[1] Reddy J (2000) Analysis of functionally graded plates. Int J Numer Meth Eng 47(1-3): 663-684.
[2] Kim N-I, Lee J (2017) Coupled vibration characteristics of shear flexible thin-walled functionally graded sandwich I-beams. Compos Part B-Eng 110(6): 229-247.
[3] Shen HS (2016) Functionally graded materials: nonlinear analysis of plates and shells. CRC press, New York.
[4] Chi S, Chung Y (2006) Mechanical behavior of functionally graded material plates under transverse load-Part I: Analysis. Int J Solids Struct 43(13): 3657-3674.
[5] Sankar B (2001) An elasticity solution for functionally graded beams. Compos Sci Technol 61(5):689-696.
[6] Zhong Z, Yu T (2007) Analytical solution of a cantilever functionally graded beam. Compos Sci Technol 67(3):481-488.
[7] Ding H, Huang D, Chen W (2007) Elasticity solutions for plane anisotropic functionally graded beams. Int J Solids Struct 44(1):176-196.
[8] Lü C, Chen W, Xu R, Lim CW (2008) Semi-analytical elasticity solutions for bi-directional functionally graded beams. Int J Solids Struct 45(1):258-275.
[9] Chen W, Chang H (2017) Closed-Form Solutions for Free Vibration Frequencies of Functionally Graded Euler-Bernoulli Beams. Mech Compos Mater 53(1):79-98.
[10] Aydogdu M, Taskin V (2007) Free vibration analysis of functionally graded beams with simply supported edges. Mater Design 28(5):1651-1656.
[11] Li X-F (2008) A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams. J Sound Vib 318(4):1210-1229.
[12] Sina S, Navazi H, Haddadpour H (2009) An analytical method for free vibration analysis of functionally graded beams. Mater Design 110:229-247.
[13] Şimşek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl Eng Des 240(4): 697-705.
[14] Kang J-H, Leissa AW (2004) Three-dimensional vibration analysis of thick, tapered rods and beams with circular cross-section. Int J Mech Sci 46(6): 929-944.
[15] Zhao Y, Huang Y, Guo M (2017) A novel approach for free vibration of axially functionally graded beams with non-uniform cross-section based on Chebyshev polynomials theory. Compos Struct 168: 277-284.
[16] Elishakoff I (2004) Eigenvalues of inhomogeneous structures: unusual closed-form solutions. CRC Press.
[17] Huang Y, Li X-F (2010) A new approach for free vibration of axially functionally graded beams with non-uniform cross-section. J Sound Vib 329(11): 2291-2303.
[18] Jafari A, Fathabadi, M (2013) Forced vibration of FGM Timoshenko beam with piezoelectric layers carrying moving load. Aerospace Mechanics Journal 9(2): 69-77. (In Persian)
[19] Mousavi Z, Saidi A (2016) Free Vibration Analysis of Thick Functionally Graded Rectangular Plates Based on The Higher-Order Shear and Normal Deformable. Aerospace Mechanics Journal 12(1): 1-12. (In Persian)
[20] Bazkiaei A, Tarzajani H, Mohammadi N (2017) Free Vibration Analisys Of Thin Functionally Graded Materials Plates On Winkler Elastic Foundation By Differential Quadrature Element Method. Journal of Modeling in Engineering 15(4): 89-99. (In Persian)
[21] Rahmani B, Gholami F (2015) Robust vibration control of a functionally graded cracked beam. J Sci Technol Compos 2(6): 41-52.
[22] Shahba A, Attarnejad R, Marvi MT, Hajilar S (2011) Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions. Compos Part B-Eng 42 (4): 801-808.
[23] Li X-F, Xi L-Y, Huang Y (2011) Stability analysis of composite columns and parameter optimization against buckling. Compos Part B-Eng 42(6): 1337-1345.
[24] Chakrabarti A, Ray P, Bera RK (2010) Large amplitude free vibration of a rotating nonhomogeneous beam with nonlinear spring and mass system. J Vib Acoust 110(3): 229-247.
[25] Wang C, Wang C (2012) Exact vibration solution for exponentially tapered cantilever with tip mass. J Vib Acoust 134 (4): 12-41.
[26] Gilat R, Calio I, Elishakoff I (2010) Inhomogeneous beams possessing an exponential mode shape. Mech Res Commun 37(4): 417-426.
[26] Karnovsky I, Lebed O (2000) Formulas for structural dynamics: tables, graphs and solutions. McGraw Hill Professional.
[27] Suppiger EW, Taleb NJ (1956) Free lateral vibration of beams of variable cross section. Z Angew Math Phys (ZAMP) 7(6): 501-520.
[28] Cranch E, Adler AA (1956) Bending vibrations of variable section beams. J Appl Mech 23(1): 103-108.
[29] Ece MC, Aydogdu M, Taskin V (2007) Vibration of a variable cross-section beam. Mech Res Commun 34(1): 78-84.
[30] Ait Atmane H, Tounsi A, Meftah SA, Belhadj HA (2011) Free vibration behavior of exponential functionally graded beams with varying cross-section. J Vib Control 17(2): 311-318.
[31] Stephen N (2006) The second spectrum of Timoshenko beam theory—Further assessment. J Sound Vib 292(1): 372-389.
[32] Tong X, Tabarrok B, Yeh K (1995) Vibration analysis of Timoshenko beams with non-homogeneity and varying cross-section. J Sound Vib 186(5): 821-835.
[33] Hosseini R, Ebrahimi mamaghani A, Nouri M (2017) An experimental investigation into width reduction effect on the efficiency of piezopolymer vibration energy harvester. Journal of Solid and Fluid Mechanics 7(3): 41-51. (In Persian)
[34] Hosseini R, Hamedi M, Ebrahimi Mamaghani A, Kim HC, Kim J, Dayou J (2017b) Parameter identification of partially covered piezoelectric cantilever power scavenger based on the coupled distributed parameter solution. Int J Smart Nano Mater 8(2-3): 110-124.
[35] Mamaghani AE, Khadem S, Bab S (2016) Vibration control of a pipe conveying fluid under external periodic excitation using a nonlinear energy sink. Nonlinear Dynam 86(3): 1761-1795.
[36] Mamaghani AE, Khadem SE, Bab S, Pourkiaee SM (2018) Irreversible passive energy transfer of an immersed beam subjected to a sinusoidal flow via local nonlinear attachment. Int J Mech Sci 138(1): 427-447.
[37] Mamaghani AE, Zohoor H, Firoozbakhsh K, Hosseini R (2013) Dynamics of a running below-knee prosthesis compared to those of a normal subject. Journal of Solid Mechanics 5(2): 152-160.
)