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http://dx.doi.org/10.12989/sem.2016.60.4.707

A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions  

Barati, Mohammad Reza (Aerospace Engineering Department & Center of Excellence in Computational Aerospace, AmirKabir University of Technology)
Shahverdi, Hossein (Aerospace Engineering Department & Center of Excellence in Computational Aerospace, AmirKabir University of Technology)
Publication Information
Structural Engineering and Mechanics / v.60, no.4, 2016 , pp. 707-727 More about this Journal
Abstract
In this paper, thermal vibration of a nonlocal functionally graded (FG) plates with arbitrary boundary conditions under linear and non-linear temperature fields is explored by developing a refined shear deformation plate theory with an inverse cotangential function in which shear deformation effect was involved without the need for shear correction factors. The material properties of FG nanoplate are considered to be temperature-dependent and graded in the thickness direction according to the Mori-Tanaka model. On the basis of non-classical higher order plate model and Eringen's nonlocal elasticity theory, the small size influence was captured. Numerical examples show the importance of non-uniform thermal loadings, boundary conditions, gradient index, nonlocal parameter and aspect and side-to-thickness ratio on vibrational responses of size-dependent FG nanoplates.
Keywords
thermal vibration; four-variable plate theory; functionally graded nanoplate; nonlocal elasticity theory; elastic foundation;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Ansari, R., Ashrafi, M.A., Pourashraf, T. and Sahmani, S. (2015), "Vibration and buckling characteristics of functionally graded nanoplates subjected to thermal loading based on surface elasticity theory", Acta. Astronautica, 109, 42-51.   DOI
2 Barati, M.R., Zenkour, A.M. and Shahverdi, H. (2016), "Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory", Compos. Struct., 141, 203-212.   DOI
3 Bouiadjra, R.B., Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., 48(4), 547-567.   DOI
4 Bourada, M., Tounsi, A. and Houari, M.S.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33.   DOI
5 Daneshmehr, A. and Rajabpoor, A. (2014), "Stability of size dependent functionally graded nanoplate based on nonlocal elasticity and higher order plate theories and different boundary conditions", Int. J. Eng. Sci., 82, 84-100.   DOI
6 Ebrahimi, F. and Barati, M.R. (2016), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690.   DOI
7 Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded sizedependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420.   DOI
8 Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710.   DOI
9 Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248.   DOI
10 Javaheri, R. and Eslami, M.R. (2002), "Thermal buckling of functionally graded plates based on higher order theory", J. Thermal. Stress., 25(7), 603-625.   DOI
11 Jung, W.Y., Han, S.C. and Park, W.T. (2014), "A modified couple stress theory for buckling analysis of SFGM nanoplates embedded in Pasternak elastic medium", Compos. Part B: Eng., 60, 746-756.   DOI
12 Kim, S.E., Thai, H.T. and Lee, J. (2009), "A two variable refined plate theory for laminated composite plates", Compos. Struct., 89(2), 197-205.   DOI
13 Kulkarni, K., Singh, B.N. and Maiti, D.K. (2015), "Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory", Compos. Struct., 134, 147-157.   DOI
14 Mechab, I., Atmane, H.A., Tounsi, A. and Belhadj, H.A. (2010), "A two variable refined plate theory for the bending analysis of functionally graded plates", Acta Mechanica Sinica, 26(6), 941-949.   DOI
15 Nami, M.R. and Janghorban, M. (2014), "Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant", Compos. Struct., 111, 349-353.   DOI
16 Narendar, S. (2011), "Buckling analysis of micro-/nano-scale plates based on two-variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., 93(12), 3093-3103.   DOI
17 Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Comput. Mater. Sci., 65, 74-80.   DOI
18 Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87.   DOI
19 Shen, H.S. and Wang, H. (2015), "Nonlinear bending and postbuckling of FGM cylindrical panels subjected to combined loadings and resting on elastic foundations in thermal environments", Compos. Part B. Eng., 78, 202-213.   DOI
20 Shimpi, R. P. (2002), "Refined plate theory and its variants", AIAA J., 40(1), 137-146.   DOI
21 Sobhy, M. (2014), "Generalized two-variable plate theory for multi-layered graphene sheets with arbitrary boundary conditions", Acta. Mechanica, 225(9), 2521-2538.   DOI
22 Sobhy, M. (2015a), "Levy-type solution for bending of single-layered graphene sheets in thermal environment using the two-variable plate theory", Int. J. Mech. Sci., 90, 171-178.   DOI
23 Sobhy, M. (2015b), "Hygrothermal deformation of orthotropic nanoplates based on the state-space concept", Compos. Part B. Eng., 79, 224-235.   DOI
24 Sobhy, M. (2015c), "A comprehensive study on FGM nanoplates embedded in an elastic medium", Compos. Struct., 134, 966-980.   DOI
25 Sobhy, M. (2016), "An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment", Int. J. Mech. Sci., 110, 62-77.   DOI
26 Ta, H.D. and Noh, H.C. (2015), "Analytical solution for the dynamic response of functionally graded rectangular plates resting on elastic foundation using a refined plate theory", Appl. Math. Model., 39(20), 6243-6257.   DOI
27 Thai, H.T. and Choi, D.H. (2011), "A refined plate theory for functionally graded plates resting on elastic foundation", Compos. Sci.Tech., 71(16), 1850-1858.   DOI
28 Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aero. Sci. technol., 24(1), 209-220.   DOI
29 Thai, H.T. and Kim, S.E. (2012), "Levy-type solution for free vibration analysis of orthotropic plates based on two variable refined plate theory", Appl. Math. Model., 36(8), 3870-3882.   DOI
30 Touloukian Y.S. (1967), Thermo-physical Properties Research Center. Thermo-physical properties of high temperature solid materials, Vol. 1, Elements.-Pt. 1, Macmillan.
31 Zare, M., Nazemnezhad, R. and Hosseini-Hashemi, S. (2015), "Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method", Meccanica, 50(9), 2391-2408.   DOI
32 Zenkour, A.M. and Sobhy, M. (2011), "Thermal buckling of functionally graded plates resting on elastic foundations using the trigonometric theory", J. Thermal. Stress., 34(11), 1119-1138.   DOI