Abstract
On the basis of the modified strain gradient theory, the present paper deals with the theoretical analysis of the free vibration of coupled double-FGM viscoelastic nanoplates by Kelvin–Voigt visco-Pasternak medium. To establish static equilibrium of atoms on the each nanoplate surface, the effects of the surface layers are considered. The properties of material in the thickness direction vary according to the power low distribution. Kirchhoff plate assumption and Hamilton’s variational principle are employed to achieve the partial differential equations for three different cases of vibration (out-of-phase, in-phase, and one nanoplate of the system being stationary) and corresponding boundary conditions. Navier’s approach which satisfies the simply supported boundary conditions applied to analytically investigate the size effect on the natural frequencies of double-FGM viscoelastic nanoplate systems. Numerical studies are carried out to illustrate the influence of viscoelastic damping structural of the nanoplates, damping coefficient of the visco-Pasternak medium, independent length scale parameter, aspect ratio, surface properties, and other factors on the frequency behavior system. Some numerical results of this research illustrate that the frequencies may increase or decrease with respect to the sign of the surface properties of FGMs.
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References
A.C. Eringen, Int. J. Eng. Sci. 10, 425 (1972)
A.C. Eringen, J. Appl. Phys. 54, 4703 (1983)
W.T. Koiter, Proc. K. Ned. Akad. van Wet. Ser. B 67, 17 (1964)
R.A. Toupin, Arch. Ration. Mech. Anal. 17, (1964)
R.D. Mindlin, Arch. Ration. Mech. Anal. 16, (1964)
R.D. Mindlin, N.N. Eshel, Int. J. Solids Struct 4, 109 (1968)
N.A. Fleck, J.W. Hutchinson, J. Mech. Phys. Solids 49, 2245 (2001)
F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Int. J. Solids Struct. 39, 2731 (2002)
D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, J. Mech. Phys. Solids 51, 1477 (2003)
S.C. Pradhan, J.K. Phadikar, J. Sound Vib. 325, 206 (2009)
T. Aksencer, M. Aydogdu, Phys. E Low Dim. Syst. Nanostruct. 44, 1752 (2012)
M. Shaat, F.F. Mahmoud, X.-L. Gao, A.F. Faheem, Int. J. Mech. Sci. 79, 31 (2014)
M.R. Nami, M. Janghorban, Compos. Struct. 111, 349 (2014)
M. Hosseini, M. Bahreman, A. Jamalpoor, Acta Mech. (2016)
B. Zhang, Y. He, D. Liu, L. Shen, J. Lei, Appl. Math. Model 39, 3814 (2015)
A.G. Shenas, P. Malekzadeh, Thin Walled Struct. 106, 294 (2016)
F. Ebrahimy, S.H.S. Hosseini Appl. Phys. A 122, 922 (2016)
A. Li, S. Zhou, L. Qi, Appl. Phys. A 122, 918 (2016)
Y. Lei, S. Adhikari, M.I. Friswell, Int. J. Eng. Sci. 66–67, 1 (2013)
S. Pouresmaeeli, E. Ghavanloo, S.A. Fazelzadeh, Compos. Struct. 96, 405 (2013)
D. Karličić, P. Kozić, R. Pavlović, Compos. Struct. 115, 89 (2014)
A. Ghorbanpour Arani, M. Shokravi, Proc. Inst. Mech. Eng. Part N J. Nanoeng. Nanosyst. 1740349914529102 (2014)
S.H. Hashemi, H. Mehrabani, A. Ahmadi-Savadkoohi, Compos. Part B Eng. 78, 377 (2015)
M. Bennoun, M.S.A. Houari, A. Tounsi, Mech, Adv. Mater. Struct. 23, 423 (2016)
Y. Beldjelili, A. Tounsi, S.R. Mahmoud, SMART Struct. Syst. 18, 755 (2016)
M. Zidi, A. Tounsi, M.S.A. Houari, E.A. Adda Bedia, O. Anwar Bég, Aerosp. Sci. Technol. 34, 24 (2014)
F. Bourada, K. Amara, A. Tounsi, Steel. Compos. Struct. 21, 1287 (2016)
S.A. Yahia, H.A. Atmane, M.S.A. Houari, A. Tounsi, Struct. Eng. Mech. 53, 1143 (2015)
Z. Belabed, M. S. Ahmed Houari, A. Tounsi, S.R. Mahmoud, O. Anwar Bég, Compos. Part B Eng. 60, 274 (2014)
A.A. Bousahla, M.S.A. Houari, A. Tounsi, E.A. Adda Bedia, Int. J. Comput. Methods 11, 1350082 (2014)
H. Hebali, A. Tounsi, M.S.A. Houari, A. Bessaim, E.AA. Bedia, J. Eng. Mech. 140, 374 (2014)
A. Mahi, E.A. Adda Bedia, A. Tounsi, Appl. Math. Model 39, 2489 (2015)
A. Hamidi, M.S.A. Houari, S.R. Mahmoud, A. Tounsi, Steel. Compos. Struct. 18, 235 (2015)
M.S.A. Houari, A. Tounsi, A. Bessaim, S. Hassan, Steel. Compos. Struct. 2, 257 (2016)
A. Tounsi, M.S.A. Houari, A. Bessaim, Struct. Eng. Mech. 60, 547 (2016)
M. Bourada, A. Kaci, M.S.A. Houari, A. Tounsi, Steel. Compos. Struct. 18, 409 (2015)
A. Tounsi, M.S.A. Houari, S. Benyoucef, E. A. Adda Bedia, Aerosp. Sci. Technol. 24, 209 (2013)
B. Bouderba, M.S.A. Houari, A. Tounsi, Steel. Compos. Struct. 14, 85 (2013)
R. Ansari, R. Gholami, M. Faghih Shojaei, V. Mohammadi, M.A. Darabi, J. Therm. Stress 36, 446 (2013)
M. Salamat-talab, A. Nateghi, J. Torabi, Int. J. Mech. Sci. 57, 63 (2012)
M. Mirsalehi, M. Azhari, H. Amoushahi, Aerosp. Sci. Technol. 47, 356 (2015)
F. Bounouara, K.H. Benrahou, I. Belkorissat, A. Tounsi, Steel. Compos. Struct. 20, 227 (2016)
I. Belkorissat, M.S.A. Houari, A. Tounsi, E.A.A. Bedia, S.R. Mahmoud, Steel. Compos. Struct. 18, 1063 (2015)
A. Tounsi, S. Benguediab, E.A. Adda Bedia, A. Semmah, Adv M. Zidour, Nano Res. 1, 1 (2013)
A. Besseghier, H. Heireche, A.A. Bousahla, A. Tounsi, Adv A. Benzair, Nano Res. 3, 29 (2015)
S. Benguediab, A. Tounsi, M. Zidour, A. Semmah, Compos. Part B Eng. 57, 21 (2014)
F.L. Chaht, A. Kaci, M.S.A. Houari, A. Tounsi, O.A. Beg, S.R. Mahmoud, Steel. Compos. Struct. 18, 425 (2015)
M. Ahouel, M.S.A. Houari, E.A.A. Bedia, A. Tounsi, Steel. Compos. Struct. 20, 963 (2016)
A. Zemri, M.S.A. Houari, A.A. Bousahla, A. Tounsi, Struct. Eng. Mech. 54, 693 (2015)
K.S. Al-Basyouni, A. Tounsi, S.R. Mahmoud, Compos. Struct. 125, 621 (2015)
M. Gurtin, A. Ian Murdoch, Arch. Ration. Mech. Anal. 57, (1975)
M.E. Gurtin, A. Ian Murdoch, Int. J. Solids Struct. 14, 431 (1978)
S. Hosseini-Hashemi, R. Nazemnezhad, H. Rokni, Eur. J. Mech. A Solids 52, 44 (2015)
M.A. Eltaher, F.F. Mahmoud, A.E. Assie, E.I. Meletis, Appl. Math. Comput. 224, 760 (2013)
R. Nazemnezhad, S. Hosseini-Hashemi, Meccanica 50, 1027 (2014)
M. Ghadiri, M. Soltanpour, A. Yazdi, M. Safi, Appl. Phys. A 122, 520 (2016)
H.-L. Lee, W.-J. Chang, J. Appl. Phys. 108, 93503 (2010)
A. Ghorbanpour Arani, M.A. Roudbari, Thin Solid Films 542, 232 (2013)
R. Bahaadini, M. Hosseini, A. Jamalpoor, Phys. B Condens. Mater. (2017). doi:10.1016/j.physb.2016.12.033
A. Assadi, Appl. Math. Model. 37, 3575 (2013)
R. Ansari, R. Gholami, Acta Astronaut. 118, 72 (2016)
P. Malekzadeh, M.R. Golbahar Haghighi, M. Shojaee, Thin Walled Struct. 78, 48 (2014)
M. Hosseini, A. Jamalpoor, A. Fath, Meccanica 1 (2016). doi:10.1007/s11012-016-0469-0
M. Hosseini, M. Bahreman, A. Jamalpoor, Microsyst. Technol. 1 (2016). doi:10.1007/s00542-016-3133-7
J. M. Seelig, W.H. Hoppmann, J. Acoust. Soc. Am. 36, 93 (1964)
J.M. Seelig, W.H. Hoppmann, J. Appl. Mech 31, 621 (1964)
A. Jamalpoor, M. Hosseini, Compos. Part B Eng. 75, 53 (2015)
S.R. Asemi, A. Farajpour, Micro. Nano Lett. 9, 280 (2014)
M. Hosseini, A. Jamalpoor, J. Therm. Stress 38, 1428 (2015)
J.N. Reddy, Energy Principles and Variational Methods in Applied Mechanics (Wiley, Oxford, 2002)
K.F. Wang, B.L. Wang, Phys. E Low Dim. Syst. Nanostruct. 44, 448 (2011)
R. Ansari, M.A. Ashrafi, T. Pourashraf, S. Sahmani. Acta Astronaut 109, 42 (2015)
P. Lu, L.H. He, H.P. Lee, C. Lu, Int. J. Solids Struct. 43, 4631 (2006)
A. Jamalpoor, A. Ahmadi-Savadkoohi, S. Hosseini-Hashemi, Smart. Mater. Struct. 25, 105035 (2016)
H.V. Vu, A.M. Ordóñez, B.H. Karnopp, J. Sound Vib. 229, 807 (2000)
M. Hosseini, A. Jamalpoor, M. Bahreman, Acta Astronaut. 129, 400 (2016)
A. Jamalpoor, A. Ahmadi-Savadkoohi, M. Hossein, S. Hosseini-Hashemi. Eur. J. Mech. A Solids (2016). doi:10.1016/j.euromechsol.2016.12.002
B. Akgöz, Ö. Civalek, Meccanica 48, 863 (2012)
B. Akgöz, Ö. Civalek, Acta Mech. 226, 2277 (2015)
H.-T. Thai, D.-H. Choi, Compos. Struct. 95, 142 (2013)
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Jamalpoor, A., Kiani, A. Vibration analysis of bonded double-FGM viscoelastic nanoplate systems based on a modified strain gradient theory incorporating surface effects. Appl. Phys. A 123, 201 (2017). https://doi.org/10.1007/s00339-017-0784-x
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DOI: https://doi.org/10.1007/s00339-017-0784-x