams based on modified couple stress theory. Applied Mathematical Modelling, 39(1), 117-127.
Yang, F. A. C. M., 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, 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.
Zhang, J., & Fu, Y. (2012). Pull-in analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory. Meccanica, 47(7), 1649-1658.
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.
Alzahrani, F. S., & Abbas, I. A. (2016). Generalized thermoelastic diffusion in a nanoscale beam using eigenvalue approach. Acta Mechanica, 227(4), 955-968.
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.
Choudhary, S., & Deswal, S. (2010). Mechanical loads on a generalized thermoelastic medium with diffusion. Meccanica, 45(3), 401-413.
Cosserat, E. & Cosserat, F. (1909). Theory of Deformable Bodies, Hermann et Fils, Paris.
Das, N. C., Lahiri, A., & Giri, R. R. (1997). Eigenvalue approach to generalized thermoelasticity. Indian Journal of Pure and Applied Mathematics, 28, 1573-1594.
Green, A. E., & Naghdi, P. M. (1993). Thermoelasticity without energy dissipation. Journal of Elasticity, 31(3), 189-208.
Honig, G., & Hirdes, U. (1984). A method for the numerical inversion of Laplace transforms. Journal of Computational and Applied Mathematics, 10(1), 113-132.
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.
Kumar, R., & Kansal, T. (2008). Propagation of Lamb waves in transversely isotropic thermoelastic diffusive plate. International Journal of Solids and Structures, 45(22), 5890-5913.
Kumar, R., Singh, R. & Chadha, T. K. (2007). Eigenvalue approach to Micropolar thermoelasticity without energy dissipation. Indian Journal of Mathematics, 49(3), 355-369.
Mindlin, R. D., & Tiersten, H. F. (1962). Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and Analysis, 11(1), 415-448.
Nowacki, W. (1974). Dynamical Problems of Thermo diffusion in Solids I. Bulletin of Polish Academy of Science and Technology, 22, 55-64.
Rao, S. S. (2007). Vibration of continuous systems. John Wiley & Sons.
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.
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.
Samaei, A. T., Aliha, M. R. M., & Mirsayar, M. M. (2015). Frequency analysis of a graphene sheet embedded in an elastic medium with consideration of small scale. Materials Physics and Mechanics, 22(2), 125-135.
Sarkar, N., & Lahiri, A. (2012). Eigenvalue approach to two-temperature magneto-thermoelasticity. Vietnam Journal of Mathematics, 40(1), 13-30.
Sengupta, P. R. & Ghosh, B. (1974a). Effect of couple stresses on surface waves in elastic media. Gerlands Beitr. Geophysik, Leipzig, 83, 309-318.
Sengupta, P. R., & Ghosh, B. (1974b). Effect of couple-stresses on the propagation of waves in an elastic layer. Pure and Applied Geophysics, 112(2), 331-338.
Shaat, M., Mahmoud, F. F., Gao, X. L., & Faheem, A. F. (2014). Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects. International Journal of Mechanical Sciences, 79, 31-37.
Sherief, H. H., & Saleh, H. A. (2005). A half-space problem in the theory of generalized thermoelastic diffusion. International Journal of Solids and Structures, 42(15), 4484-4493.
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.
Şimşek, 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.
Toupin, R. A. (1962). Elastic materials with couple-stresses. Archive for Rational Mechanics and Analysis, 11(1), 385-414.
Voigt, W. (1887). Theoretische Studien uber die Elasticitatsverhaltnisse der Krystalle Abh. Ges. Wiss. p, 34.
Wang, Y. G., Lin, W. H., & Liu, N. (2015). Nonlinear bending and post-buckling of extensible microscale beams based on modified couple stress theory. Applied Mathematical Modelling, 39(1), 117-127.
Yang, F. A. C. M., 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, 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.
Zhang, J., & Fu, Y. (2012). Pull-in analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory. Meccanica, 47(7), 1649-1658.