|Table of Contents|

[1] Zhou Bo, Zheng Xueyao, Kang Zetian, Xue Shifeng, et al. Size-dependent behaviors of viscoelastic axially functionallygraded Timoshenko micro-beam considering Poisson effects [J]. Journal of Southeast University (English Edition), 2020, 36 (2): 170-180. [doi:10.3969/j.issn.1003-7985.2020.02.007]
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Size-dependent behaviors of viscoelastic axially functionallygraded Timoshenko micro-beam considering Poisson effects()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
36
Issue:
2020 2
Page:
170-180
Research Field:
Computer Science and Engineering
Publishing date:
2020-06-20

Info

Title:
Size-dependent behaviors of viscoelastic axially functionallygraded Timoshenko micro-beam considering Poisson effects
Author(s):
Zhou Bo;  Zheng Xueyao;  Kang Zetian;  Xue Shifeng
College of Pipeline and Civil Engineering, China University of Petroleum(East China), Qingdao 266580, China
Keywords:
viscoelastic functionally graded micro-beam;  size-dependent behaviors;  size effect;  functionally graded effect;  Poisson effect space
PACS:
TP324
DOI:
10.3969/j.issn.1003-7985.2020.02.007
Abstract:
A size-dependent continuum-based model is developed for the functionally graded(FG)Timoshenko micro-beams with viscoelastic properties, in which material parameters vary according to the power law along its axial direction. The size effect is incorporated by employing the modified couple stress theory and Kelvin-Voigt viscoelastic model, so that viscous components are included in the stress and the deviatoric segments of the symmetric couple stress tensors. The components of strain, curvature, stress and couple stress are formulated by combining them with the Timoshenko beam theory. Based on the Hamilton principle, the governing differential equations and boundary conditions for the micro-beam are expressed with arbitrary beam section shape and arbitrary type of loads. The size effect, FG effect, Poisson effect, and the influence of the beam section shape on the mechanical behaviors of viscoelastic FG micro-beams are investigated by taking the simply supported micro-beam subjected to point load as an example. Results show that the size effect on deflection, normal stress and couple stress are obvious when the size of the micro-beam is small enough, and the FG effects are obvious when the size of the micro-beam is large enough. Moreover, the Poisson ratio influences the size effect significantly and the beam section shape is also an important factor influencing the mechanical behavior of the micro-beam.

References:

[1] Witvrouw A, Mehta A. The use of functionally graded poly-SiGe layers for MEMS applications[J]. Materials Science Forum, 2005, 492/493: 255-260. DOI:10.4028/www.scientific.net/msf.492-493.255.
[2] Lü C F, Lim C W, Chen W Q. Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory[J]. International Journal of Solids and Structures, 2009, 46(5): 1176-1185. DOI:10.1016/j.ijsolstr.2008.10.012.
[3] McFarland A W, Colton J S. Role of material microstructure in plate stiffness with relevance tomicrocantilever sensors[J]. Journal of Micromechanics and Microengineering, 2005, 15(5): 1060-1067. DOI:10.1088/0960-1317/15/5/024.
[4] Lam D C C, Yang F, Chong A C M, et al. Experiments and theory in strain gradient elasticity[J]. Journal of the Mechanics and Physics of Solids, 2003, 51(8): 1477-1508. DOI:10.1016/s0022-5096(03)00053-x.
[5] Yang F, Chong A C M, Lam D C C, et al. Couple stress based strain gradient theory for elasticity[J]. International Journal of Solids and Structures, 2002, 39(10): 2731-2743. DOI:10.1016/s0020-7683(02)00152-x.
[6] Ke L L, Yang J, Kitipornchai S, et al. Bending, buckling and vibration of size-dependent functionally graded annular microplates[J]. Composite Structures, 2012, 94(11): 3250-3257. DOI:10.1016/j.compstruct.2012.04.037.
[7] Lei J, He Y M, Zhang B, et al. Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory[J]. International Journal of Engineering Science, 2013, 72: 36-52. DOI:10.1016/j.ijengsci.2013.06.012.
[8] Thai H T, Vo T P, Nguyen T K, et al. Size-dependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory[J]. Composite Structures, 2015, 123: 337-349. DOI:10.1016/j.compstruct.2014.11.065.
[9] Abazid M A, Sobhy M. Thermo-electro-mechanical bending of FG piezoelectric microplates on Pasternak foundation based on a four-variable plate model and the modified couple stress theory[J]. Microsystem Technologies, 2018, 24(2): 1227-1245. DOI:10.1007/s00542-017-3492-8.
[10] 瘙塁im瘙塂ek M, Reddy J N. Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory[J]. International Journal of Engineering Science, 2013, 64: 37-53. DOI:10.1016/j.ijengsci.2012.12.002.
[11] 瘙塁im瘙塂ek M, Kocatürk T, Akba瘙塂 瘙塁 D. Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory[J]. Composite Structures, 2013, 95: 740-747. DOI:10.1016/j.compstruct.2012.08.036.
[12] Chen X C, Li Y H. Size-dependent post-buckling behaviors of geometrically imperfect microbeams[J]. Mechanics Research Communications, 2018, 88: 25-33. DOI:10.1016/j.mechrescom.2017.12.005.
[13] Alshorbagy A E, Eltaher M A, Mahmoud F F. Free vibration characteristics of a functionally graded beam by finite element method[J]. Applied Mathematical Modelling, 2011, 35(1): 412-425. DOI:10.1016/j.apm.2010.07.006.
[14] Akgöz B, Civalek Ö. Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory[J]. Composite Structures, 2013, 98: 314-322. DOI:10.1016/j.compstruct.2012.11.020.
[15] 瘙塁im瘙塂ek M. Size dependent nonlinear free vibration of an axially functionally graded(AFG)microbeam using He’s variational method[J]. Composite Structures, 2015, 131:207-214. DOI:10.1016/j.compstruct.2015.05.004.
[16] Shafiei N, Mirjavadi S S, Afshari B M, et al. Nonlinear thermal buckling of axially functionally graded micro and nanobeams[J]. Composite Structures, 2017, 168: 428-439. DOI:10.1016/j.compstruct.2017.02.048.
[17] Reddy J N, El-Borgi S, Romanoff J. Non-linear analysis of functionally graded microbeams using Eringen’s non-local differential model[J]. International Journal of Non-Linear Mechanics, 2014, 67: 308-318. DOI:10.1016/j.ijnonlinmec.2014.09.014.
[18] Ghayesh M H. Nonlinear dynamics of multilayered microplates[J]. Journal of Computational and Nonlinear Dynamics, 2018, 13(2): 1-12. DOI:10.1115/1.4037596.
[19] Ghayesh M H, Farokhi H. Global dynamics of imperfect axially forced microbeams[J]. International Journal of Engineering Science, 2017, 115: 102-116. DOI:10.1016/j.ijengsci.2017.01.005.
[20] Ghayesh M H, Farokhi H, Gholipour A, et al. On the nonlinear mechanics of layered microcantilevers[J]. International Journal of Engineering Science, 2017, 120: 1-14. DOI:10.1016/j.ijengsci.2017.06.012.
[21] Ghayesh M H, Farokhi H. Nonlinear mechanics of doubly curved shallow microshells[J]. International Journal of Engineering Science, 2017, 119: 288-304. DOI:10.1016/j.ijengsci.2017.06.015.
[22] Gholipour A, Farokhi H, Ghayesh M H. In-plane and out-of-plane nonlinear size-dependent dynamics of microplates[J]. Nonlinear Dynamics, 2015, 79(3): 1771-1785. DOI:10.1007/s11071-014-1773-7.
[23] Hamed E. Bending and creep buckling response of viscoelastic functionally graded beam-columns[J]. Composite Structures, 2012, 94(10): 3043-3051. DOI:10.1016/j.compstruct.2012.04.029.
[24] Ebrahimi F, Barati M R. Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory[J]. Composite Structures, 2017, 159: 433-444. DOI:10.1016/j.compstruct.2016.09.092.
[25] Ghayesh M H. Dynamics of functionally graded viscoelastic microbeams[J]. International Journal of Engineering Science, 2018, 124: 115-131. DOI:10.1016/j.ijengsci.2017.11.004.

Memo

Memo:
Biography: Zhou Bo(1972—), male, doctor, professor, zhoubo@upc.edu.cn.
Foundation items: The National Science and Technology Major Project(No.2017ZX05009-003), the National Key Research and Development Program of China(No.2017YFC0307604), the Talent Foundation of China University of Petroleum(No.Y1215042).
Citation: Zhou Bo, Zheng Xueyao, Kang Zetian, et al.Size-dependent behaviors of viscoelastic axially functionally graded Timoshenko micro-beam considering Poisson effects[J].Journal of Southeast University(English Edition), 2020, 36(2):170-180.DOI:10.3969/j.issn.1003-7985.2020.02.007.
Last Update: 2020-06-20