Abstract
In this study, natural frequency and dynamic stability of functionally graded (FG) viscoelastic nanobeams based on the Euler–Bernoulli theory on the visco-Pasternak foundation are predicted. The material characteristics of FG nanobeam are temperature-dependent, and vary according to power-law model along thickness. The FG viscoelastic nanobeam is located on a two-dimensional magnetic field which considers the effects of transverse and longitudinal magnetic field. The uniform, linear, and sinusoidal temperature fields are applied on the FG viscoelastic nanobeam. The governing equations are derived through Hamilton’s principle and Eringen’s nonlocal theory. The equations are solved by a Navier-type method and the Bolotin method for simply supported conditions. The effect of three different temperature fields on natural frequency and dynamic stability region of the nanobeam is analyzed. The importance of various parameters such as nonlocal parameter, gradient indexes, magnitude of magnetic field, angle of magnetic field, temperature changes, and aspect ratio on both natural frequency and dynamic stability region of the FG viscoelastic nanobeam is investigated.
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I. Bharti, N. Gupta, K.M. Gupta, Ijmmm 3, 221–224 (2013)
E. Müller, Č. Drašar, J. Schilz, W.A. Kaysser, Mat. Sci. Eng A Struct. 362, 17–39 (2003)
J. Woo, S.A. Meguid, L.S. Ong, J. Sound Vib. 289, 595–611 (2006)
S. Abrate, Compos. Part B Eng. 39, 151–158 (2008)
D.G. Zhang, Y.H. Zhou, Comput. Mater. Sci. 44, 716–720 (2008)
M. Bourada, A. Kaci, M.S.A. Houari, A. Tounsi, Steel. Compos. Struct. 18, 409–423 (2015)
A. Tounsi, M.S.A. Houari, A. Bessaim, Struct. Eng. Mech. 60, 547–565 (2016)
A. Tounsi, M.S. A. Houari, S. Benyoucef, E.A. Adda Bedia, Aerosp. Sci. Technol. 24, 209–220 (2013)
M.S.A. Houari, A. Tounsi, A. Bessaim, S.R. Mahmoud, Steel. Compos. Struct. 22, 257–276 (2016)
A.C. Eringen, J. Appl. Phys. 54, 4703–4710 (1983)
A. Ghorbanpour Arani, A. Fereidoon, R. Kolahchi, J. Intel. Mat. Syst. Str. 26, 1150–1163 (2015)
D.S. Mashat, A.M. Zenkour, M. Sobhy, J. Mech. 32, 277–287 (2016)
H.B. Li, X. Wang, Phys. E. 46, 198–205 (2012)
A.A. Jandaghian, O. Rahmani, Smart. Mater. Struct. 25, 035023 (2016)
A.A. Jandaghian, O. Rahmani, J. Mech. 32, 143–151 (2016)
O. Rahmani, O. Pedram, Int. J. Eng. Sci. 77, 55–70 (2014)
A. Besseghier, H. Heireche, A.A. Bousahla, A. Tounsi, A. Benzair. Adv. Nano Res. 3, 29–37 (2015)
M. Akbarzadeh Khorshidi, M. Shariati, J. Braz. Soc. Mech. Sci. 38, 1–13 (2013)
M.A. Eltaher, S.A. Emam, F.F. Mahmoud, Appl. Math. Comput. 218, 7406–7420 (2012)
M.A. Hamed, M.A. Eltaher, A.M. Sadoun, K.H. Almitani, Appl. Phys. A Mater. 122, 829 (2016)
M. Simsek, H.H. Yurtcu, Compos. Struct. 97, 378–386 (2013)
M. Simsek, Int. J. Eng. Sci. 105, 12–27 (2016)
F.L. Chaht, A. Kaci, M.S.A. Houari, A. Tounsi, O. Anwar Beg, S.R. Mahmoud, Steel. Compos. Struct. 18, 425–442 (2015)
A.H. S. Hosseini, O. Rahmani, Appl. Phys. A Mater. 122, 1–11 (2016)
M. Zamani Nejad, A. Hadi, Int. J. Eng. Sci. 105, 1–11 (2016)
M. Zamani Nejad, A. Hadi, Int. J. Eng. Sci. 106, 1–9 (2016)
F.L. Chaht, A. Kaci, M.S.A. Houari, A. Tounsi, O.A. Bég, Steel. Compos. Struct. 18, 425–442 (2015)
M. Ahouel, M.S.A. Houari, E.A. Bedia, A. Tounsi, Steel. Compos. Struct. 20, 963–981 (2016)
A. Zemri, M.S.A. Houari, A.A. Bousahla, A. Tounsi, Struct. Eng. Mech. 54, 693–710 (2015)
K.S. Al-Basyouni, A. Tounsi, S.R. Mahmoud, Compos. Struct. 125, 621–630 (2015)
I. Mechab, B. Mechab, S. Benaissa, B. Bachir Bouiadjra, J. Braz. Soc. Mech. Sci. 38, 1–19 (2016)
R. Ansari, A. Norouzzadeh, Phys. E 84, 84–97 (2016)
R. Ansari, A. Shahabodini, M. Faghih Shojaei, Phys. E 76, 70–81 (2016)
H. Salehipour, H. Nahvi, A. R. Shahidi, Phys. E 66, 350–358 (2015)
A. Fereidoon, H. Yaghoobi, A. Dehghanian, Int. J. Comput. Methods 11,1350099 (2014)
H. Yaghoobi, A. Fereidoon, Comp. Part B Eng. 62, 54–64 (2014)
A.H. S. Hosseini, O. Rahmani, J. Therm. Stress 39, 1–16 (2016)
F. Ebrahimi, E. Salari, Comp. Part B Eng. 78, 272–290 (2015)
F. Ebrahimi, M.R. Barati, Appl. Phys. A Mater. 122, 880 (2016)
Sh.. Hosseini Hashemi, H. Mehrabani, A. Ahmadi-Savadkoohi, Compos. Struct. 133, 8–15 (2015)
A. Fereidoon, E. Andalib, A. Mirafzal, Phys. E 81, 205–218 (2016)
M. Hosseini, A. Jamalpoor, J. Therm. Stress 38, 1428–1456 (2015)
F. Ebrahimi, M.R. Barati, Int. J. Eng. Sci. 107, 183–196 (2016)
Y.S. Touloukian, Thermophysical Properties of High Temperature Solid Materials. (Macmillan, New York, 1967)
K. Kiani, J. Phys. Chem. Solids 75, 15–22 (2014)
Y. Kiani, M.R. Eslami, Comp. Part B Eng. 45, 101–110 (2013)
K.S. Na, J.H. Kim, Comp. Part B Eng. 35, 429–437 (2004)
S.N. Patel, P.K. Datta, A.H. Sheikh, Thin Wall. Struct. 44, 321–333 (2006)
T. Tauchert, Energy Principles in Structural Mechanics. (Mc Graw-Hill, 1974)
A. Ghorbanpour Arani, Z. Khoddami Maraghi, Ain Shams Eng. J. 7, 361–369 (2016)
V.V. Bolotin, The Dynamic Stability of Elastic Systems. (Holden-Day, San Francisco, 1964)
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Mirafzal, A., Fereidoon, A. Dynamic characteristics of temperature-dependent viscoelastic FG nanobeams subjected to 2D-magnetic field under periodic loading. Appl. Phys. A 123, 247 (2017). https://doi.org/10.1007/s00339-017-0829-1
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DOI: https://doi.org/10.1007/s00339-017-0829-1