Browse > Article
http://dx.doi.org/10.12989/scs.2018.28.1.099

A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates  

Karami, Behrouz (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University)
Janghorban, Maziar (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University)
Shahsavari, Davood (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Publication Information
Steel and Composite Structures / v.28, no.1, 2018 , pp. 99-110 More about this Journal
Abstract
In this paper, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment. This quasi-3D plate theory considers both thickness stretching influences and shear deformation with the variations of displacements in the thickness direction as a parabolic function. Moreover, the stress-free boundary conditions on both sides of the plate are satisfied without using a shear correction factor. This theory includes five independent unknowns with results in only five governing equations. Size effects are obtained via a higher-order nonlocal strain gradient theory of elasticity. A variational approach is adopted to owning the governing equations employing Hamilton's principle. Solving analytically via Fourier series, these equations gives wave frequencies and phase velocities as a function of wave numbers. The validity of the present results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for material composition, size dependency, two parametric elastic foundation, temperature and moisture differences, and wave number. Some conclusions are drawn from the parametric studies with respect to the wave characteristics.
Keywords
functionally graded materials; wave propagation; quasi-3D plate theory; higher-order nonlocal strain gradient elasticity theory; hygrothermal environment;
Citations & Related Records
Times Cited By KSCI : 18  (Citation Analysis)
연도 인용수 순위
1 Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., Int. J., 64(4), 391-402.
2 Koutsoumaris, C.C., Vogiatzis, G.G., Theodorou, D. and Tsamasphyros, G. (2015), "Application of bi-Helmholtz nonlocal elasticity and molecular simulations to the dynamical response of carbon nanotubes", AIP Conference Proceedings, AIP Publishing, 190011.
3 Li, L. and Hu, Y. (2017), "Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects", Int. J. Mech. Sci., 120, 159-170.   DOI
4 Li, L., Hu, Y. and Ling, L. (2015), "Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory", Compos. Struct., 133, 1079-1092.   DOI
5 Li, L., Hu, Y. and Ling, L. (2016a), "Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimensional Syst. Nanostruct., 75, 118-124.   DOI
6 Li, L., Li, X. and Hu, Y. (2016b), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92.   DOI
7 Li, X., Li, L., Hu, Y., Ding, Z. and Deng, W. (2017), "Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory", Compos. Struct., 165, 250-265.   DOI
8 Li, L., Tang, H. and Hu, Y. (2018), "The effect of thickness on the mechanics of nanobeams", Int. J. Eng. Sci., 123, 81-91.   DOI
9 Lim, C., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313.   DOI
10 Mahi, A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508.   DOI
11 Miyamoto, Y., Kaysser, W., Rabin, B., Kawasaki, A. and Ford, R. G. (2013), Functionally Graded Materials: Design, Processing and Applications, Springer Science & Business Media.
12 Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752.   DOI
13 Moradi-Dastjerdi, R. and Momeni-Khabisi, H. (2016), "Dynamic analysis of functionally graded nanocomposite plates reinforced by wavy carbon nanotube", Steel Compos. Struct., Int. J., 22(2), 277-299.   DOI
14 Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new twounknown trigonometric shear deformation beam theory", Smart Struct. Syst., Int. J., 20(3), 369-383.
15 Movchan, B. and Yakovchuk, K.Y. (2004), "Graded thermal barrier coatings, deposited by EB-PVD", Surf. Coatings Technol., 188, 85-92.
16 Papargyri-Beskou, S. and Beskos, D. (2008), "Static, stability and dynamic analysis of gradient elastic flexural Kirchhoff plates", Arch. Appl. Mech., 78(8), 625-635.   DOI
17 Rajanna, T., Banerjee, S., Desai, Y.M. and Prabhakara, D. (2016), "Vibration and buckling analyses of laminated panels with and without cutouts under compressive and tensile edge loads", Steel Compos. Struct., Int. J., 21(1), 37-55.   DOI
18 Reddy, J. (2000), "Analysis of functionally graded plates", Int. J. Numer. Methods Eng., 47(1-3), 663-684.   DOI
19 Romano, G., Barretta, R., Diaco, M. and De Sciarra, F.M. (2017), "Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams", Int. J. Mech. Sci., 121, 151-156.   DOI
20 Shaat, M. and Abdelkefi, A. (2017), "New insights on the applicability of Eringen's nonlocal theory", Int. J. Mech. Sci., 121, 67-75.   DOI
21 Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Brazil. Soc Mech. Sci. Eng., 39(10), 3849-3861.   DOI
22 Sharma, N., Mahapatra, T.R. and Panda, S.K. (2017), "Vibroacoustic analysis of un-baffled curved composite panels with experimental validation", Struct. Eng. Mech., Int. J., 64(1), 93-107.
23 Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Express, 4(8), 085013.   DOI
24 Shahsavari, D., Karami, B. and Mansouri, S. (2018a), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech.-A/Solids, 67, 200-214.   DOI
25 Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018b), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149.   DOI
26 She, G.-L., Yuan, F.-G. and Ren, Y.-R. (2017a), "Nonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory", Compos. Struct., 165, 74-82.   DOI
27 She, G.-L., Yuan, F.-G. and Ren, Y.-R. (2017b), "Research on nonlinear bending behaviors of FGM infinite cylindrical shallow shells resting on elastic foundations in thermal environments", Compos. Struct., 170, 111-121.   DOI
28 Barati, M.R. (2017b), "Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermomechanical loading using nonlocal strain gradient theory", Struct.Eng. Mech., Int. J., 64(6), 683-693.
29 Atmane, H.A., Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84.   DOI
30 Barati, M.R. (2017a), "Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities", Adv. Nano Res., Int. J., 5(4), 393-414.   DOI
31 Bennai, R., Atmane, H.A. and Tounsi, A. (2015), "A new higherorder shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546.   DOI
32 Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., Int. J., 19(6), 601-614.
33 Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., Int. J., 19(2), 115-126.   DOI
34 Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B: Eng., 42(2), 123-133.   DOI
35 Wang, Y.-Z., Li, F.-M. and Kishimoto, K. (2010a), "Scale effects on flexural wave propagation in nanoplate embedded in elastic matrix with initial stress", Appl. Phys. A: Mater. Sci. Process., 99(4), 907-911.   DOI
36 She, G.-L., Yuan, F.-G. and Ren, Y.-R. (2017c), "Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory", Appl. Math. Model., 47, 340-357.   DOI
37 She, G.-L., Yuan, F.-G., Ren, Y.-R. and Xiao, W.-S. (2017d), "On buckling and postbuckling behavior of nanotubes", Int. J. Eng. Sci., 121, 130-142.   DOI
38 She, G.-L., Ren, Y.-R., Yuan, F.-G. and Xiao, W.-S. (2018), "On vibrations of porous nanotubes", Int. J. Eng. Sci., 125, 23-35.   DOI
39 Suresh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Materials, The Institut of Materials.
40 Vecchio, K.S. (2005), "Synthetic multifunctional metallicintermetallic laminate composites", Jom, 57(3), 25-31.   DOI
41 Wang, Y.-Z., Li, F.-M. and Kishimoto, K. (2010b), "Scale effects on the longitudinal wave propagation in nanoplates", Physica E: Low-dimensional Syst. Nanostruct., 42(5), 1356-1360.   DOI
42 Xiong, Q.-L. and Tian, X. (2017), "Transient thermo-piezo-elastic responses of a functionally graded piezoelectric plate under thermal shock", Steel Compos. Struct., Int. J., 25(2), 187-196.
43 Zeighampour, H., Beni, Y.T. and Karimipour, I. (2017), "Wave propagation in double-walled carbon nanotube conveying fluid considering slip boundary condition and shell model based on nonlocal strain gradient theory", Microfluid. Nanofluid., 21(5), 85.   DOI
44 Atmane, H.A., Tounsi, A., Bernard, F. and Mahmoud, S. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., Int. J., 19(2), 369-384.   DOI
45 Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A. and Mahmoud, S. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442.   DOI
46 Ebrahimi, F. and Barati, M.R. (2016), "Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory", Appl. Phys. A, 122(9), 843.   DOI
47 Arefi, M. (2015), "Nonlinear electromechanical analysis of a functionally graded square plate integrated with smart layers resting on Winkler-Pasternak foundation", Smart Struct. Syst., Int. J., 16(1), 195-211.   DOI
48 Ebrahimi, F. and Barati, M.R. (2017), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444.   DOI
49 Ebrahimi, F. and Jafari, A. (2016), "Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., Int. J., 59(2), 343-371.   DOI
50 Ehyaei, J., Farazmandnia, N. and Jafari, A. (2017), "Rotating effects on hygro-mechanical vibration analysis of FG beams based on Euler-Bernoulli beam theory", Struct. Eng. Mech., Int. J., 63(4), 471-480.
51 El-Wazery, M. and El-Desouky, A. (2015), "A review on functionally graded ceramic-metal materials", J. Mater. Environ. Sci., 6(5), 1369-1376.
52 Zhu, X. and Li, L. (2017c), "On longitudinal dynamics of nanorods", Int. J. Eng. Sci., 120, 129-145.   DOI
53 Zhang, L., Liu, J., Fang, X. and Nie, G. (2014), "Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates", Eur. J. Mech.-A/Solids, 46, 22-29.   DOI
54 Zhu, X. and Li, L. (2017a), "Closed form solution for a nonlocal strain gradient rod in tension", Int. J. Eng. Sci., 119, 16-28.   DOI
55 Zhu, X. and Li, L. (2017b), "Longitudinal and torsional vibrations of size-dependent rods via nonlocal integral elasticity", Int. J. Mech. Sci., 133, 639-650.   DOI
56 Hanifi Hachemi Amar, L., Kaci, A. and Tounsi, A. (2017), "On the size-dependent behavior of functionally graded micro-beams with porosities", Struct Eng. Mech., Int. J., 64(5), 527-541.
57 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
58 Gasik, M.M., Zhang, B.S., Van Der Biest, O., Vleugels, J., Anne, G. and Put, S. (1984), "Design and fabrication of symmetric FGM plates", Materials Science Forum, Aedermannsdorf, Switzerland, pp. 23-28.
59 Ghadiri, M., Shafiei, N. and Babaei, R. (2017), "Vibration of a rotary FG plate with consideration of thermal and Coriolis effects", Steel Compos Struct., Int. J., 25(2), 197-207.
60 Hamidi, A., Houari, M.S.A., Mahmoud, S. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 235-253.   DOI
61 Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Modern Phys. Lett. B, 30(36), 1650421.   DOI
62 Karami, B., Janghorban, M. and Li, L. (2017a), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronautica.
63 Karami, B., Janghorban, M. and Tounsi, A. (2017b), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., Int. J., 25(3), 361-374.
64 Karami, B., Shahsavari, D. and Li, L. (2018d), "Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimensional Syst. Nanostruct., 97, 317-327.   DOI
65 Zhu, X. and Li, L. (2017d), "Twisting statics of functionally graded nanotubes using Eringen's nonlocal integral model", Compos. Struct., 178, 87-96.   DOI
66 Karami, B., Shahsavari, D. and Janghorban, M. (2017c), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 1-11.
67 Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248.   DOI
68 Karami, B., Janghorban, M. and Tounsi, A. (2018a), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., Int. J., 27(2), 201-216.
69 Karami, B., Janghorban, M. and Tounsi, A. (2018b), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264.   DOI
70 Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2018c), "Wave dispersion of mounted graphene with initial stress", Thin-Walled Structures, 122, 102-111.   DOI
71 Karami, B., Shahsavari, D. and Li, L. (2018e), "Temperaturedependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Thermal Stress., 41(4), 483-499.   DOI
72 Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2018f), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.