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http://dx.doi.org/10.12989/anr.2017.5.4.281

Investigating vibration behavior of smart imperfect functionally graded beam subjected to magnetic-electric fields based on refined shear deformation theory  

Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
Jafari, Ali (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
Publication Information
Advances in nano research / v.5, no.4, 2017 , pp. 281-301 More about this Journal
Abstract
In this disquisition, an exact solution method is developed for analyzing the vibration characteristics of magneto-electro-elastic functionally graded (MEE-FG) beams by considering porosity distribution and various boundary conditions via a four-variable shear deformation refined beam theory for the first time. Magneto-electroelastic properties of porous FG beam are supposed to vary through the thickness direction and are modeled via modified power-law rule which is formulated using the concept of even and uneven porosity distributions. Porosities possibly occurring inside functionally graded materials (FGMs) during fabrication because of technical problem that lead to creation micro-voids in FG materials. So, it is necessary to consider the effect of porosities on the vibration behavior of MEE-FG beam in the present study. The governing differential equations and related boundary conditions of porous MEE-FG beam subjected to physical field are derived by Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factor. An analytical solution procedure is used to achieve the natural frequencies of porous-FG beam supposed to magneto-electrical field which satisfies various boundary conditions. A parametric study is led to carry out the effects of material graduation exponent, porosity parameter, external magnetic potential, external electric voltage, slenderness ratio and various boundary conditions on dimensionless frequencies of porous MEE-FG beam. It is concluded that these parameters play noticeable roles on the vibration behavior of MEE-FG beam with porosities. Presented numerical results can be applied as benchmarks for future design of MEE-FG structures with porosity phases.
Keywords
magneto-electro-elastic FG material; porous materials; analytical solution; free vibration; refined beam theory;
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Times Cited By KSCI : 11  (Citation Analysis)
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1 Ebrahimi, F., Naei, M.H. and Rastgoo, A. (2009), "Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation", J. Mech. Sci. Technol., 23(8), 2107-2124.   DOI
2 Ebrahimi, F., Rastgoo, A. and Bahrami, M.N. (2010), "Investigating the thermal environment effects on geometrically nonlinear vibration of smart functionally graded plates", J. Mech. Sci. Technol., 24(3), 775-791.   DOI
3 Ebrahimi, F., Ghadiri, M., Salari, E., Hoseini, S.A.H. and Shaghaghi, G.R. (2015a), "Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams", J. Mech. Sci. Technol., 29(3), 1207-1215.   DOI
4 Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015b), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and nonlinear temperature distributions", J. Therm. Stress., 38(12), 1360-1386.   DOI
5 Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016a), "Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams", Appl. Phys. A, 122(11), 949.   DOI
6 Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016b), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci., 107, 169-182.   DOI
7 Ebrahimi, F., Barati, M.R. and Haghi, P. (2016c), "Nonlocal thermo-elastic wave propagation in temperature-dependent embedded small-scaled nonhomogeneous beams", Eur. Phys. J. Plus, 131(11), 383.   DOI
8 Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2016e), "In-plane thermal loading effects on vibrational characteristics of functionally graded nanobeams", Meccanica, 51(4), 951-977.   DOI
9 Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447.   DOI
10 Ebrahimi, F., Barati, M.R. and Haghi, P. (2016d), "Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams", J. Therm. Stress., 1-13.
11 Ebrahimi, F., Ghasemi, F. and Salari, E. (2016f), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccanica, 51(1), 223-249.   DOI
12 Harshe, G., Dougherty, J. and Newnham, R. (1993), "Theoretical modelling of multilayer magnetoelectric composites", Int. J. Appl. Electromagnet. Mater., 4(2), 145-145.
13 Huang, D., Ding, H. and Chen, W. (2007), "Analytical solution for functionally graded magneto-electroelastic plane beams", Int. J. Eng. Sci., 45(2), 467-485.   DOI
14 Benferhat, R., Hassaine, D., Hadji, L. and Said, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., Int. J., 21(1), 123-136.   DOI
15 Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, B.B. (2016), "Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories", J. Brazil. Soc. Mech. Sci. Eng., 38(8), 2193-2211.   DOI
16 Kattimani, S. and Ray, M. (2015), "Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates", Int. J. Mech. Sci., 99, 154-167.   DOI
17 Ke, L.-L. and Wang, Y.-S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory", Physica E: Low-Dimens. Syst. Nanostruct., 63, 52-61.   DOI
18 Kumaravel, A., Ganesan, N. and Sethuraman, R. (2007), "Buckling and vibration analysis of layered and multiphase magneto-electro-elastic beam under thermal environment", Multidiscipl. Model. Mater. Struct., 3(4), 461-476.   DOI
19 Lang, Z. and Xuewu, L. (2013), "Buckling and vibration analysis of functionally graded magneto-electrothermo-elastic circular cylindrical shells", Appl. Math. Model., 37(4), 2279-2292.   DOI
20 Mantari, J., Bonilla, E. and Soares, C.G. (2014), "A new tangential-exponential higher order shear deformation theory for advanced composite plates", Compos. Part B: Eng., 60, 319-328.   DOI
21 Pan, E. (2001), "Exact solution for simply supported and multilayered magneto-electro-elastic plates", J. Appl. Mech., 68(4), 608-618.   DOI
22 Pan, E. and Han, F. (2005), "Exact solution for functionally graded and layered magneto-electro-elastic plates", Int. J. Eng. Sci., 43(3), 321-339.   DOI
23 Jiang, A. and Ding, H. (2004), "Analytical solutions to magneto-electro-elastic beams", Struct. Eng. Mech., Int. J., 18(2), 195-209.   DOI
24 Ebrahimi, F. and Barati, M.R. (2016a), "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
25 Chen, W., Lee, K.Y. and Ding, H. (2005), "On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates", J. Sound Vib., 279(1), 237-251.   DOI
26 Daga, A., Ganesan, N. and Shankar, K. (2009), "Transient dynamic response of cantilever magneto-electroelastic beam using finite elements", Int. J. Comput. Method. Eng. Sci. Mech., 10(3), 173-185.   DOI
27 Ebrahimi, F. (2013), "Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment", Mech. Adv. Mater. Struct., 20(10), 854-870.   DOI
28 Ebrahimi, F. and Barati, M.R. (2016b), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279.   DOI
29 Ebrahimi, F. and Barati, M.R. (2016c), "Buckling analysis of smart size-dependent higher order magnetoelectro-thermo-elastic functionally graded nanosize beams", J. Mech., 1-11.
30 Ebrahimi, F. and Barati, M.R. (2016d), "On nonlocal characteristics of curved inhomogeneous Euler-Bernoulli nanobeams under different temperature distributions", Appl. Phys. A, 122(10), 880.   DOI
31 Ebrahimi, F. and Barati, M.R. (2016e), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", Int. J. Eng. Sci., 107, 183-196.   DOI
32 Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method", Meccanica, 50(5), 1331-1342.   DOI
33 Rezaei, A. and Saidi, A. (2016), "Application of Carrera Unified Formulation to study the effect of porosity on natural frequencies of thick porous-cellular plates", Compos. Part B: Eng., 91, 361-370.   DOI
34 Razavi, S. and Shooshtari, A. (2015), "Nonlinear free vibration of magneto-electro-elastic rectangular plates", Compos. Struct., 119, 377-384.   DOI
35 Sladek, J., Sladek, V., Krahulec, S., Chen, C. and Young, D. (2015), "Analyses of Circular Magnetoelectroelastic Plates with Functionally Graded Material Properties", Mech. Adv. Mater. Struct., 22(6), 479-489.   DOI
36 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
37 Song, G., Sethi, V. and Li, H.-N. (2006), "Vibration control of civil structures using piezoceramic smart materials: a review", Eng. Struct., 28(11), 1513-1524.   DOI
38 Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120.   DOI
39 Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190.   DOI
40 Wu, C.-P. and Tsai, Y.-H. (2007), "Static behavior of functionally graded magneto-electro-elastic shells under electric displacement and magnetic flux", Int. J. Eng. Sci., 45(9), 744-769.   DOI
41 Ebrahimi, F. and Barati, M.R. (2016f), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444.
42 Ebrahimi, F. and Barati, M.R. (2016g), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 1-16.
43 Ebrahimi, F. and Barati, M.R. (2016h), "Magnetic field effects on buckling behavior of smart sizedependent graded nanoscale beams", Eur. Phys. J. Plus, 131(7), 1-14.   DOI
44 Ebrahimi, F. and Barati, M.R. (2016i), "Buckling analysis of smart size-dependent higher order magnetoelectro-thermo-elastic functionally graded nanosize beams", J. Mech., 1-11.
45 Ebrahimi, F. and Barati, M.R. (2016j), "Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory", Arab. J. Sci. Eng., 1-12.
46 Ebrahimi, F. and Barati, M.R. (2016k), "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 Ebrahimi, F. and Barati, M.R. (2016l), "An exact solution for buckling analysis of embedded piezoelectromagnetically actuated nanoscale beams", Adv. Nano Res., Int. J., 4(2), 65-84.   DOI
48 Ebrahimi, F. and Barati, M.R. (2016m), "Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment", Int. J. Smart Nano Mater., 7(2), 69-90.   DOI
49 Xin, L. and Hu, Z. (2015), "Free vibration of layered magneto-electro-elastic beams by SS-DSC approach", Compos. Struct., 125, 96-103.   DOI
50 Wu, C.-P. and Tsai, Y.-H. (2010), "Dynamic responses of functionally graded magneto-electro-elastic shells with closed-circuit surface conditions using the method of multiple scales", Eur. J. Mech.-A/Solids, 29(2), 166-181.   DOI
51 Wu, C.-P., Chen, S.-J. and Chiu, K.-H. (2010), "Three-dimensional static behavior of functionally graded magneto-electro-elastic plates using the modified Pagano method", Mech. Res. Commun., 37(1), 54-60.   DOI
52 Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng Mech., Int. J., 53(6), 1143-1165.   DOI
53 Zhang, R., Duan, Y., Or, S.W. and Zhao, Y. (2014), "Smart elasto-magneto-electric (EME) sensors for stress monitoring of steel cables: design theory and experimental validation", Sensors, 14(8), 13644-13660.   DOI
54 Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO 2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68(1), 130-135.   DOI
55 Ebrahimi, F. and Barati, M.R. (2016s), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A, 122(9), 792.   DOI
56 Ebrahimi, F. and Barati, M.R. (2016n), "Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 1-13.
57 Ebrahimi, F. and Barati, M.R. (2016o), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", Int. J. Smart Nano Mater., 7(3), 1-25.   DOI
58 Ebrahimi, F. and Barati, M.R. (2016p), "Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field", J. Intel. Mater. Syst. Struct., 1045389X16672569.
59 Ebrahimi, F. and Barati, M.R. (2016q), "Thermal environment effects on wave dispersion behavior of inhomogeneous strain gradient nanobeams based on higher order refined beam theory", J. Therm. Stress., 39(12), 1560-1571.   DOI
60 Ebrahimi, F. and Barati, M.R. (2016r), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", Eur. Phys. J. Plus, 131(8), 279.   DOI
61 Ebrahimi, F. and Barati, M.R. (2017), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182.   DOI
62 Ebrahimi, F. and Boreiry, M. (2015), "Investigating various surface effects on nonlocal vibrational behavior of nanobeams", Appl. Phys. A, 121(3), 1305-1316.   DOI
63 Ebrahimi, F. and Hosseini, S.H.S. (2016a), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Therm. Stress., 39(5), 606-625.   DOI
64 Ebrahimi, F. and Hosseini, S.H.S. (2016b), "Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates", Appl. Phys. A, 122(10), 922.   DOI
65 Ebrahimi, F. and Mokhtari, M. (2014), "Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method", J. Brazil. Soc. Mech. Sci. Eng., 37(4), 1435-1444.   DOI
66 Ebrahimi, F. and Hosseini, S.H.S. (2016c), "Double nanoplate-based NEMS under hydrostatic and electrostatic actuations", Eur. Phys. J. Plus, 131(5), 1-19.   DOI
67 Ebrahimi, F. and Jafari, A. (2016a), "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
68 Ebrahimi, F. and Jafari, A. (2016b), "A higher-order thermomechanical vibration analysis of temperaturedependent FGM beams with porosities", J. Eng.
69 Ebrahimi, F. and Rastgoo, A. (2009), "Nonlinear vibration of smart circular functionally graded plates coupled with piezoelectric layers", Int. J. Mech. Mater. Des., 5(2), 157-165.   DOI
70 Ebrahimi, F. and Rastgoo, A. (2011), "Nonlinear vibration analysis of piezo-thermo-electrically actuated functionally graded circular plates", Archive Appl. Mech., 81(3), 361-383.   DOI
71 Ebrahimi, F. and Salari, E (2015a), "Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment", Acta Astronautica, 113, 29-50.   DOI
72 Ebrahimi, F. and Salari, E. (2015b), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007.   DOI
73 Ebrahimi, F. and Salari, E. (2015c), "Thermo-mechanical vibration analysis of a single-walled carbon nanotube embedded in an elastic medium based on higher-order shear deformation beam theory", J. Mech. Sci. Technol., 29(9), 3797-3803.   DOI
74 Ebrahimi, F. and Shafiei, N. (2016), "Influence of initial shear stress on the vibration behavior of singlelayered graphene sheets embedded in an elastic medium based on Reddy's higher-order shear deformation plate theory", Mech. Adv. Mater. Struct., 1-41.
75 Ebrahimi, F. and Salari, E. (2015d), "Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007.   DOI
76 Ebrahimi, F. and Salari, E. (2016), "Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams", Mech. Adv. Mater. Struct., 23(12), 1379-1397.   DOI
77 Ebrahimi, F. and Sepiani, H. (2010), "Transverse shear and rotary inertia effects on the stability analysis of functionally graded shells under combined static and periodic axial loadings", J. Mech. Sci. Technol., 24(12), 2359-2366.   DOI
78 Ebrahimi, F. and Zia, M. (2015), "Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities", Acta Astronautica, 116, 117-125.   DOI