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http://dx.doi.org/10.12989/sss.2016.18.6.1087

Thermal effects on nonlocal vibrational characteristics of nanobeams with non-ideal boundary conditions  

Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
Shaghaghi, Gholam Reza (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
Publication Information
Smart Structures and Systems / v.18, no.6, 2016 , pp. 1087-1109 More about this Journal
Abstract
In this manuscript, the small scale and thermal effects on vibration behavior of preloaded nanobeams with non-ideal boundary conditions are investigated. The boundary conditions are assumed to allow small deflections and moments and the concept of non-ideal boundary conditions is applied to the nonlocal beam problem. Governing equations are derived through Hamilton's principle and then are solved applying Lindstedt-Poincare technique to derive fundamental natural frequencies. The good agreement between the results of this research and those available in literature validated the presented approach. The influence of various parameters including nonlocal parameter, thermal effect, perturbation parameter, aspect ratio and pre-stress load on free vibration behavior of the nanobeams are discussed in details.
Keywords
small scale effect; nonlocal beam theory; non-ideal boundary conditions; vibration; thermal effect; preload parameter; perturbation parameter;
Citations & Related Records
Times Cited By KSCI : 8  (Citation Analysis)
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1 Ansari, R. and Sahmani, S. (2012), "Small scale effect on vibrational response of single-walled carbon nanotubes with different boundary conditions based on nonlocal beam models", Commun. Nonlinear Sci. Numer. Simul., 17(4), 1965-1979.   DOI
2 Zhang, Y., Liu, G. and Wang, J. (2004), "Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression", Phys. Rev. B, 70(20), 205430.   DOI
3 Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34.   DOI
4 Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E: Low-dimensional Systems and Nanostructures, 41(9), 1651-1655.   DOI
5 Aydogdu, M. and Ece, M.C. (2006), "Buckling and vibration of non-ideal simply supported rectangular isotropic plates", Mech. Res. Commun., 33(4), 532-540.   DOI
6 Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S. and Beg, O.A. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Composites Part B: Engineering, 60, 274-283.   DOI
7 Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104.   DOI
8 Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431.   DOI
9 Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N. and Boumia, L. (2008), "The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 41(22), 225404.   DOI
10 Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., 3(1), 029.   DOI
11 Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249.   DOI
12 Chang, T.P. (2012), "Thermal-mechanical vibration and instability of a fluid-conveying single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Appl. Math. Model., 36(5), 1964-1973.   DOI
13 Civalek, O. and Demir, C. (2011a), "Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory", Appl. Math.Model., 35(5), 2053-2067.   DOI
14 Civalek, O. and Demir, C. (2011b), "Buckling and bending analyses of cantilever carbon nanotubes using the euler-bernoulli beam theory based on non-local continuum model", Asian J. Civil Eng. (Building and Housing), 12(5), 651-661.
15 Civalek, O., Demir, C. and AkgOz, B. (2010), "Free vibration and bending analyses of cantilever microtubules based on nonlocal continuum model", Math. Comput. Appl., 15(2), 289-298.
16 Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98(12), 124301.   DOI
17 Tounsi, A., Bourada, M., Kaci, A. and Houari, M.S.A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409.   DOI
18 Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220.   DOI
19 Wang, L., Ni, Q., Li, M. and Qian, Q. (2008), "The thermal effect on vibration and instability of carbon nanotubes conveying fluid", Physica E: Low-dimensional Systems and Nanostructures, 40(10), 3179-3182.   DOI
20 Wang, Q., Zhou, G. and Lin, K. (2006), "Scale effect on wave propagation of double-walled carbon nanotubes", Int. J. Solids Struct., 43(20), 6071-6084.   DOI
21 Wattanasakulpong, N. and Mao, Q. (2015), "Dynamic response of Timoshenko functionally graded beams with classical and non-classical boundary conditions using Chebyshev collocation method", Compos. Struct., 119, 346-354.   DOI
22 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., 53(6), 1143.   DOI
23 Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710.   DOI
24 Zhang, C.L. and Shen, H.S. (2007), "Buckling and postbuckling of single-walled carbon nanotubes under combined axial compression and torsion in thermal environments", Phys. Rev. B, 75(4), 045408.   DOI
25 Demir, C. and Civalek, O. (2013), "Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models", Appl. Math. Model., 37(22), 9355-9367.   DOI
26 Ebrahimi, F. and Salari E. (2015a), "A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position", CMES: Computer Modeling in Engineering & Sciences 105.2, 151-181.
27 Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16.   DOI
28 Ebrahimi, F. and Salari E. (2015b), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Composites Part B: Engineering, 79,156-169.   DOI
29 Eigoli, A.K. and Ahmadian, M. (2011), "Nonlinear vibration of beams under nonideal boundary conditions", Acta Mechanica, 218(3-4), 259-267.   DOI
30 Ekici, H.O. and Boyaci, H. (2007), "Effects of non-ideal boundary conditions on vibrations of microbeams", J. Vib.Control, 13(9-10), 1369-1378.   DOI
31 Eringen, A.C. (2002), Nonlocal continuum field theories: Springer Science & Business Media.
32 Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248.   DOI
33 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., 18(1), 235-253.   DOI
34 Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E.A.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech. - ASCE, 140(2), 374-383.   DOI
35 Mahmoud, S., Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A. and Beg, O.A. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425.   DOI
36 Pakdemirli, M. and Boyac, H. (2003), "Non-linear vibrations of a simple-simple beam with a non-ideal support in between", J. Sound Vib., 268(2), 331-341.   DOI
37 Malekzadeh, K., Khalili, S. and Abbaspour, P. (2010), "Vibration of non-ideal simply supported laminated plate on an elastic foundation subjected to in-plane stresses", Compos. Struct., 92(6), 1478-1484.   DOI
38 Murmu, T. and Pradhan, S. (2009), "Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory", Comput. Mater. Sci., 46(4), 854-859.   DOI
39 Pakdemirli, M. and Boyac, H. (2001), "Vibrations of a stretched beam with non-ideal boundary", Math. Comput. Appl., 6(3), 217-220.
40 Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41(3), 305-312.   DOI
41 Pradhan, S. and Reddy, G. (2011), "Thermo mechanical buckling analysis of carbon nanotubes on winkler foundation using non-local elasticity theory and DTM", Sadhana, 36(6), 1009-1019.   DOI
42 Reddy, J. (2007), "Nonlocal theories for bending, buckling and vibration of beams", I Int. J. Eng. Sci., 45(2), 288-307.   DOI
43 Sari, G. and Pakdemirli, M. (2012), "Effects of non-ideal boundary conditions on the vibrations of a slightly curved micro beam. Paper presented at the 9th international conference on mathematical problems in engineering, aerospace and sciences: ICNPAA 2012.
44 Thai, H.T. (2012), "A nonlocal beam theory for bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 52, 56-64.   DOI