[1] Nayfeh AH, Mook DT (1995) Nonlinear oscillation. Wiley, New York, USA.

[2] Nayfeh AH, Pai PF (2004) Linear and nonlinear structural mechanics.Wiley, New Jersey, USA.

[3] Reissner E (1972) On one dimensional finite strain beam theory, the plane problem. J Appl Mech Tech Phy 23(5): 795-894.

[4] Simo JC (1985) A finite strain beam formulation, the three dimensional dynamic problem, part I, computational methods. Appl Mech Eng 49: 55-70.

[5] Simo JC, Vu-quoc L (1986) A three dimensional finite-strain rod model. part II, Ccmputational aspects, computational methods. Appl Mech Eng 58: 79-116.

[6] Crespodasilva MRM (1988) Nonlinear flexural-flexural-torsional-extensional dynamics of beams-I. Int J Solids Struct 24(12): 1225-1234.

[7] Crespodasilva MRM (1988) Nonlinear flexural-flexural-torsional-extensional dynamics of beams-II, responses analysis. Int J Solids Struct 24(12): 1235-1242.

[8] Singh G, Rao GV, and Iyengar NGR (1990) Re-investigation of large-amplitude free vibrations of beams using finite element. J Sound Vib 143(2): 351-355.

[9] Lewandowski R (1994) Nonlinear free vibration of beams by the finite element and continuation method. J Sound Vib 170(5): 577-593.

[10] Foda MA (1999) Influence of shear deformation and rotary inertia on nonlinear free vibration of beam with pinned ends. Comput Struct 71: 663-670.

[11] Ribeiro P, Petyt M (1999) Nonlinear vibration of beams with internal resonance by the hierarchical and finite element method. J Sound Vib 244(4) 591-624.

[12] Patel BP, Ganapathi M (2001) Nonlinear torsional vibration and damping analysis of sandwich beams. J Sound Vib 240(2): 385-393.

[13] Luczko J (2002) Bifurcations and internal resonances in space curved Rrods. Comput Methods Appl Mech Eng 191: 3271-3296.

[14] Attard MM (2003) Finite strain beam-theory. Int J Solids Struct 40(17): 4563-4584.

[15] Agrawal S, Chakraborty A, Gopaluhrishnan S, (2006) Large deformation analysis for anisotropic and inhomogeneous beams using exact linear static solution. Compos Struct 72: 91-104.

[16] Mata P, Oller S, Barbat AH (2008) Dynamic analysis of beam structures considering geometric and constitutive nonlinearity, computational Mmethod. Appl Mech Eng 197: 857-878.

[17] Gupta RK, Balou GJ, Janardhan GR, Rao GV (2009) Relatively simple finite element formulation for the large amplitude free vibrations of uniform beam. Finite Elem Anal Des 45: 624-631.

[18] Stoykov S, Ribeiro P (2010) Nonlinear forced vibrations and static deformations of 3D beams with rectangular cross sections, the influence of warping, shear deformation and longitudinal displacement. Int J Mech Sci 52(11): 1505-1521.

[19] Ke L-L (2011) Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory. Compos Struct 93: 342-350.

[20] Simsek M, Yurtcu HH (2013) Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Composite Structures 97: 378-386.

[21] Simsek M, Reddy JN (2013) A unified higher order beam theory for buckling of a functionally graded microbeam embedded in elastic medium using modified couple stress theory. Compos Struct 101: 47-58.

[22] Simsek M (2014) Nonlinear static and free vibration analysis of microbeams based on the nonlinear elastic foundation using modified couple stress theory and He’s variational method. Compos Struct 112: 264-272.

[23] Zhang B, He Y, Liu D, Gan Z, Shen L (2013) A novel size-dependent functionally graded curved mircobeam model based on the strain gradient elasticity theory. Compos Struct 106: 374-392.

]24[ عطار ع، طهماسبی پور م، دهقان محمد (1397) بررسی تاثیر پارامترهای هندسی بر جابه‌جایی خارج از صفحه میکروتیر پیزوالکتریکی با سطح مقطع T شکل. مجله علمی پژوهشی مکانیک سازه‌ها و شاره‌ها 9-1 :(4)8.

]25[ سام‌پور س، معین خواه ح، رحمانی ح (1398) حل تحلیلی پاسخ گذرای غیرخطی میکروتیر ویسکوالاستیک با تحریک الکتریکی بر اساس تئوری الاستیسیته ریز قطبی. مجله علمی پژوهشی مکانیک سازه‌ها و شاره‌ها 138-125 :(3)9.

[26] Mamaghani AE, Khadem SE, Bab S (2016) Vibration control of a pipe conveying fluid under external periodic excitation using a nonlinear energy sink. Nonlinear Dyn 86(3): 1761-1795.

[27] Mamaghani AE, Khadem SE, Bab S (2018) Irreversible passive energy transfer of an immersed beam subjected to a sinusoidal flow via local nonlinear attachment. Int J Mech Sci 138: 427-447

[28] Ebrahimi-Mamaghani A, Khadem SE (2016) Vibration analysis of a beam under external periodic excitation using anonlinear energy sink. Modares Mechanical Engineering 16(9): 186-194. (in Persian)

[29] Ebrahimi-Mamaghani A, Sotudeh-ghrebagh R, Zarghami R, Mostoufi N (2019) Dynamics of two-phase flow in vertical pipes. J Fluid Struct 87: 150-173.

[30] Ebrahimi-Mamaghani A, Mirtalebi SH, Ahmadian MT, Mostoufi N (2020) Magneto-mechanical stability of axially functionally graded supported nanotubes. Mater Res Express 6(12): 1250c5.

[31] Mirtalebi SH, Ebrahimi-Mamaghani A, Ahmadian MT, Mostoufi N (2019) Vibration control and manufacturing of intelligibly designed axially functionally graded cantilevered macro/micro-tubes. IFAC-PapersOnLine 52(10): 382-387.