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 M. Koizumi, FGM activities in Japan, Composites, Part B: Engineering. 28(1) (1997) 1–4.
 T. Nguyen, T. Vo, H. Thai, Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory, Compos. Part B. 55 (2013) 147-157.
 S. Suresh, A. Mortensen, Fundamentals of Functionally Graded Materials, IOM Communications Limited, London, (1998).
 H. Su, J.R. Banerjee, C.W. Cheung, Dynamic stiffness formulation and free vibration analysis of functionally graded beams, Composite Structures. 106 (2013) 854-862.
 R. Kadoli, K. Akhtar, N. Ganesan, Static analysis of functionally graded beams using higher order shear deformation theory, Applied Mathematical Modelling. 32 (2008) 2509-2525.
 C. Jin, X. Wang, Accurate free vibration analysis of Euler functionally graded beams by the weak form quadrature element method, Composite Structures. 125 (2015) 41-50.
 H. Yaghoobi, A. Fereidoon, Influence of neutral surface position on deflection of functionally graded beam under uniformly distributed load, World Applied Science Journal. 10 (2010) 337-341.
 X.L. Jia et al., Size effect on the free vibration of geometrically nonlinear functionally graded micro-beams under electrical actuation and temperature change, Composite Structures. 133 (2015) 1137-1148.
 F. Ebrahimi, E. Salari, Thermal buckling and free vibration analysis of size dependent timoshenko FG nanobeams, in thermal environments, Composite Structures. 128 (2015) 363-380.
 K. K Pradhan, S. Chakraverty, Effects of different shear deformation theories on free vibration of functionally graded beams, International Journal of Mechanical Sciences. 82 (2014) 149-160.
 D. Chen, J. Yang, S. Kitipornchai, Elastic buckling and static bending of shear deformable functionally graded porous beam, Composite Structures. 133 (2015) 54-61.
 F. Ebrahimi, M. Zia, Large amplitude nonlinear vibration analysis of functionally graded timoshenko beams with porosities, Acta Astronautica. 116 (2015) 117-125.
 M. Hemmatnezhad, R. Ansari, G. H. Rahimi, Large-amplitude free vibrations of functionally graded beams by means of a finite element formulation, Applied Mathematical Modelling. 37 (2013) 8495–8504.
 X.F. Li, Y.A. Kang, J.X. Wu, Exact frequency equations of free vibration of exponentially functionally graded beams, Applied Acoustics. 74 (2013) 413-420.
 Y. Huang, Q. Luo, A simple method to determine the critical buckling loads for axially inhomogeneous beams with elastic restraint, Computers and Mathematics with Applications. 61 (2011) 2510-2517.
 B. Akgöz, Ö. Civalek, Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modiﬁed couple stress theory, Composite Structures. 98 (2013) 314-322.
 A. Shahba et al., Free vibration and stability analysis of axially functionally graded tapered timoshenko beams with classical and non-classical boundary conditions, Composites: Part B 42 (2011) 801-808.
 Y. Huang, L. Yang, Q. Luo, Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section, Composites: Part B. 45 (2013) 1493-1498.
 A. Shahba, S. Rajasekaran, Free vibration and stability of tapered euler–bernoulli beams made of axially functionally graded materials, Applied Mathematical Modelling. 36 (2012) 3094-3111.
 H. Zeighampour, Y.T. Beni, Free vibration analysis of axially functionally graded nanobeam with radius varies along the length based on strain gradient theory, Applied Mathematical Modelling. 39 (2015) 5354-5369.
 N. Kien, Large displacement response of tapered cantilever beams made of axially functionally graded material, Composites: Part B. 55 (2013) 298–305.
 S. Kumar, A. Mitra, H. Roy, Geometrically nonlinear free vibration analysis of axially functionally graded taper beams, Engineering Science and Technology, an International Journal. 18 (2015) 579-593.
 K. Sarkar, R. Ganguli, Closed-form solutions for axially functionally graded timoshenko beams having uniform cross-section and ﬁxed–ﬁxed boundary condition, Composites: Part B. 58 (2014) 361-370.
 M.H. Yas, N. Samadi, Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation, International Journal of Pressure Vessels and Piping. 98 (2012) 119-128.
 M. Simsek, S. Cansız, Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load, Composite Structures. 94 (2012) 2861-2878.
 J. Murin et al., Modal analysis of the FGM beams with effect of axial force under longitudinal variable elastic winkler foundation, Engineering Structures. 49 (2013) 234-247.
 M. Simsek, J.N. Reddy, A unified higher order beam theory for buckling of a functionally graded microbeam embedded in elastic medium using modified couple stress theory, Composite Structures. 101 (2013) 47-58.
 B. Akgöz, Ö. Civalek, Bending analysis of fg microbeams resting on winkler elastic foundation via strain gradient elasticity, Composite Structures. 134 (2015) 294-301.
 A.S. Kanani et al., Effect of nonlinear elastic foundation on large amplitude free and forced vibration of functionally graded beam, Composite Structures. 115 (2014) 60-68.
 H. Niknam, M.M. Aghdam, A semi analytical approach for large amplitude free vibration and buckling of nonlocal FG beams resting on elastic foundation, Composite Structures. 119 (2015) 452-462.
 R. K. Gupta et al., Relatively simple finite element formulation for the large amplitude free vibrations of uniform beams, Fin. El. Anal. Des. 45 (2009) 624-631.
 H. Lohar, A. Mitra, S. Sahoo, "Large amplitude forced vibration analysis of an axially functionally graded tapered beam resting on elastic foundation", Materials Today: Proceedings, Vol. 5, p. 5303, 2018DOI: https://doi.org/10.1016/j.matpr.2017.12.114
 H. Lohar, A. Mitra, S. Sahoo, "Geometrically Non-Linear Frequency Response of Axially Functionally Graded Beams Resting on Elastic Foundation Under Harmonic Excitation", International Journal of Manufacturing, Materials, and Mechanical Engineering, Vol. 8, p. 23, 2018DOI: https://doi.org/10.4018/IJMMME.2018070103