تحلیل ارتعاشات طولی میله‌های ساخته‌شده از مواد مدرج تابعی بر اساس نظریه گرادیان کرنشی غیرموضعی

[1]   Faruqui S. S. I. Thermal Buckling and Post-Buckling Analysis of FGM Bar. PhD Thesis, Department of Mechanical Eng., Bangladesh University of Engineering and Technology, 2019.

[2]   Fatoni N. F., Park W. R., and Kwon O.-H. Mechanical property evaluation of functionally graded materials using two-scale modeling. Journal of the Korean Society of Marine Engineering, Vol. 41, No. 5, pp. 431–438, 2017.

[3]   Eringen A. C., and Edelen D. G. B. On nonlocal elasticity. Int. J. Eng. Sci., Vol. 10, No. 3, pp. 233–248, 1972.

[4]   Eltaher M. A., Khater M. E., and Emam S. A. A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams. Appl. Math. Model., Vol. 40, No. 5, pp. 4109–4128, 2016.

[5]   Ebrahimi F., Ghadiri M., Salari E., Hoseini S. A. H., and Shaghaghi G. R. Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams. J. Mech. Sci. Technol., Vol. 29, No. 3, pp. 1207–1215, 2015.

[6]   Fotouhi M. M., Firouz-Abadi R. D., and Haddadpour H. Free vibration analysis of nanocones embedded in an elastic medium using a nonlocal continuum shell model. Int. J. Eng. Sci., Vol. 64, pp. 14–22, 2013.

[7]   Li L., Hu Y., and Li X. Longitudinal vibration of size-dependent rods via nonlocal strain gradient theory. Int. J. Mech. Sci., Vol. 115, 135–144, 2016.

[8]   Naderi A., and Saidi A. R. Nonlocal postbuckling analysis of graphene sheets in a nonlinear polymer medium. Int. J. Eng. Sci., Vol. 81, pp. 49–65, 2014.

[9]   Nejad M. Z., Hadi A., Omidvari A., and Rastgoo A. Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen’s non-local elasticity theory. Struct. Eng. Mech., Vol. 67, No. 4, pp. 417–425, 2018.

[10]               Reddy J. N. Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci., Vol. 45, No. 2, pp. 288–307, 2007.

[11]               Reddy J. N., and El-Borgi S. Eringen’s nonlocal theories of beams accounting for moderate rotations. Int. J. Eng. Sci., Vol. 82, pp. 159–177, 2014.

[12]               Mindlin R. D. Microstructure in linear elasticity. Columbia Univ New York Dept of Civil Engineering and Engineering Mechanics, 1963.

[13]               Mindlin R. D., and Eshel N. N. On first strain-gradient theories in linear elasticity. Int. J. Solids Struct., Vol. 4, No. 1, pp. 109–124, 1968.

[14]               Fleck N. A., and Hutchinson J. W. A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids, Vol. 41, No. 12, pp. 1825–1857, 1993.

[15]               Stölken J. S., and Evans A. G. A microbend test method for measuring the plasticity length scale. Acta Mater., Vol. 46, No. 14, pp. 5109–5115, 1998.

[16]               Yang F., Chong A. C. M., Lam D. C. C., and Tong P. Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct., Vol. 39, No. 10, pp. 2731–2743, 2002.

[17]               Mohammad-Abadi M., and Daneshmehr A. R. Size dependent buckling analysis of microbeams based on modified couple stress theory with high order theories and general boundary conditions. Int. J. Eng. Sci., Vol. 74, pp. 1–14, 2014.

[18]               Akgöz B., and Civalek Ö. Bending analysis of FG microbeams resting on Winkler elastic foundation via strain gradient elasticity. Compos. Struct., Vol. 134, pp. 294–301, 2015.

[19]               Lim C. W., Zhang G., and Reddy J. N. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids, Vol. 78, pp. 298–313, 2015.

[20]               Aifantis E. C. On the role of gradients in the localization of deformation and fracture. Int. J. Eng. Sci., Vol. 30, No. 10, pp. 1279–1299, 1992.

[21]               Li L., and Hu Y. Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. Int. J. Eng. Sci., Vol. 97, pp. 84–94, 2015.

[22]               Farajpour A., Yazdi M. H., Rastgoo A., and Mohammadi M. A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment. Acta Mech., Vol. 227, No. 7, pp. 1849–1867, 2016.

[23]               Asghari M., Ahmadian M. T., Kahrobaiyan M. H., and Rahaeifard M. On the size-dependent behavior of functionally graded micro-beams. Mater. Des. (1980-2015), Vol. 31, No. 5, pp. 2324–2329, 2010.

[24]               Kong S., Zhou S., Nie Z., and Wang K. The size-dependent natural frequency of Bernoulli–Euler micro-beams. Int. J. Eng. Sci., Vol. 46, No. 5, pp. 427–437, 2008.

[25]               Alshorbagy A. E., Eltaher M. A., and Mahmoud F. F. Free vibration characteristics of a functionally graded beam by finite element method. Appl. Math. Model., Vol. 35, No. 1, pp. 412–425, 2011.

[26]               Akgöz B., and Civalek Ö. Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM). Compos. Part B Eng., Vol. 55, pp. 263–268, 2013.

[27]               Civalek Ö., Akgöz B., and Deliktaş B. Axial Vibration of Strain Gradient Micro-rods. Handbook of Nonlocal Continuum Mechanics for Materials and Structures, G. Z. Voyiadjis, Ed. Cham: Springer International Publishing, pp. 1–15, 2018.

[28]               Şimşek M. Nonlocal effects in the free longitudinal vibration of axially functionally graded tapered nanorods. Comput. Mater. Sci., Vol. 61, pp. 257–265, 2012.

[29]               Xu X.-J., Zheng M.-L., and Wang X.-C. On vibrations of nonlocal rods: Boundary conditions, exact solutions and their asymptotics. Int. J. Eng. Sci., Vol. 119, pp. 217–231, 2017.

[30]               Koteswara Rao D., Roy Tarapada. Vibration Analysis of Functionally Graded Rotating Shaft System. Procedia Engineering, Vol. 144, pp. 775 – 780, 2016.

[31]               Xu X. J., Zheng M. L., and Wang X. C. On vibrations of nonlocal rods: Boundary conditions, exact solutions and their asymptotics. Int. J. Eng. Sci., Vol. 119, pp. 217–231, 2017.

[32]               Elhannani A., Refassi K., Elmeiche A., and Bouamama M. Vibration analysis of functionally graded tapered rotor shaft system. Mechanics and Mechanical Engineering; Vol. 23, pp. 241–245, 2019.