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7 Mathematical Models of Functionally Graded Beams in Temperature Field
149. Gupta, R.K., Jagadish, B.G., Ranga, J.G., Venkateswara, R.G.: Thermal post-buckling analysis
of slender columns using the concept of coupled displacement field. Int. J. Mech. Sci. 52(4),
590–594 (2010)
150. He, P., Liu, Z., Li, C.: An improved beam element for beams with variable axial parameters.
Shock Vib. 20, 601–617 (2013)
151. Nayak, S., Bisoi, A., Dash, P.R., Pradhan, P.K.: Static stability of a viscoelastically supported
asymmetric sandwich beam with thermal gradient. Int. J. Adv. Struct. Eng. 65 (2014), 7 pp
152. Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N., Boumia, L.: The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam
theory. J. Phys. D: Appl. Phys. 41 (2008) 225404 (10 pp)
153. Kiani, Y., Eslami, M.R.: Thermomechanical buckling of temperature-dependent FGM beams.
Lat. Am. J. Solids Struct. 10, 223–246 (2013)
154. Youssef, H.M., El-Bary, A.A., Elsibai, K.A.: Vibration of gold nano beam in context of twotemperature generalized thermoelasticity subjected to laser pulse. Lat. Am. J. Solids Struct.
11(13), 2460–2482 (2014)
155. Prabhakar, S., Vengallatore, S.: Theory of thermoelastic damping in micromechanical resonators with two-dimensional heat conduction. J. Microelectromech. Syst. 17(2), 494–502
(2008)
156. Akbas, S.D.: Free vibration of axially functionally graded beams in thermal environment. Int.
J. Eng. Appl. Sci. 6(3), 37–51 (2014)
157. Esfahani, S.E., Kiani, Y., Komijani, M., Eslami, M.R.: Vibration of a temperature-dependent
thermally pre/postbuckled FGM beam over a nonlinear hardening elastic foundation. J. Appl.
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158. Awrejcewicz, J., Krysko, V.A.: Nonclassical Thermoelastic Problems in Nonlinear Dynamics
of Shells. Springer, Berlin (2003)
159. Awrejcewicz, J., Krysko, V.A., Krysko, A.V.: Thermo-Dynamics of Plates and Shells.
Springer, Berlin (2007)
160. Krysko, A.V., Awrejcewicz, J., Kuznetsova, E.S., Krysko, V.A.: Chaotic vibrations of closed
cylindrical shells in a temperature field. Shock Vib. 15(3–4), 335–343 (2008)
161. Krysko, A.V., Awrejcewicz, J., Kutepov, I.E., Krysko, V.A.: On a contact problem of two-layer
beams coupled by boundary conditions in a temperature field. J. Therm. Stress. 38, 468–484
(2015)
162. Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Dover Publications, New
York (1944)
163. Kármán, T.L.: The Collected Works. Butterworths, London (1956)
164. Vlasov, V.Z.: General Theory for Shells and Its Application in Engineering. Gostekhizdat
Publication, Moscow (1949)
165. Duhamel, J.M.C.: Second memoire sur les phenomenes thermoomecaniques. de l’Ecole Polytechnique 15 (1837)
166. Volmir, A.S.: Stability of Deformable Bodies. Nauka, Moscow (1968)
167. Bolotin, V.V., Novichkov, Yu.N.: Mechanics of Multilayer Constructions. Mashinostroenie,
Moscow (1980)
168. Krysko, A.V., Awrejcewicz, J., Zagniboroda, N.A., Dobriyan, V., Krysko, V.A., Kutepov, I.E.:
Chaotic dynamics of flexible Euler-Bernoulli beams. Chaos 34(4), 043130 (2014)
169. Carslou, H., Jaeger, J.: Conduction of Heat in Solids. Oxford University Press, Oxford (1959)
170. Krysko, A.V., Awrejcewicz, J., Pavlov, S.P., Zhigalov, M.V., Krysko, V.A.: Mathematical
model of a three-layer micro- and nano-beams based on the hypotheses of the GrigolyukChulkov and the modified couple stress theory. Int. J. Solids Struct. 117, 39–50 (2017)
171. Zenkour, A.M.: Transverse shear and normal deformation theory for bending analysis of
laminated and sandwich elastic beams. Mech. Compos. Mater. Struct. 6(3), 267–283 (1999)
172. Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements.
Nanotechnology 11, 139–147 (2000)
173. Chong, A.C.M., Yang, F., Lam, D.C.C., Tong, P.: Torsion and bending of micron-scaled
structures. J. Mater. Res. 14, 1052–1058 (2001)
7 Mathematical Models of Functionally Graded Beams in Temperature Field
149. Gupta, R.K., Jagadish, B.G., Ranga, J.G., Venkateswara, R.G.: Thermal post-buckling analysis
of slender columns using the concept of coupled displacement field. Int. J. Mech. Sci. 52(4),
590–594 (2010)
150. He, P., Liu, Z., Li, C.: An improved beam element for beams with variable axial parameters.
Shock Vib. 20, 601–617 (2013)
151. Nayak, S., Bisoi, A., Dash, P.R., Pradhan, P.K.: Static stability of a viscoelastically supported
asymmetric sandwich beam with thermal gradient. Int. J. Adv. Struct. Eng. 65 (2014), 7 pp
152. Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N., Boumia, L.: The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam
theory. J. Phys. D: Appl. Phys. 41 (2008) 225404 (10 pp)
153. Kiani, Y., Eslami, M.R.: Thermomechanical buckling of temperature-dependent FGM beams.
Lat. Am. J. Solids Struct. 10, 223–246 (2013)
154. Youssef, H.M., El-Bary, A.A., Elsibai, K.A.: Vibration of gold nano beam in context of twotemperature generalized thermoelasticity subjected to laser pulse. Lat. Am. J. Solids Struct.
11(13), 2460–2482 (2014)
155. Prabhakar, S., Vengallatore, S.: Theory of thermoelastic damping in micromechanical resonators with two-dimensional heat conduction. J. Microelectromech. Syst. 17(2), 494–502
(2008)
156. Akbas, S.D.: Free vibration of axially functionally graded beams in thermal environment. Int.
J. Eng. Appl. Sci. 6(3), 37–51 (2014)
157. Esfahani, S.E., Kiani, Y., Komijani, M., Eslami, M.R.: Vibration of a temperature-dependent
thermally pre/postbuckled FGM beam over a nonlinear hardening elastic foundation. J. Appl.
Mech. 81, 011004 (2014)
158. Awrejcewicz, J., Krysko, V.A.: Nonclassical Thermoelastic Problems in Nonlinear Dynamics
of Shells. Springer, Berlin (2003)
159. Awrejcewicz, J., Krysko, V.A., Krysko, A.V.: Thermo-Dynamics of Plates and Shells.
Springer, Berlin (2007)
160. Krysko, A.V., Awrejcewicz, J., Kuznetsova, E.S., Krysko, V.A.: Chaotic vibrations of closed
cylindrical shells in a temperature field. Shock Vib. 15(3–4), 335–343 (2008)
161. Krysko, A.V., Awrejcewicz, J., Kutepov, I.E., Krysko, V.A.: On a contact problem of two-layer
beams coupled by boundary conditions in a temperature field. J. Therm. Stress. 38, 468–484
(2015)
162. Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Dover Publications, New
York (1944)
163. Kármán, T.L.: The Collected Works. Butterworths, London (1956)
164. Vlasov, V.Z.: General Theory for Shells and Its Application in Engineering. Gostekhizdat
Publication, Moscow (1949)
165. Duhamel, J.M.C.: Second memoire sur les phenomenes thermoomecaniques. de l’Ecole Polytechnique 15 (1837)
166. Volmir, A.S.: Stability of Deformable Bodies. Nauka, Moscow (1968)
167. Bolotin, V.V., Novichkov, Yu.N.: Mechanics of Multilayer Constructions. Mashinostroenie,
Moscow (1980)
168. Krysko, A.V., Awrejcewicz, J., Zagniboroda, N.A., Dobriyan, V., Krysko, V.A., Kutepov, I.E.:
Chaotic dynamics of flexible Euler-Bernoulli beams. Chaos 34(4), 043130 (2014)
169. Carslou, H., Jaeger, J.: Conduction of Heat in Solids. Oxford University Press, Oxford (1959)
170. Krysko, A.V., Awrejcewicz, J., Pavlov, S.P., Zhigalov, M.V., Krysko, V.A.: Mathematical
model of a three-layer micro- and nano-beams based on the hypotheses of the GrigolyukChulkov and the modified couple stress theory. Int. J. Solids Struct. 117, 39–50 (2017)
171. Zenkour, A.M.: Transverse shear and normal deformation theory for bending analysis of
laminated and sandwich elastic beams. Mech. Compos. Mater. Struct. 6(3), 267–283 (1999)
172. Miller, R.E., Shenoy, V.B.: Size-dependent elastic properties of nanosized structural elements.
Nanotechnology 11, 139–147 (2000)
173. Chong, A.C.M., Yang, F., Lam, D.C.C., Tong, P.: Torsion and bending of micron-scaled
structures. J. Mater. Res. 14, 1052–1058 (2001)