[1] Koizumi, M., The concept of FGM, Ceramic Transactions, 34, 1993, 3–10.
[2] Suresh, S., Mortensen, A., Fundamentals of Functionally Graded Materials, IOM Communications, London, 1998.
[3] Kieback, B., Neubrand, A., Riedel, H., Processing techniques for functionally graded materials, Materials Science and Engineering: A, 362, 2003, 81-106.
[4] Pourabdy, M., Shishesaz, M., Shahrooi, S., Roknizadeh, S.A.S., Analysis of Axisymmetric Vibration of Functionally-Graded Circular Nano-Plate Based on the Integral Form of the Strain Gradient Model, Journal of Applied and Computational Mechanics, 7(4), 2021, 2196-2220.
[5] Karsh, P.K., Mukhopadhyay, T., Dey, S., Stochastic dynamic analysis of twisted functionally graded plates, Composites Part B: Engineering, 147, 2018, 259-278.
[6] Gupta, A., Talha, M., Singh, B.N., Vibration characteristics of functionally graded material plate with various boundary constraints using higher order shear deformation theory, Composites Part B: Engineering, 94, 2016, 64-74.
[7] Fazzolari, F.A., Natural frequencies and critical temperatures of functionally graded sandwich plates subjected to uniform and non-uniform temperature distributions, Composite Structures, 121, 2014, 197-210.
[8] Zhang, W., Liu, T., Xi, A., Wang, Y.N., Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes, Journal of Sound and Vibration, 423, 2018, 65-99.
[9] Wang, Y., Ye, C., Zu, J.W., Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities, Applied Mathematics and Mechanics, 39(11), 2018, 1587-1604.
[10] Liu, Y.Z., Hao, Y.X., Zhang, W., Chen, J., Li, S.B., Nonlinear dynamics of initially imperfect functionally graded circular cylindrical shell under complex loads, Journal of Sound and Vibration, 348, 2015, 294-328.
[11] Strozzi, M., Pellicano, F., Nonlinear vibrations of functionally graded cylindrical shells, Thin-Walled Structures, 67, 2013, 63-77.
[12] Shafiei, N., Kazemi, M., Ghadiri, M., Nonlinear vibration of axially functionally graded tapered microbeams, International Journal of Engineering Science, 102, 2016, 12-26.
[13] Simsek, M., Nonlinear static and free vibration analysis of microbeams based on the nonlinear elastic foundation using modified couple stress theory and He’s variational method, Composite Structures, 112, 2014, 264-272.
[14] Abouelregal, A.E., Mohammad-Sedighi, H., Faghidian, S.A., Shirazi, A.H., Temperature-dependent physical characteristics of the rotating nonlocal nanobeams subject to a varying heat source and a dynamic load, Facta Universitatis, Series: Mechanical Engineering, 19(4), 2021, 633-656.
[15] Sedighi, H.M., Shirazi, K.H., Noghrehabadi, A.R., Yildirim, A., Asymptotic investigation of buckled beam nonlinear vibration, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 36(M2), 2012, 107-116.
[16] Jena, S.K., Chakraverty, S., Malikan, M., Sedighi, H.M., Implementation of Hermite–Ritz method and Navier’s technique for vibration of functionally graded porous nanobeam embedded in Winkler–Pasternak elastic foundation using bi-Helmholtz nonlocal elasticity, Journal of Mechanics of Materials and Structures, 15(3), 2020, 405-434.
[17] Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M., Mansour, A., Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position, Applied Mathematics and Computation, 235, 2014, 512-529.
[18] Eltaher, M.A., Alshorbagy, A.E., Mahmoud, F.F., Vibration analysis of Euler–Bernoulli nanobeams by using finite element method, Applied Mathematical Modelling, 37(7), 2012, 4787-4797.
[19] Bashiri, A.H., Akbas, S.D., Abdelrahman, A.A., Assie, A., Eltaher, M.A., Mohamed, E.F., The vibration of multilayered functionally graded deep beams under thermal load, Geomechanics and Engineering, 24(6), 2021, 545-557.
[20] Alnujaie, A., Akbas, S.D., Eltaher, M.A., Assie, A.E., Damped forced vibration analysis of layered functionally graded thick beams with porosity, Smart Structures and Systems, 27(4), 2021, 679-689.
[21] Asiri, S.A., Akbaş, S.D., Eltaher, M.A., Dynamic analysis of layered functionally graded viscoelastic deep beams with different boundary conditions due to a pulse load, International Journal of Applied Mechanics, 12(05), 2020, 2050055.
[22] Jena, S.K., Chakraverty, S., Malikan, M., Sedighi, H.M., Implementation of Hermite–Ritz method and Navier’s technique for vibration of functionally graded porous nanobeam embedded in Winkler–Pasternak elastic foundation using bi-Helmholtz nonlocal elasticity, Journal of Mechanics of Materials and Structures, 15(3), 2020, 405-434.
[23] Shabani, S., Cunedioglu, Y., Free vibration analysis of functionally graded beams with cracks, Journal of Applied and Computational Mechanics, 6(4), 2020, 908-919.
[24] Su, Z., Jin, G., Ye, T., Vibration analysis of multiple-stepped functionally graded beams with general boundary conditions, Composite Structures, 186, 2018, 315-323.
[25] Lee, J.W., Lee, J.Y., Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression, International Journal of Mechanical Sciences, 122, 2017, 1-17.
[26] Jing, L.L., Ming, P.J., Zhang, W.P., Fu, L.R., Cao, Y.P., Static and free vibration analysis of functionally graded beams by combination Timoshenko theory and finite volume method, Composite Structures, 138, 2015, 192-213.
[27] Li, S.R., Wan, Z.Q., Zhang, J.H., Free vibration of functionally graded beams based on both classical and first-order shear deformation beam theories, Applied Mathematics and Mechanics, 35(5), 2014, 591-606.
[28] Liu, Y., Shu, D.W., Free vibration analysis of exponential functionally graded beams with a single delamination, Composites Part B: Engineering, 59, 2014, 166-172.
[29] Cao, D., Gao, Y., Yao, M., Zhang, W., Free vibration of axially functionally graded beams using the asymptotic development method, Engineering Structures, 173, 2018, 442-448.
[30] Li, X.F., Kang, Y.A., Wu, J.X., Exact frequency equations of free vibration of exponentially functionally graded beams, Applied Acoustics, 74(3), 2013, 413-420.
[31] Akgöz, B., Civalek, Ö., Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM), Composites Part B: Engineering, 55, 2013, 263-268.
[32] Shahba, A., Rajasekaran, S., Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials, Applied Mathematical Modelling, 36(7), 2012, 3094-3111.
[33] Alshorbagy, A.E., Eltaher, M.A., Mahmoud, F.F., Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35(1), 2011, 412-425.
[34] Fariborz, J., Batra, R.C., Free vibration of bi-directional functionally graded material circular beams using shear deformation theory employing logarithmic function of radius, Composite Structures, 210, 2019, 217-230.
[35] Ahlawat, N., Numerical solution for buckling and vibration of bi-directional FGM circular plates, AIP Conference Proceedings, 2061, 2019, 020020.
[36] Pydah, A., Sabale, A., Static analysis of bi-directional functionally graded curved beams, Composite Structures, 160, 2017, 867-876.