How to cite this paper
Mondal, S., Sur, A & Kanoria, M. (2017). Modeling and analysis of vibration of a gold nano-beam under two-temperature theory.Engineering Solid Mechanics, 5(1), 15-30.
Refrences
Ackerman, C. C., Bertman, B., Fairbank, H. A., & Guyer, R. A. (1966). Second sound in solid helium. Physical Review Letters, 16(18), 789.
Ackerman, C. C., & Guyer, R. A. (1968). Temperature pulses in dielectric solids. Annals of Physics, 50(1), 128-185.
Bagri, A., & Eslami, M. R. (2004). Generalized coupled thermoelasticity of disks based on the Lord–Shulman model. Journal of Thermal Stresses, 27(8), 691-704.
Al-Huniti, N. S., Al-Nimr, M. A., & Naji, M. (2001). Dynamic response of a rod due to a moving heat source under the hyperbolic heat conduction model. Journal of Sound and Vibration, 242(4), 629-640.
Bagri, A., & Eslami, M. R. (2007). A unified generalized thermoelasticity formulation; application to thick functionally graded cylinders. Journal of Thermal Stresses, 30(9-10), 911-930.
Bagri, A., & Eslami, M. R. (2007). Analysis of thermoelastic waves in functionally graded hollow spheres based on the Green-Lindsay theory. Journal of Thermal Stresses, 30(12), 1175-1193.
Banik, S., & Kanoria, M. (2011). Two-temperature generalized thermoelastic interactions in an infinite body with a spherical cavity. International Journal of Thermophysics, 32(6), 1247-1270.
Banik, S., & Kanoria, M. (2012). Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical cavity. Applied Mathematics and Mechanics, 33(4), 483-498.
Boley, B. A. (1972). Approximate analyses of thermally induced vibrations of beams and plates. Journal of Applied Mechanics, 39(1), 212-216.
Chandrasekharaiah, D. S. (1996). Thermoelastic plane waves without energy dissipation. Mechanics research communications, 23(5), 549-555.
Chandrasekharaiah, D. S. (1996). A note on the uniqueness of solution in the linear theory of thermoelasticity without energy dissipation. Journal of Elasticity, 43(3), 279-283.
Chen, P. J., & Gurtin, M. E. (1968). On a theory of heat conduction involving two temperatures. Zeitschrift für angewandte Mathematik und Physik (ZAMP), 19(4), 614-627.
Chen, P. J., & Williams, W. O. (1968). A note on non-simple heat conduction. Zeitschrift für 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 für angewandte Mathematik und Physik ZAMP, 20(1), 107-112.
Das, N. C., & Lahiri, A. (2000). Thermo-elastic interactions due to prescribed pressure inside a spherical cavity in an unbounded medium. International Journal of Pure and Applied Mathematics, 31, 19-32.
Dhaliwal, R. S., & SHERIEF, H. H. (1980). Generalized thermoelasticity for anisotropic media. Quarterly of Applied Mathematics, 38(1), 1-8.
Diao, J., Gall, K., & Dunn, M. L. (2004). Atomistic simulation of the structure and elastic properties of gold nanowires. Journal of the Mechanics and Physics of Solids, 52(9), 1935-1962.
El-Karamany, A. S., & Ezzat, M. A. (2011). On the two-temperature Green–Naghdi thermoelasticity theories. Journal of Thermal Stresses, 34(12), 1207-1226.
Elsibai*, K. A., & Youssef†, H. M. (2011). State-space approach to vibration of gold nano-beam induced by ramp type heating without energy dissipation in femtoseconds scale. Journal of Thermal Stresses, 34(3), 244-263.
Ghosh, M. K., & Kanoria, M. (2008). Generalized thermoelastic problem of a spherically isotropic infinite elastic medium containing a spherical cavity. Journal of Thermal Stresses, 31(8), 665-679.
Ghosh, M. K., & Kanoria, M. (2009). Analysis of thermoelastic response in a functionally graded spherically isotropic hollow sphere based on Green–Lindsay theory. Acta mechanica, 207(1-2), 51-67.
Kanoria, M., & Ghosh, M. K. (2010). Study of dynamic response in a functionally graded spherically isotropic hollow sphere with temperature dependent elastic parameters. Journal of Thermal Stresses, 33(5), 459-484.
Green A. E., & Lindsay, K. A. (1972). Thermoelasticity, Journal of Elasticity, 2, 1-7.
Green, A. E., & Naghdi, P. M. (1991, February). A re-examination of the basic postulates of thermomechanics. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (Vol. 432, No. 1885, pp. 171-194). The Royal Society.
Green, A. E., & Naghdi, P. M., (1992). An unbounded heat wave in an elastic solid, Journal of Thermal Stresses, 15, 253-264.
Green, A. E., & Naghdi, P. M. (1993). Thermoelasticity without energy dissipation. Journal of elasticity, 31(3), 189-208.
Gurtin, M. E., & Williams, W. O. (1966). On the clausius-duhem inequality, Z. angew. Math. Phys., 7, 626-633.
Gurtin, M. E., & Williams, W. O. (1967). An axiomatic foundation for continuum thermodynamics, Archive for Rational Mechanics and Analysis, 26, 83-117.
Honig, G., & Hirdes, U. (1984). A method for the numerical inversion of Laplace transforms. Journal of Computational and Applied Mathematics, 10(1), 113-132.
Ignaczak, J. (1979). Uniqueness in generalized thermoelasticity. Journal of Thermal Stresses, 2(2), 171-175.
Ignaczak, J. (1982). A note on uniqueness in thermoelasticity with one relaxation time. Journal of Thermal Stresses, 5(3-4), 257-263.
Ignaczak, J., & Ostoja-Starzewski, M. (2010). Thermoelasticity with finite wave speeds. Oxford University Press.
Islam, M., Kar, A., & Kanoria, M. (2013). Two-temperature generalized thermoelasticity in a fiber-reinforced hollow cylinder under thermal shock. International Journal for Computational Methods in Engineering Science and Mechanics, 14(5), 367-390.
Islam, M., Mallik, S. H., & Kanoria, M. (2011). Dynamic response in two-dimensional transversely isotropic thick plate with spatially varying heat sources and body forces. Applied Mathematics and Mechanics, 32(10), 1315-1332.
Kar, A., & Kanoria, M. (2007a). Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc. European Journal of Mechanics A/Solids, 26, 969-981.
Kar, A., & Kanoria, M. (2007b). Thermoelastic interaction with energy dissipation in an unbounded body with a spherical hole. International Journal of Solids and Structures, 44, 2961-2971.
Kar, A., & Kanoria, M. (2009). Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect. Applied Mathematical Modeling, 33, 3287-3298.
Kar, A., & Kanoria, M. (2009). Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect. European Journal of Mechanics A/Solids, 28, 757-767.
Kidawa-Kukla, J. (2003). Application of the Green functions to the problem of the thermally induced vibration of a beam. Journal of Sound and Vibration, 262, 865-876.
Kumar, R., Prasad, R., & Mukhopadhyay, S. (2010). Variational and reciprocal principles in two-temperature generalized thermoelasticity. Journal of Thermal Stresses, 33(3), 161-171.
Kumar, R., Prasad, R., & Mukhopadhyay, S. (2011). Some theorems on two-temperature generalized thermoelasticity. Archive of Applied Mechanics, 81(8), 1031-1040.
Chen, P. J., Gurtin, M. E., & Williams, W. O. (1969). On the thermodynamics of non-simple elastic materials with two temperatures. Zeitschrift für angewandte Mathematik und Physik ZAMP, 20(1), 107-112.
Lord, H. W., & Shulman, Y. (1967). A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15(5), 299-309.
Manolis, G. D., & Beskos, D. E. (1980). Thermally induced vibrations of beam structures. Computer Methods in Applied Mechanics and Engineering, 21(3), 337-355.
Puri, P., & Jordan, P. M. (2006). On the propagation of harmonic plane waves under the two-temperature theory. International Journal of Engineering Science, 44(17), 1113-1126.
Quintanilla, R. (2004a). Exponential stability and uniqueness in thermoelasticity with two temperature. Dynamics of Continuous Discrete and Impulsive Systems A, 11, 57-68.
Quintanilla, R. (2004). On existence, structural stability, convergence and spatial behavior in thermoelasticity with two temperatures. Acta Mechanica, 168(1-2), 61-73.
Quintanilla, R. (2008). A well-posed problem for the dual-phase-lag heat conduction. Journal of Thermal Stresses, 31(3), 260-269.
Quintanilla, R. (2009). A well-posed problem for the three-dual-phase-lag heat conduction. Journal of Thermal Stresses, 32(12), 1270-1278.
Choudhuri, S. R. (2007). On a thermoelastic three-phase-lag model. Journal of Thermal Stresses, 30(3), 231-238.
Sur, A., & Kanoria, M. (2014). Thermoelastic interaction in a viscoelastic functionally graded half-space under three-phase-lag model. European Journal of Computational Mechanics, 23(5-6), 179-198.
Soh, A. K., Sun, Y., & Fang, D. (2008). Vibration of microscale beam induced by laser pulse. Journal of sound and vibration, 311(1), 243-253.
Sun, Y., Fang, D., Saka, M., & Soh, A. K. (2008). Laser-induced vibrations of micro-beams under different boundary conditions. International Journal of Solids and Structures, 45(7), 1993-2013.
Sur, A., & Kanoria, M. (2014b). Vibration of a gold nano beam induced by ramp-type laser pulse under three-phase-lag model. International Journal of Applied Mathematics and Mechanics, 10(5), 86-104.
Sur, A., & Kanoria, M. (2014). Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell. Latin American Journal of Solids and Structures, 11(7), 1132-1162.
Sur, A., & Kanoria, M. (2014). Fractional order generalized thermoelastic functionally graded solid with variable material properties. Journal of Solid Mechanics, 6(1), 54-69.
Sur, A., & Kanoria, M. (2012). Fractional order two-temperature thermoelasticity with finite wave speed. Acta Mechanica, 223(12), 2685-2701.
Sur, A., & Kanoria, M. (2014). Finite thermal wave propagation in a half-space due to variable thermal loading. Applications and Applied Mathematics, 9(1), 94-120.
Warren, W. E., & Chen, P. J. (1973). Wave propagation in the two temperature theory of thermoelasticity. Acta Mechanica, 16(1-2), 21-33.
Youssef, H. M., & Al-Lehaibi, E. A. (2007). State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem. International journal of solids and structures, 44(5), 1550-1562.
Youssef, H. M. (2006). Theory of two-temperature-generalized thermoelasticity. IMA Journal of Applied Mathematics, 71(3), 383-390.
Youssef, H. M. (2008). Two-dimensional problem of a two-temperature generalized thermoelastic half-space subjected to ramp-type heating. Computational Mathematics and Modeling, 19(2), 201-216.
Ackerman, C. C., & Guyer, R. A. (1968). Temperature pulses in dielectric solids. Annals of Physics, 50(1), 128-185.
Bagri, A., & Eslami, M. R. (2004). Generalized coupled thermoelasticity of disks based on the Lord–Shulman model. Journal of Thermal Stresses, 27(8), 691-704.
Al-Huniti, N. S., Al-Nimr, M. A., & Naji, M. (2001). Dynamic response of a rod due to a moving heat source under the hyperbolic heat conduction model. Journal of Sound and Vibration, 242(4), 629-640.
Bagri, A., & Eslami, M. R. (2007). A unified generalized thermoelasticity formulation; application to thick functionally graded cylinders. Journal of Thermal Stresses, 30(9-10), 911-930.
Bagri, A., & Eslami, M. R. (2007). Analysis of thermoelastic waves in functionally graded hollow spheres based on the Green-Lindsay theory. Journal of Thermal Stresses, 30(12), 1175-1193.
Banik, S., & Kanoria, M. (2011). Two-temperature generalized thermoelastic interactions in an infinite body with a spherical cavity. International Journal of Thermophysics, 32(6), 1247-1270.
Banik, S., & Kanoria, M. (2012). Effects of three-phase-lag on two-temperature generalized thermoelasticity for infinite medium with spherical cavity. Applied Mathematics and Mechanics, 33(4), 483-498.
Boley, B. A. (1972). Approximate analyses of thermally induced vibrations of beams and plates. Journal of Applied Mechanics, 39(1), 212-216.
Chandrasekharaiah, D. S. (1996). Thermoelastic plane waves without energy dissipation. Mechanics research communications, 23(5), 549-555.
Chandrasekharaiah, D. S. (1996). A note on the uniqueness of solution in the linear theory of thermoelasticity without energy dissipation. Journal of Elasticity, 43(3), 279-283.
Chen, P. J., & Gurtin, M. E. (1968). On a theory of heat conduction involving two temperatures. Zeitschrift für angewandte Mathematik und Physik (ZAMP), 19(4), 614-627.
Chen, P. J., & Williams, W. O. (1968). A note on non-simple heat conduction. Zeitschrift für 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 für angewandte Mathematik und Physik ZAMP, 20(1), 107-112.
Das, N. C., & Lahiri, A. (2000). Thermo-elastic interactions due to prescribed pressure inside a spherical cavity in an unbounded medium. International Journal of Pure and Applied Mathematics, 31, 19-32.
Dhaliwal, R. S., & SHERIEF, H. H. (1980). Generalized thermoelasticity for anisotropic media. Quarterly of Applied Mathematics, 38(1), 1-8.
Diao, J., Gall, K., & Dunn, M. L. (2004). Atomistic simulation of the structure and elastic properties of gold nanowires. Journal of the Mechanics and Physics of Solids, 52(9), 1935-1962.
El-Karamany, A. S., & Ezzat, M. A. (2011). On the two-temperature Green–Naghdi thermoelasticity theories. Journal of Thermal Stresses, 34(12), 1207-1226.
Elsibai*, K. A., & Youssef†, H. M. (2011). State-space approach to vibration of gold nano-beam induced by ramp type heating without energy dissipation in femtoseconds scale. Journal of Thermal Stresses, 34(3), 244-263.
Ghosh, M. K., & Kanoria, M. (2008). Generalized thermoelastic problem of a spherically isotropic infinite elastic medium containing a spherical cavity. Journal of Thermal Stresses, 31(8), 665-679.
Ghosh, M. K., & Kanoria, M. (2009). Analysis of thermoelastic response in a functionally graded spherically isotropic hollow sphere based on Green–Lindsay theory. Acta mechanica, 207(1-2), 51-67.
Kanoria, M., & Ghosh, M. K. (2010). Study of dynamic response in a functionally graded spherically isotropic hollow sphere with temperature dependent elastic parameters. Journal of Thermal Stresses, 33(5), 459-484.
Green A. E., & Lindsay, K. A. (1972). Thermoelasticity, Journal of Elasticity, 2, 1-7.
Green, A. E., & Naghdi, P. M. (1991, February). A re-examination of the basic postulates of thermomechanics. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (Vol. 432, No. 1885, pp. 171-194). The Royal Society.
Green, A. E., & Naghdi, P. M., (1992). An unbounded heat wave in an elastic solid, Journal of Thermal Stresses, 15, 253-264.
Green, A. E., & Naghdi, P. M. (1993). Thermoelasticity without energy dissipation. Journal of elasticity, 31(3), 189-208.
Gurtin, M. E., & Williams, W. O. (1966). On the clausius-duhem inequality, Z. angew. Math. Phys., 7, 626-633.
Gurtin, M. E., & Williams, W. O. (1967). An axiomatic foundation for continuum thermodynamics, Archive for Rational Mechanics and Analysis, 26, 83-117.
Honig, G., & Hirdes, U. (1984). A method for the numerical inversion of Laplace transforms. Journal of Computational and Applied Mathematics, 10(1), 113-132.
Ignaczak, J. (1979). Uniqueness in generalized thermoelasticity. Journal of Thermal Stresses, 2(2), 171-175.
Ignaczak, J. (1982). A note on uniqueness in thermoelasticity with one relaxation time. Journal of Thermal Stresses, 5(3-4), 257-263.
Ignaczak, J., & Ostoja-Starzewski, M. (2010). Thermoelasticity with finite wave speeds. Oxford University Press.
Islam, M., Kar, A., & Kanoria, M. (2013). Two-temperature generalized thermoelasticity in a fiber-reinforced hollow cylinder under thermal shock. International Journal for Computational Methods in Engineering Science and Mechanics, 14(5), 367-390.
Islam, M., Mallik, S. H., & Kanoria, M. (2011). Dynamic response in two-dimensional transversely isotropic thick plate with spatially varying heat sources and body forces. Applied Mathematics and Mechanics, 32(10), 1315-1332.
Kar, A., & Kanoria, M. (2007a). Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc. European Journal of Mechanics A/Solids, 26, 969-981.
Kar, A., & Kanoria, M. (2007b). Thermoelastic interaction with energy dissipation in an unbounded body with a spherical hole. International Journal of Solids and Structures, 44, 2961-2971.
Kar, A., & Kanoria, M. (2009). Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect. Applied Mathematical Modeling, 33, 3287-3298.
Kar, A., & Kanoria, M. (2009). Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect. European Journal of Mechanics A/Solids, 28, 757-767.
Kidawa-Kukla, J. (2003). Application of the Green functions to the problem of the thermally induced vibration of a beam. Journal of Sound and Vibration, 262, 865-876.
Kumar, R., Prasad, R., & Mukhopadhyay, S. (2010). Variational and reciprocal principles in two-temperature generalized thermoelasticity. Journal of Thermal Stresses, 33(3), 161-171.
Kumar, R., Prasad, R., & Mukhopadhyay, S. (2011). Some theorems on two-temperature generalized thermoelasticity. Archive of Applied Mechanics, 81(8), 1031-1040.
Chen, P. J., Gurtin, M. E., & Williams, W. O. (1969). On the thermodynamics of non-simple elastic materials with two temperatures. Zeitschrift für angewandte Mathematik und Physik ZAMP, 20(1), 107-112.
Lord, H. W., & Shulman, Y. (1967). A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15(5), 299-309.
Manolis, G. D., & Beskos, D. E. (1980). Thermally induced vibrations of beam structures. Computer Methods in Applied Mechanics and Engineering, 21(3), 337-355.
Puri, P., & Jordan, P. M. (2006). On the propagation of harmonic plane waves under the two-temperature theory. International Journal of Engineering Science, 44(17), 1113-1126.
Quintanilla, R. (2004a). Exponential stability and uniqueness in thermoelasticity with two temperature. Dynamics of Continuous Discrete and Impulsive Systems A, 11, 57-68.
Quintanilla, R. (2004). On existence, structural stability, convergence and spatial behavior in thermoelasticity with two temperatures. Acta Mechanica, 168(1-2), 61-73.
Quintanilla, R. (2008). A well-posed problem for the dual-phase-lag heat conduction. Journal of Thermal Stresses, 31(3), 260-269.
Quintanilla, R. (2009). A well-posed problem for the three-dual-phase-lag heat conduction. Journal of Thermal Stresses, 32(12), 1270-1278.
Choudhuri, S. R. (2007). On a thermoelastic three-phase-lag model. Journal of Thermal Stresses, 30(3), 231-238.
Sur, A., & Kanoria, M. (2014). Thermoelastic interaction in a viscoelastic functionally graded half-space under three-phase-lag model. European Journal of Computational Mechanics, 23(5-6), 179-198.
Soh, A. K., Sun, Y., & Fang, D. (2008). Vibration of microscale beam induced by laser pulse. Journal of sound and vibration, 311(1), 243-253.
Sun, Y., Fang, D., Saka, M., & Soh, A. K. (2008). Laser-induced vibrations of micro-beams under different boundary conditions. International Journal of Solids and Structures, 45(7), 1993-2013.
Sur, A., & Kanoria, M. (2014b). Vibration of a gold nano beam induced by ramp-type laser pulse under three-phase-lag model. International Journal of Applied Mathematics and Mechanics, 10(5), 86-104.
Sur, A., & Kanoria, M. (2014). Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell. Latin American Journal of Solids and Structures, 11(7), 1132-1162.
Sur, A., & Kanoria, M. (2014). Fractional order generalized thermoelastic functionally graded solid with variable material properties. Journal of Solid Mechanics, 6(1), 54-69.
Sur, A., & Kanoria, M. (2012). Fractional order two-temperature thermoelasticity with finite wave speed. Acta Mechanica, 223(12), 2685-2701.
Sur, A., & Kanoria, M. (2014). Finite thermal wave propagation in a half-space due to variable thermal loading. Applications and Applied Mathematics, 9(1), 94-120.
Warren, W. E., & Chen, P. J. (1973). Wave propagation in the two temperature theory of thermoelasticity. Acta Mechanica, 16(1-2), 21-33.
Youssef, H. M., & Al-Lehaibi, E. A. (2007). State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem. International journal of solids and structures, 44(5), 1550-1562.
Youssef, H. M. (2006). Theory of two-temperature-generalized thermoelasticity. IMA Journal of Applied Mathematics, 71(3), 383-390.
Youssef, H. M. (2008). Two-dimensional problem of a two-temperature generalized thermoelastic half-space subjected to ramp-type heating. Computational Mathematics and Modeling, 19(2), 201-216.