Orhan S (2007) Analysis of free and forced vibration of a cracked cantilever beam. NDT&E INT 40(6): 443-450.
 Aydogdu M, Taskin V (2007) Free vibration analysis of functionally graded beams with simply supported edges. Mater Des 28(5): 1651-1656.
 Yang J, Chen Y, Xiang Y, Jia X (2008) Free and forced vibration of cracked in homogeneous beams under an axial force and a moving load. J Sound Vib 312(1): 166-181.
 Sina S, Navazi H, Haddadpour H (2009) An analytical method for free vibration analysis of functionally graded beams. Mater Des 30(3): 741-747.
 Bakhsheshy A, Mahbadi H, Khorshidi K (2018) Free vibration analysis of two-dimensional functionally graded annular sector plates with piezoelectric layers resting on two-parameter elastic foundation. Amirkabir Journal of Mechanical Engineering 50(5): 35-38. (In Persian)
 Ke LL, Yang J, Kitipornchai S (2009) Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening. Compos Struct 90(2): 152-160.
 Kitipornchai S, Ke L, Yang J, Xiang Y (2009) Nonlinear vibration of edge cracked functionally graded Timoshenko beams. J Sound Vib 324(3): 962-982.
 Khorshidi K, Ghasemi M, Fallah A (2018) Buckling analysis of functionally graded rectangular microplate in thermal environment based on exponential shear deformation theory using the modified couple stress theory. Journal of Solid and Fluid Mechanics 8 (4): 179-196. (In Persian)
 Şimşek M (2010) Vibration analysis of a functionally graded beam under a moving mass by using different beam theories. Compos Struct 92(4): 904-917.
 Rezaee M, Shaterian-Alghalandis V(2020) An Analytical Method for Damped Free Vibration Analysis of a Cracked Beam Considering the Coupled Multimode Equations. Amirkabir Journal of Mechanical Engineering 52(1): 41-44. (In Persian)
 Rezaee M, Hassannejad R (2011) A new approach to free vibration analysis of a beam with a breathing crack based on mechanical energy balance method. ACTA Mech Solida Sin 24(2): 185-194.
 Yan T, Yang J (2011) Forced vibration of edge-cracked functionally graded beams due to a transverse moving load. Procedia Eng 14: 3293-3300.
 Khorshidi K, Bakhsheshi A, Ghadirian H (2016)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 6(3): 137-147. (In Persian)
 Ebrahimi-Mamaghani A, Sotudeh-Gharebagh R, Zarghami R, Mostoufi N (2020) Thermo-mechanical stability of axially graded Rayleigh pipes. Mech Based Des Struc 1-30.
 Zheng T, Ji T (2012) An approximate method for determining the static deflection and natural frequency of a cracked beam. J Sound Vib 331(11): 2654-2670.
 Zhu X, Lu Z, Wang Z, Xue L, Ebrahimi-Mamaghani A (2020) Vibration of spinning functionally graded nanotubes conveying fluid. Eng Comput 1-22.
 Wei D, Liu Y, Xiang Z (2012) An analytical method for free vibration analysis of functionally graded beams with edge cracks. J Sound Vib 331(7): 1686-1700.
 Ebrahimi-Mamaghani A, Forooghi A, Sarparast H, Alibeigloo A, Friswell MI (2021) Vibration of viscoelastic axially graded beams with simultaneous axial and spinning motions under an axial load. Appl Math Model 90: 131-150.
 Mirtalebi, SH, Ebrahimi-Mamaghani A, Ahmadian MT (2019) Vibration control and anufacturing of intelligibly designed axially functionally graded cantilevered macro/micro-tubes. IFAC Papersonline 52(10): 382-387. Eskandarzadeh Sabet A, Jabari m (2020) Study of functional materials (FGM) Properties and their application in different industries. Journal of Iranian Ceramic Society 2(62): 52-65. (In Persian)
 Banerjee A, Panigrahi B, Pohit G (2016) Crack modelling and detection in Timoshenko FGM beam under transverse vibration using frequency contour and response surface model with GA. Nondestruct Test Eval 31(2): 142-164.
 Timoshenko SP, Woinowsky-Krieger S (1959) Theory of plates and shells. McGraw-hill.
 Arbind A, Reddy JN, Srinivasa AR (2014) Modified couple stress-based third-order theory for nonlinear analysis of functionally graded beams. Lat Am J Solids Stru 11(3): 459-487.