Details

Title

Transverse vibration analysis of nonlocal beams with various slenderness ratios, undergoing thermal stress

Journal title

Archive of Mechanical Engineering

Yearbook

2019

Volume

vol. 66

Issue

No 1

Affiliation

Babaei, Alireza : Department of Mechanical Engineering,University of North Dakota, Grand Forks, North Dakota, USA. ; Babaei, Alireza : Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky, USA. ; Rahmani, Arash : Faculty of Mechanical Engineering, Urmia University of Technology, Urmia, Iran. ; Ahmadi, Isa : Faculty of Mechanical Engineering, University of Zanjan, Zanjan, Iran.

Authors

Keywords

small-sized beam ; nonlocal theory ; temperature-dependent properties ; free lateral vibration

Divisions of PAS

Nauki Techniczne

Coverage

5-24

Publisher

Polish Academy of Sciences, Committee on Machine Building

Bibliography

[1] R.A. Toupin. Elastic materials with couple-stresses. Archive for Rational Mechanics and Analysis, 11(1):385–414, 1962. doi: 10.1007/BF00253945.
[2] R. Mindlin and H. Tiersten. Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and Analysis, 11(1):415–448, 1962. doi: 10.1007/BF00253946.
[3] A. Ghanbari and A. Babaei. The new boundary condition effect on the free vibration analysis of micro-beams based on the modified couple stress theory. International Research Journal of Applied and Basic Sciences, 9(3):274–9, 2015.
[4] N. Fleck and J. Hutchinson. A phenomenological theory for strain gradient effects in plasticity. Journal of the Mechanics and Physics of Solids, 41(12):1825–1857,1993. doi: 10.1016/0022-5096(93)90072-N.
[5] R. Mindlin. Influence of couple-stresses on stress concentrations. Experimental Mechanics, 3(1):1–7, 1963. doi: 10.1007/BF02327219.
[6] A.C. Eringen. Theory of micropolar plates. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 18(1):12–30, 1967. doi: 10.1007/BF01593891.
[7] A.C. Eringen. Nonlocal polar elastic continua. International Journal of Engineering Science, 10(1):1–16, 1972. doi: 10.1016/0020-7225(72)90070-5.
[8] E.C. Aifantis. Strain gradient interpretation of size effects. International Journal of Fracture, 95(1):299–314, 1999. doi: 10.1023/A:1018625006804.
[9] F. Yang, A.C.M. Chong, D.C.C. Lam, and P. Tong. Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39(10):2731–2743, 2002. doi: 10.1016/S0020-7683(02)00152-X.
[10] M. Gurtin, J. Weissmüller, and F. Larché. A general theory of curved deformable interfaces in solids at equilibrium. Philosophical Magazine A, 78(5):1093–1109, 1998. doi: 10.1080/01418619808239977.
[11] C.M.C Roque, D.S. Fidalgo, A.J.M. Ferreira, and J.N. Reddy. A study of a microstructure-dependent composite laminated Timoshenko beam using a modified couple stress theory and a meshless method. Composite Structures, 96:532–537, 2013. doi: 10.1016/j.compstruct.2012.09.011.
[12] A. Ghanbari, A. Babaei, and F. Vakili-Tahami. Free vibration analysis of micro beams based on the modified couple stress theory, using approximate methods. International Journal of Engineering and Technology Sciences, 3(2):136–143, 2015.
[13] A.R. Askari and M. Tahani. Size-dependent dynamic pull-in analysis of beam-type MEMS under mechanical shock based on the modified couple stress theory. Applied Mathematical Modelling, 39(2):934–946, 2015. doi: 10.1016/j.apm.2014.07.019.
[14] W.-Y. Jung, W.-T. Park, and S.-C. Han. Bending and vibration analysis of S-FGM microplates embedded in Pasternak elastic medium using the modified couple stress theory. International Journal of Mechanical Sciences, 87:150–162, 2014. doi: 10.1016/j.ijmecsci.2014.05.025.
[15] A. Babaei, A. Ghanbari, and F. Vakili-Tahami. Size-dependent behavior of functionally graded micro-beams, based on the modified couple stress theory. International Journal of Engineering and Technology Sciences, 3(5):364–372, 2015.
[16] N. Shafiei, A. Mousavi, and M. Ghadiri. Vibration behavior of a rotating non-uniform FG microbeam based on the modified couple stress theory and GDQEM. Composite Structures, 149:157–169, 2016. doi: 10.1016/j.compstruct.2016.04.024.
[17] R. Aghazadeh, E. Cigeroglu, and S. Dag. Static and free vibration analyses of smallscale functionally graded beams possessing a variable length scale parameter using different beam theories. European Journal of Mechanics – A/Solids, 46:1–11, 2014. doi: 10.1016/j.euromechsol.2014.01.002.
[18] M. Fathalilou, M. Sadeghi, and G. Rezazadeh. Micro-inertia effects on the dynamic characteristics of micro-beams considering the couple stress theory. Mechanics Research Communications, 60:74–80, 2014. doi: 10.1016/j.mechrescom.2014.06.003.
[19] R. Ansari, R. Gholami, M.F. Shojaei, V. Mohammadi, and S. Sahmani. Bending, buckling and free vibration analysis of size-dependent functionally graded circular/annular microplates based on the modified strain gradient elasticity theory. European Journal of Mechanics – A/Solids, 49:251–267, 2015. doi: 10.1016/j.euromechsol.2014.07.014.
[20] M.A. Eltaher, S.A. Emam, and F.F. Mahmoud. Free vibration analysis of functionally graded size-dependent nanobeams. Applied Mathematics and Computation, 218(14):7406–7420, 2012. doi: 10.1016/j.amc.2011.12.090.
[21] F. Ebrahimi and E. Salari. Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments. Composite Structures, 128:363–380, 2015. doi: 10.1016/j.compstruct.2015.03.023.
[22] F. Ebrahimi and E. Salari. Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment. Acta Astronautica, 113:29–50, 2015. doi: 10.1016/j.actaastro.2015.03.031.
[23] A. Babaei and I. Ahmadi. Dynamic vibration characteristics of non-homogenous beam-model MEMS. Journal of Multidisciplinary Engineering Science Technology, 4(3):6807–6814, 2017.
[24] A. Babaei and C.X.Yang.Vibration analysis of rotating rods based on the nonlocal elasticity theory and coupled displacement field. Microsystem Technologies, 1–9, 2018. doi: 10.1007/s00542-018-4047-3.
[25] A. Babaei and A. Rahmani. On dynamic-vibration analysis of temperature-dependent Timoshenko micro-beam possessing mutable nonclassical length scale parameter. Mechanics of Advanced Materials and Structures, 2018. doi: 10.1080/15376494.2018.1516252.
[26] S. Azizi, B. Safaei, A.M. Fattahi, and M. Tekere. Nonlinear vibrational analysis of nanobeams embedded in an elastic medium including surface stress effects. Advances in Materials Science and Engineering, ID 318539, 2015. doi: 10.1155/2015/318539.
[27] B. Safaei and A.M. Fattahi. Free vibrational response of single-layered graphene sheets embedded in an elastic matrix using different nonlocal plate models. Mechanics, 23(5):678–687, 2017. doi: 10.5755/j01.mech.23.5.14883.
[28] A.M. Fattahi and B. Safaei. Buckling analysis of CNT-reinforced beams with arbitrary boundary conditions. Microsystem Technologies, 23:5079–5091, 2017. doi: 10.1007/s00542-017-3345-5.
[29] A. Chakraborty, S. Gopalakrishnan, and J.N. Reddy. A new beam finite element for the analysis of functionally graded materials. International Journal of Mechanical Sciences, 45(3):519–539, 2003. doi: 10.1016/S0020-7403(03)00058-4.
[30] H.J. Xiang and J. Yang. Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction. Composites Part B: Engineering, 39(2):292–303, 2008. doi: 10.1016/j.compositesb.2007.01.005.
[31] S. Pradhan and T. Murmu. Thermo-mechanical vibration ofFGMsandwich beam under variable elastic foundations using differential quadrature method. Journal of Sound and Vibration, 321(1):342–362, 2009. doi: 10.1016/j.jsv.2008.09.018.
[32] A. Nateghi and M. Salamat-talab. Thermal effect on size dependent behavior of functionally graded microbeams based on modified couple stress theory. Composite Structures, 96:97–110, 2013. doi: 10.1016/j.compstruct.2012.08.048.
[33] A. Mahi, E.A. Bedia, A. Tounsi, and I. Mechab. An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions. Composite Structures, 92(8):1877–1887, 2010. doi: 10.1016/j.compstruct.2010.01.010.
[34] A. Babaei, M.R.S. Noorani, and A. Ghanbari. Temperature-dependent free vibration analysis of functionally graded micro-beams based on the modified couple stress theory. Microsystem Technologies, 23(10):4599–4610, 2017. doi: 10.1007/s00542-017-3285-0.
[35] B. Safaei, R. Moradi-Dastjerdi, and F. Chu. Effect of thermal gradient load on thermo-elastic vibrational behavior of sandwich plates reinforced by carbon nanotube agglomerations. Composite Structures, 192:28–37, 2018. doi: 10.1016/j.compstruct.2018.02.022.
[36] J.N. Reddy. Nonlocal theories for bending, buckling and vibration of beams. International Journal of Engineering Science, 45(2-8):288–307, 2007. doi: 10.1016/j.ijengsci.2007.04.004.

Date

2019.01.25

Type

Artykuły / Articles

Identifier

DOI: 10.24425/ame.2019.126368 ; ISSN 0004-0738, e-ISSN 2300-1895

Source

Archive of Mechanical Engineering; 2019; vol. 66; No 1; 5-24
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