1 .Aifantis, E.C, Strain gradient interpretation of size effects. Int. J. Fract. 95(1999) 299-314.
2 .Ansari, R. Gholami, R. Faghih Shojaei, M. Mohammadi, V. Sahmani, S., Size-dependent bending, buckling and free vibration of functionally graded Timoshenko microbeams based on the most general strain gradient theory. Compos. Struct. 100 (2013) 385-397.
3 .Ansari, R. Gholami, R. Sahmani, S, Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory. Compos. Struct. 94(2011)221-228.
4 .Asghari. M, Kahrobaiyan, M. H, Ahmadian M.T, A nonlinear Timoshenko beam formulation based on the modified couple stress theory. International Journal of Eng. Sci. 48 (2010a) 1749-1761.
5 .Asghari.M. Ahmadian, M.T, Kahrobaiyan, M.H, Rahaeifard, M, On the size-dependent behavior of functionally graded micro-beams. Materials & Design 31,(2010b) 2324-2329.
6 .Asghari. M, Kahrobaiyan, M.H, Nikfar. M, Ahmadian. M.T, A size-dependent nonlinear Timoshenko microbeam model based on the strain gradient theory. Acta Mech. 223 (2012) 1233-1249.
7 .Beskou. S.P, Polyzos. D, Beskos. D.E, Dynamic analysis of gradient elastic flexural beams. Struct. Eng. Mech. Material 15, (2003a)705-716.
8 .Beskou. S.P, Tsepoura. K.G, Polyzos. D, Bending and stability analysis of gradient elastic beams. Int. J. Solid Struct. 40 (2003b) 385-400.
9 .Boer. M.P.D, Luck. D.L, Ashurst. W.R, High-performance surface-micromachined inchworm actuator. J. Microelectromech. System 13(2004) 63-74.
10 .Danesh. V, Asghari. M, Analysis of micro-rotating disks based on the strain gradient elasticity. Acta Mech.(2013).
11 .Fleck. N.A, Muller. G.M, Ashby. M.F, Strain gradient plasticity: theory and experiment. Acta Metallurgica et Materialia 42, (1994) 475-487.
12 .Ghayesh. M.H, Amabili. M, Farokhi, H, Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory. Int. J. Eng. Sci. 63 (2013) 52-60.
13 .Hall. N.A, Okandan. M, Degertekin. F.L, Surface and bulk-silicon-micromachined optical displacement sensor fabricated with the Swift-Lite process. J. Microelectromechanic System 15 (2006) 770-776.
14 .Kahrobaiyan. M.H, Asghari. M, Ahmadian. M.T, Strain gradient beam element. Finite Elements in Analysis and Design 68 (2013) 63-75.
15 .Kahrobaiyan. M.H, Asghari. M, Rahaeifard. M, Ahmadian. M.T, A nonlinear strain gradient beam formulation. Int. J. Eng. Sci. 49 (2011) 1256-1267.
16 .Kahrobaiyan. M.H, Rahaeifard. M, Tajalli. S.A, Ahmadian. M.T, A strain gradient functionally graded Euler–Bernoulli beam formulation. Int. J. Eng. Sci. 52(2012) 65-76.
17 .Kang. X and Xi. Z.W, Size effect on the dynamic characteristic of a micro beam based on cosserat theory. J. Mech. Strength 29(2007) 1-4.
18 .Ke. L-L, Wang. Y-S, Yang. J, Kitipornchai. S, Nonlinear free vibration of size-dependent functionally graded microbeams. Int. J. Eng. Sci. 50(2012) 256-267.
19 .Kong. S, Zhou. S, Nie. Z, Wang. K, The size-dependent natural frequency of Bernoulli–Euler micro-beams. Int. J. Eng. Sci. 46 ( 2008) 427-437.
20 .Kong. S, Zhou. S, Nie. Z, Wang. K, Static and dynamic analysis of micro beams based on strain gradient elasticity theory. Int. J. Eng. Sci. 47(2009) 487-498.
21 .Lam. D.C.C, Yang. F, Chong. A.C.M, Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solid 51(2003) 1477-1508.
22 .Lun. F.Y, Zhang. P, Gao. F.B, Jia. H.G, Design and fabrication of micro-optomechanical vibration sensor. Microfabrication Tech. 120 (2006) 61-64.
23 .McFarland. A.W, Colton. J.S, Role of material microstructure in plate stiffness with relevance to microcantilever sensors, J. Micromechanic Microengi. 15(2005) 1060-1067.
24 .Mindlin. R.D and Eshel. N.N, On first strain-gradient theories in linear elasticity, Int. J. Solid Struct. 4 (1968)109-124.
25 .Moser. Y, Gijs. M.A.M, Miniaturized flexible temperature sensor. J. Microelectromech. Sys. 16 (2007) 1349-1354.
26 .Ramezani. S, A micro scale geometrically non-linear Timoshenko beam model based on strain gradient elasticity theory. Int. J. Non-Linear Mech. 47(2012) 863-873.
27 .Roy. S.F.S and Mehregany. M, Determination of Young’s modulus and residual stress of electroless nickel using test structures fabricated in a new surface micromachining process. Microsystem Tech. 2(1996) 92-96.
28 .Wang. B, Zhao. J, Zhou. S, A microscale Timoshenko beam model based on strain gradient elasticity theory. Euro J. Mech. A/Solid 29 (2010) 591-599.
29 .Wang. WL, Hu. S.J, Modal response and frequency shift of the cantilever in a noncontact atomic force microscope. App. Physic Letters 87(2005) 18350-18356.
30 .Xia. W, Wang. L, Yin. L, Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration. Int. J. Eng. Sci. 48(2010) 2044-2053.