1. Li X, Bhushan B, Takashima K, Baek CW, Kim YK. Mechanical characterization of micro/nanoscale structures for MEMS/NEMS applications using nanoindentation techniques. Ultramicroscopy. 2003;97(1-4):481-94. [
Link] [
DOI:10.1016/S0304-3991(03)00077-9]
2. de Souza Pereira R. Atomic force microscopy as a novel pharmacological tool. Biochemical Pharmacology. 2001;62(8):975-83. [
Link] [
DOI:10.1016/S0006-2952(01)00746-8]
3. McFarland AW, Colton JS. Role of material microstructure in plate stiffness with relevance to microcantilever sensors. Journal of Micromechanics and Microengineering, 2005;15(5):1060-7. [
Link] [
DOI:10.1088/0960-1317/15/5/024]
4. Yang F, Chong ACM, Lam DCC, Tong P. Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures. 2002;39(10):2731-43. [
Link] [
DOI:10.1016/S0020-7683(02)00152-X]
5. Mindlin RD. Influence of couple-stresses on stress concentrations. Experimental Mechanics. 1963;3(1):1-7. [
Link] [
DOI:10.1007/BF02327219]
6. Mindlin RD, Tiersten HF. Effects of couple-stresses in linear elasticity. Archive for Rational Mechanics and Analysis. 1962;11(1):415-48. [
Link] [
DOI:10.1007/BF00253946]
7. Toupin RA. Theories of elasticity with couple-stress. Archive for Rational Mechanics and Analysis. 1964;17(2):85-112. [
Link] [
DOI:10.1007/BF00253050]
8. Asghari M, Rahaeifard M, Kahrobaiyan MH, Ahmadian MT. The modified couple stress functionally graded Timoshenko beam formulation. Materials & Design. 2011;32(3):1435-43. [
Link] [
DOI:10.1016/j.matdes.2010.08.046]
9. Salamat-talab M, Nateghi A, Torabi J. Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory. International Journal of Mechanical Sciences. 2012;57(1):63-73. [
Link] [
DOI:10.1016/j.ijmecsci.2012.02.004]
10. Akgöz B, Civalek Ö. Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory. Composite Structures. 2013;98:314-22. [
Link] [
DOI:10.1016/j.compstruct.2012.11.020]
11. Şimşek M, Reddy JN. Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory. International Journal of Engineering Science. 2013;64:37-53. [
Link] [
DOI:10.1016/j.ijengsci.2012.12.002]
12. 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. 2015;125:621-30. [
Link] [
DOI:10.1016/j.compstruct.2014.12.070]
13. Ganapathi M, Polit O. Dynamic characteristics of curved nanobeams using nonlocal higher-order curved beam theory. Physica E: Low-dimensional Systems and Nanostructures. 2017;91:190-202. [
Link] [
DOI:10.1016/j.physe.2017.04.012]
14. Ghodssi R, Lin P, editors. MEMS materials and processes handbook. Volume 1. New York: Springer; 2011. [
Link] [
DOI:10.1007/978-0-387-47318-5]
15. David M, Kishi T, Kisaku M, Nakanishi H, Kasai H. Carbon nanoarch encapsulating Fe nanowire on Ni (111). Japanese Journal of Applied Physics. 2006;45(4A):2869. [
Link] [
DOI:10.1143/JJAP.45.2869]
16. Mohammadi H, Mahzoon M, Mohammadi M, MohammadiM. Postbuckling instability of nonlinear nanobeam with geometric imperfection embedded in elastic foundation. Nonlinear Dynamics. 2014;76(4):2005-16. [
Link] [
DOI:10.1007/s11071-014-1264-x]
17. Liu Y, Reddy J. A nonlocal curved beam model based on a modified couple stress theory. International Journal of Structural Stability and Dynamics, 2011;11(3):495-512. [
Link] [
DOI:10.1142/S0219455411004233]
18. Yang F, Sedaghati R, Esmailzadeh E. Free in-plane vibration of curved beam structures: a tutorial and the state of the art. Journal of Vibration and Control. 2018;24(12):2400-17. [
Link] [
DOI:10.1177/1077546317728148]
19. Fang J, Gu J, Wang H. Size-dependent three-dimensional free vibration of rotating functionally graded microbeams based on a modified couple stress theory. International Journal of Mechanical Sciences. 2018;136:188-99. [
Link] [
DOI:10.1016/j.ijmecsci.2017.12.028]
20. Rahmani O, Hosseini SAH, Ghoytasi I, Golmohammadi H. Free vibration of deep curved FG nano-beam based on modified couple stress theory. Steel and Composite Structures. 2018;26(5):607-20. [
Link]
21. Najafi F, Shojaeefard MH, Googarchin HS. Nonlinear dynamic response of FGM beams with Winkler-Pasternak foundation subject to noncentral low velocity impact in thermal field. Composite Structures. 2017;167:132-43. [
Link] [
DOI:10.1016/j.compstruct.2017.01.063]
22. Deng H, Chen K, Cheng W, Zhao S. Vibration and buckling analysis of double-functionally graded Timoshenko beam system on Winkler-Pasternak elastic foundation. Composite Structures. 2017;160:152-68. [
Link] [
DOI:10.1016/j.compstruct.2016.10.027]
23. Ghorbanpour Arani A, BabaAkbar-Zarei H, Pourmousa P, Eskandari M. Investigation of free vibration response of smart sandwich micro-beam on Winkler-Pasternak substrate exposed to multi physical fields. Microsystem Technologies. 2018;24(7):3045-60. [
Link] [
DOI:10.1007/s00542-017-3681-5]
24. Sobhy M, Zenkour AM. The modified couple stress model for bending of normal deformable viscoelastic nanobeams resting on visco-Pasternak foundations. Mechanics of Advanced Materials and Structures. 2018:1-14. [
Link] [
DOI:10.1080/15376494.2018.1482579]
25. Moradi Dastjerdi R, Payganeh G, Rajabizadeh Mirakabad S, Jafari Mofrad-Taheri M. Static and free vibration analyses of functionally graded nano-composite plates reinforced by wavy carbon nanotubes resting on a Pasternak elastic foundation. Mechanics of Advanced Composite Structures. 2016;3(2):123-35. [
Link]
26. Bouderba B, Houari MSA, Tounsi A. Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations. Steel and Composite Structures. 2013;14(1):85-104. [
Link] [
DOI:10.12989/scs.2013.14.1.085]
27. Zamanzadeh M, Rezazadeh G, Jafarsadeghi Pournaki I, Shabani R. Thermally induced vibration of a functionally graded micro-beam subjected to a moving laser beam. International Journal of Applied Mechanics. 2014;6(6):1450066. [
Link] [
DOI:10.1142/S1758825114500665]
28. Ghadiri M, Shafiei N. Vibration analysis of rotating functionally graded Timoshenko microbeam based on modified couple stress theory under different temperature distributions. Acta Astronautica. 2016;121:221-40. [
Link] [
DOI:10.1016/j.actaastro.2016.01.003]
29. Akgöz B, Civalek Ö. Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams. Composites Part B: Engineering. 2017;129:77-87. [
Link] [
DOI:10.1016/j.compositesb.2017.07.024]
30. Khorshidi K, Bakhsheshi A, Ghadirian H. The study of the effects of thermal environment on free vibration analysis of two dimensional functionally graded rectangular plates on Pasternak elastic foundation. Journal of solid and fluid mechanics. 2016;6(3):137-47. [Persian] [
Link]
31. Mirjavadi SS, Mohasel afshari B, Shafiei N, Rabby S, Kazemi M. Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale Timoshenko beam. Journal of Vibration and Control. 2018;24(18):1-15. [
Link] [
DOI:10.1177/1077546317721871]
32. Rahmani O, HosseiniI SAH. Ghoytasi I, Golmohammadi H. Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties. Applied Physics A. 2017;123(1):4. [
Link] [
DOI:10.1007/s00339-016-0591-9]
33. Komijani M, Esfahani SE, Reddy JN, Liu YP, Eslami MR. Nonlinear thermal stability and vibration of pre/post-buckled temperature-and microstructure-dependent functionally graded beams resting on elastic foundation. Composite Structures. 2014;112:292-307. [
Link] [
DOI:10.1016/j.compstruct.2014.01.041]
34. Ke LL, Wang YS, Wang ZD. Thermal effect on free vibration and buckling of size-dependent microbeams. Physica E: Low-dimensional Systems and Nanostructures. 2011;43(7):1387-93. [
Link] [
DOI:10.1016/j.physe.2011.03.009]
35. Timoshenko S, Goodier JN. Theory of elasticity. New York: McGraw-Hill; 1970. [
Link]
36. Lam DCC, Yang F, Chong ACM, Wang J, Tong P. Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids. 2003;51(8):1477-508. [
Link] [
DOI:10.1016/S0022-5096(03)00053-X]
37. Ansari R, Gholami R, Sahmani S. Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory. Archive of Applied Mechanics. 2013;83(10):1439-49. [
Link] [
DOI:10.1007/s00419-013-0756-3]