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http://dx.doi.org/10.12989/scs.2018.26.6.673

Nonlinear forced vibration of FG-CNTs-reinforced curved microbeam based on strain gradient theory considering out-of-plane motion  

Allahkarami, Farshid (Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University)
Nikkhah-bahrami, Mansour (Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University)
Saryazdi, Maryam Ghassabzadeh (Vehicle Technology Research Institute, Amirkabir University of Technology)
Publication Information
Steel and Composite Structures / v.26, no.6, 2018 , pp. 673-691 More about this Journal
Abstract
The main goal of this research is to examine the in-plane and out-of-plane forced vibration of a curved nanocomposite microbeam. The in-plane and out-of-plane displacements of the structure are considered based on the first order shear deformation theory (FSDT). The curved microbeam is reinforced by functionally graded carbon nanotubes (FG-CNTs) and thus the extended rule of mixture is employed to estimate the effective material properties of the structure. Also, the small scale effect is captured using the strain gradient theory. The structure is rested on a nonlinear orthotropic viscoelastic foundation and is subjected to concentrated transverse harmonic external force, thermal and magnetic loads. The derivation of the governing equations is performed using energy method and Hamilton's principle. Differential quadrature (DQ) method along with integral quadrature (IQ) and Newmark methods are employed to solve the problem. The effect of various parameters such as volume fraction and distribution type of CNTs, boundary conditions, elastic foundation, temperature changes, material length scale parameters, magnetic field, central angle and width to thickness ratio are studied on the frequency and force responses of the structure. The results indicate that the highest frequency and lowest vibration amplitude belongs to FGX distribution type while the inverse condition is observed for FGO distribution type. In addition, the hardening-type response of the structure with FGX distribution type is more intense with respect to the other distribution types.
Keywords
forced vibration; curved nanocomposite microbeam; strain gradient theory; viscoelastic foundation; DQ-IQ-Newmark method;
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Times Cited By KSCI : 4  (Citation Analysis)
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1 Younis, M.I. and Nayfeh, A.H. (2003), "A study of the nonlinear response of a resonant microbeam to an electric actuation", Nonlinear Dyn., 31(1), 91-117.   DOI
2 Zhang, B., He, Y., Liu, D., Gan, Zh. and Shen, L. (2013), "A novel size-dependent functionally graded curved mircobeam model based on the strain gradient elasticity theory", Compos. Struct., 106, 374-392.   DOI
3 Atci, D. and Bagdatli, S.M. (2017a), "Free vibrations of fluid conveying microbeams under non-ideal boundary conditions", Steel Compos. Struct., Int. J., 24(2), 141-149.
4 Atci, D. and Bagdatli, S.M. (2017b), "Vibrations of fluid conveying microbeams under non-ideal boundary conditions", Microsyst. Technol., 23(10), 4741-4752.   DOI
5 Allahkarami, F. and Nikkhah-bahrami, M. (2017), "Effects of agglomerated CNTs as reinforcement on the size-dependent vibration of embedded curved microbeams based on the modified couple stress theory", Mech. Adv. Mat. Struct., 1-14.
6 Allahkarami, F., Nikkhah-bahrami, M. and Ghassabzadeh Saryazdi, M. (2017), "Magneto-thermo-mechanical dynamic buckling analysis of a FG-CNTs-reinforced curved microbeam with different boundary conditions using strain gradient theory", Int. J. Mech. Mater. Des., 1-19.
7 Dehrouyeh-Semnani, A.M., Dehrouyeh, M., Zafari-Koloukhi, H. and Ghamami, M. (2015), "Size-dependent frequency and stability characteristics of axially moving microbeams based on modified couple stress theory", Int. J. Eng. Sci., 97, 98-112.   DOI
8 Aydin Aya, S.A. and Tufekci, E. (2017), "Modeling and analysis of out-of-plane behavior of curved nanobeams based on nonlocal elasticity", Compos. Part B: Eng., 119, 184-195.   DOI
9 Bataineh, A.M. and Younis, M.I. (2015), "Dynamics of a clamped-clamped microbeam resonator considering fabrication imperfections", Microsyst. Technol., 21(11), 2425-2434.   DOI
10 Dai, H.L., Wang, Y.K. and Wang, L. (2015), "Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory", Int. J. Eng. Sci., 94, 103-112.   DOI
11 Dehrouyeh-Semnani, A.M., Mostafaei, H. and Nikkhah-Bahrami, M. (2016), "Free flexural vibration of geometrically imperfect functionally graded microbeams", Int. J. Eng. Sci., 105, 56-79.   DOI
12 Gutschmidt, S. and Gottlieb, O. (2012), "Nonlinear dynamic behavior of a microbeam array subject to parametric actuation at low, medium and large DC-voltages", Nonlinear. Dyn., 67(1), 1-36.   DOI
13 Erfani, S. and Akrami, V. (2016), "Evaluation of cyclic fracture in perforated beams using micromechanical fatigue model", Steel Compos. Struct., Int. J., 20(4), 913-930.   DOI
14 Ghayesh, M.H. and Farokhi, H. (2017), "Global dynamics of imperfect axially forced microbeams", Int. J. Eng. Sci., 115, 102-116.
15 Ghayesh, M.H., Farokhi, H. and Gholipour, A. (2017), "Coupled vibrations of functionally graded Timoshenko microbeams", Europ. J. Mech. A/Solids, 65, 289-300.   DOI
16 Kolahchi, R. (2017b), "A comparative study on the bending vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC HDQ and DQ methods", Aerosp. Sci. Tech., 66, 235-248.   DOI
17 He, X.j., Wu, Q., Wang, Y., Song, M.x. and Yin, J.h. (2009), "Numerical simulation and analysis of electrically actuated microbeam-based MEMS capacitive switch", Microsyst. Technol., 15(2), 301-307.   DOI
18 Jafari-Talookolaei, R.A., Abedi, M. and Attar, M. (2017), "Inplane and out-of-plane vibration modes of laminated composite beams with arbitrary lay-ups", Aerosp. Sci. Tech., 66, 366-379.   DOI
19 Jahangiri, R., Jahangiri, H. and Khezerloo, H. (2015), "FGM micro-gripper under electrostatic and intermolecular Van-der Waals forces using modified couple stress theory", Steel Compos. Struct., Int. J., 18(6), 1541-1555.   DOI
20 Kolahchi, R. and Moniribidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech. -Engl Ed, 37(2), 265-274.   DOI
21 Liu, B., Xing, Y., Wang, Z., Lu, X. and Sun, H. (2017), "Nonuniform rational Lagrange functions and its applications to isogeometric analysis of in-plane and flexural vibration of thin plates", Comput. Meth Appl. Mech. Eng., 321, 173-208.   DOI
22 Kolahchi, R., Rabani Bidgoli, M., Beygipoor, Gh. and Fakhar, M.H. (2015), "A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field", J. Mech. Sci. Tech., 29(9), 3669-3677.   DOI
23 Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016a), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos, Struct., 157, 174-186.   DOI
24 Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016b), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265.   DOI
25 Kolahchi, R., Zarei, M.Sh., Hajmohammad, M.H. and Naddaf Oskouei, A. (2017a), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Wall. Struct., 113, 162-169.
26 Krylov, S., Ilic, B.R. and Lulinsky, S. (2011), "Bistability of curved microbeams actuated by fringing electrostatic fields", Nonlinear Dyn., 66(3), 403-411.   DOI
27 Malekzadeh, P., Golbahar Haghighi, M.R. and Atashi, M.M. (2010), "Out-of-plane free vibration of functionally graded circular curved beams in thermal environment", Compos. Struct. 92(2), 541-552 .   DOI
28 Pan, F., Chen, Y., Liu, Y. and Guo, Z. (2017), "Out-of-plane bending of carbon nanotube films", Int. J. Solids Struct., 106-107, 183-199.   DOI
29 Rezaei, M.P. and Zamanian, M. (2017), "A two-dimensional vibration analysis of piezoelectrically actuated microbeam with nonideal boundary conditions", Physica E, 85, 285-293.   DOI
30 Peng, J., Yang, L., Lin, F. and Yang, J. (2017), "Dynamic analysis of size-dependent micro-beams with nonlinear elasticity under electrical actuation", Appl. Math. Model., 43, 441-453.   DOI
31 Rostami, H., Rahbar Ranji, A. and Bakhtiarinejad, F. (2016), "Free in-plane vibration analysis of rotating rectangular orthotropic cantilever plates", Int. J. Mech. Sci., 115-116, 438-456.
32 Shafiei, N., Kazemi, M. and Ghadiri, M. (2016), "Nonlinear vibration of axially functionally graded tapered microbeams", Int. J. Eng. Sci., 102, 12-26.   DOI
33 Shen, H.Sh. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19.   DOI
34 Shen, H.Sh. and Zhang, Ch.L. (2011), "Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates", Comput. Mat. Sci., 50(3), 1022-1029.   DOI
35 Shu, C., Chew, Y.T. and Richards, E. (1995), "Generalized differential and integral quadrature and their application to solve boundary layer equations", Int. J. Num. Meth. Fluids, 21(9), 723-733.   DOI
36 Simsek, M. and Kocaturk, T. (2009), "Nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load", J. Sound Vib., 320(1-2), 235-253.   DOI
37 Wang, Ch., Ayalew, B., Rhyne, T., Cron, S. and Daolliez, B. (2016), "Forced in-plane vibration of a thick ring on a unilateral elastic foundation", J. Sound Vib., 380, 279-294.
38 Wu, J.S. and Chiang, L.K. (2003), "Out-of-plane response of a circular Timoshenko beam due to moving load", Int. J. Solids Struct., 40(26), 7425-7448.   DOI