Subject Areas :
Research On Surface Engineering and Nanomaterials Science
بهروز آرین نژاد
1
,
مهران فاضلی
2
1 - گروه مهندسی مکانیک، واحد اهواز، دانشگاه آزاد اسلامی، اهواز، ایران
2 - گروه مهندسی مکانیک، واحد اهواز، دانشگاه آزاد اسلامی، اهواز، ایران
Received: 2023-04-30
Accepted : 2023-06-10
Published : 2023-05-22
Keywords:
References:
-L. Kuo, T. Masuzawa, M. Fujino, A micropipe fabrication process, in: Micro Electro Mechanical Systems, 1991, MEMS'91, Proceedings. An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots. IEEE, (1991) 80-85.
Fleck, G. Muller, M. Ashby, J. Hutchinson, Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia, 42 (1994) 475-487.
Stölken, A. Evans, A microbend test method for measuring the plasticity length scale, Acta Materialia, 46 (1998) 5109-5115.
Lam, F. Yang, A. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51 (2003) 1477-1508.
W. McFarland, J.S. Colton, Role of material microstructure in plate stiffness with relevance to microcantilever sensors, Journal of Micromechanics and Microengineering, 15 (2005) 1060.
Mindlin, H. Tiersten, Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11 415-448 (1962).
Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, 11 (1962) 385-414.
Koiter, Couple stresses in the theory of elasticity, I and II, in: Nederl. Akad. Wetensch. Proc. Ser. B,( 1964) 17-29.
Zhou, Z. Li, Length scales in the static and dynamic torsion of a circular cylindrical micro-bar, Journal of Shandong university of technology, 31 (2001) 401-407.
Kang, Z. Xi, Size effect on the dynamic characteristic of a micro beam based on cosserat theory, Journal of Mechanical Strength, 29 (2007) 1-4.
Yang, A. Chong, D. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39 (2002) 2731-2743.
Kong, S. Zhou, Z. Nie, K. Wang, The size-dependent natural frequency of Bernoulli–Euler micro-beams, International Journal of Engineering Science, 46 (2008) 427-437.
Ma, X.-L. Gao, J. Reddy, A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids, 56 (2008) 3379-3391.
Asghari, M. Kahrobaiyan, M. Ahmadian, A nonlinear Timoshenko beam formulation based on the modified couple stress theory, International Journal of Engineering Science, 48 (2010) 1749-1761.
Jomehzadeh, H. Noori, A. Saidi, The size-dependent vibration analysis of micro-plates based on a modified couple stress theory, Physica E: Low-dimensional Systems and Nanostructures, 43 (2011) 877-883.
Wang, Size-dependent vibration characteristics of fluid-conveying microtubes, Journal of Fluids and Structures, 26 (2010) 675-684.
Xia, L. Wang, Microfluid-induced vibration and stability of structures modeled as microscale pipes conveying fluid based on non-classical Timoshenko beam theory, Microfluidics and nanofluidics, 9 (2010) 955-962.
Ahangar, G. Rezazadeh, R. Shabani, G. Ahmadi, A. Toloei, On the stability of a microbeam conveying fluid considering modified couple stress theory, International Journal of Mechanics and Materials in Design, 7 (2011) 327-342.
-Z. Yang, S. Ji, X.-D. Yang, B. Fang, Microfluid-induced nonlinear free vibration of microtubes, International Journal of Engineering Science, 76 (2014) 47-55.
D. Mindlin, Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures, 1 (1965) 417-438.
Fleck, J. Hutchinson, A reformulation of strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 49 (2001) 2245-2271.
Fleck, J. Hutchinson, Strain gradient plasticity, Advances in applied mechanics, 33 (1997) 295-361.
Kong, S. Zhou, Z. Nie, K. Wang, Static and dynamic analysis of micro beams based on strain gradient elasticity theory, International Journal of Engineering Science, 47 (2009) 487-498.
Kahrobaiyan, M. Asghari, M. Rahaeifard, M. Ahmadian, A nonlinear strain gradient beam formulation, International Journal of Engineering Science, 49 (2011) 1256-126 7.
Asghari, M. Kahrobaiyan, M. Nikfar, M. Ahmadian, A size-dependent nonlinear Timoshenko microbeam model based on the strain gradient theory, Acta Mechanica, 223 (2012) 1233-1249.
Zhao, S. Zhou, B. Wang, X. Wang, Nonlinear microbeam model based on strain gradient theory, Applied Mathematical Modelling, 36 (2012) 2674-2686.
Ramezani, A micro scale geometrically non-linear Timoshenko beam model based on strain gradient elasticity theory, International Journal of Non-Linear Mechanics 47, (2012) 873-863.
Rajabi, S. Ramezani, A nonlinear microbeam model based on strain gradient elasticity theory with surface energy, Archive of Applied Mechanics, 82 (2012) 363-376.
H. Ghayesh, M. Amabili, H. Farokhi, Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory, International Journal of Engineering Science, 63 (2013) 52-60.
Wang, S. Zhou, J. Zhao, X. Chen, A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory, European Journal of Mechanics-A/Solids, 30 (2011) 517-524.
Ramezani, A shear deformation micro-plate model based on the most general form of strain gradient elasticity, International Journal of Mechanical Sciences, 57 (2012) 34-42.
L. Yin, Q. Qian, L. Wang, Strain gradient beam model for dynamics of microscale pipes conveying fluid, Applied Mathematical Modelling, 35 (2011) 2864-2873.
Farshidianfar A, Samadi F. A microstructure-dependent Timoshenko beam model for vibration analysis of micropipes conveying fluid based on strain gradient theory. In19th International Congress on Sound and Vibration,(2012).
Al-Basyouni KS, Tounsi A, Mahmoud SR. Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position. Composite Structures.125(2015)621-30.
Thai CH, Ferreira AJ, Nguyen-Xuan H. Isogeometric analysis of size-dependent isotropic and sandwich functionally graded microplates based on modified strain gradient elasticity theory. Composite Structures. 192(2018)274-88.
Yu T, Zhang J, Hu H, Bui TQ. A novel size-dependent quasi-3D isogeometric beam model for two-directional FG microbeams analysis. Composite Structures. 211(2019)76-88.
Hu H, Yu T, Bui TQ. Functionally graded curved Timoshenko microbeams: A numerical study using IGA and modified couple stress theory. Composite Structures. 254(2020)112841.
Dinachandra M, Alankar A. Static and dynamic modeling of functionally graded Euler–Bernoulli microbeams based on reformulated strain gradient elasticity theory using isogeometric analysis. Composite Structures. 280(2022)114923.
Païdoussis, F.S. Interactions, Slender Structures and Axial Flow, vol, in, 1Academic Press, London, 1998.
Zhang, X. Liu, J. Zhao, Influence of temperature change on column buckling of multiwalled carbon nanotubes, Physics Letters A, 372 (2008) 1676-1681.
B. Benjamin, Dynamics of a system of articulated pipes conveying fluid. II. Experiments, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 261 (1961) 487-499.
Nayfeh, D. Mook, Nonlinear oscillations. 1979, John Willey and Sons, New York.
Liu, G.R. and Gu, Y.T.An introduction to meshfree methods and their programming.(2005)Springer Science & Business Media.