[1] Koizumi M (1997) FGM activities in Japan. Composites Part B: Engineering 28 (1):1-4
[2] Ebrahimi F (2013) Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment. Mechanics of Advanced Materials and Structures 20 (10):854-870
[3] El-wazery M, El-Desouky A (2015) A review on functionally graded ceramic-metal materials. J Mater Environ Sci 6 (5):1369-1376.
[4] Chmielewski M, Pietrzak K (2016) Metal-ceramic functionally graded materials–manufacturing, characterization, application. Bulletin of the Polish Academy of Sciences Technical Sciences 64 (1):151-160.
[5] Kitipornchai S, Ke L, Yang J, Xiang Y (2009) Nonlinear vibration of edge cracked functionally graded Timoshenko beams. Journal of sound and vibration 324 (3):962-982
[6] Ke L-L, Yang J, Kitipornchai S (2010) Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Composite Structures 92 (3):676-683
[7] Akgöz B, Civalek Ö (2013) Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM). Composites Part B: Engineering 55:263-268
[8] Pradhan K, Chakraverty S (2013) Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritz method. Composites Part B: Engineering 51:175-184
[9] Ansari R, Gholami R, Sahmani S (2013) Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory. Archive of Applied Mechanics 83 (10)
[10] Mashat DS, Carrera E, Zenkour AM, Al Khateeb SA, Filippi M (2014) Free vibration of FGM layered beams by various theories and finite elements. Composites Part B: Engineering 59:269-278
[11] Hadji L, Daouadji T, Tounsi A, Bedia E (2014) A higher order shear deformation theory for static and free vibration of FGM beam. Steel and Composite Structures 16 (5):507-519
[12] Sofiyev A (2015) On the vibration and stability of shear deformable FGM truncated conical shells subjected to an axial load. Composites Part B: Engineering 80:53-62
[13] Chen, Y., Jin, G., Zhang, C., Ye, T., & Xue, Y (2018) Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory Composites Part B: Engineering 153:376-386.
[14] Zhang, K., Ge, M. H., Zhao, C., Deng, Z. C., & Xu, X. J (2019) Free vibration of nonlocal Timoshenko beams made of functionally graded materials by Symplectic method Composites Part B: Engineering 156:174-184.
[15] Wattanasakulpong N, Ungbhakorn V (2014) Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerospace Science and Technology 32 (1):111-120
[16] Ebrahimi F, Zia M (2015) Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities. Acta Astronautica 116:117-125
[17] Chen D, Yang J, Kitipornchai S (2016) Free and forced vibrations of shear deformable functionally graded porous beams. International Journal of Mechanical Sciences 108:14-22
[18] Shafiei N, Mousavi A, Ghadiri M (2016) On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams. International Journal of Engineering Science 106:42-56
[19] Ebrahimi F, Ghasemi F, Salari E (2016) Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica 51 (1):223-249
[20] Taya, M., Almajid, A. A., Dunn, M., & Takahashi, H (2003) Design of bimorph piezo-composite actuators with functionally graded microstructure Sensors and Actuators A: Physical 107(3):248-260.
[21] She, G. L., Ren, Y. R., Yuan, F. G., & Xiao, W. S (2018) On vibrations of porous nanotubes International Journal of Engineering Science 125:23-35.
[22] Li Y, Shi Z (2009) Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature. Composite Structures 87 (3):257-264
[23] Armin A, Behjat B, Abbasi M, Eslami M (2010) Finite element analysis of functionally graded piezoelectric beams. Iran J Mech Eng (English) 11 (1):45-72
[24] Doroushi A, Eslami M, Komeili A (2011) Vibration analysis and transient response of an FGPM beam under thermo-electro-mechanical loads using higher-order shear deformation theory. Journal of Intelligent Material Systems and Structures 22 (3):231-243
[25] Ke L-L, Wang Y-S (2012) Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory. Smart Materials and Structures 21 (2):025018
[26] Barati MR, Zenkour AM (2016) Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions. Journal of Vibration and Control:1077546316672788
[27] Ebrahimi F, Salari E (2016) Thermal loading effects on electro-mechanical vibration behavior of piezoelectrically actuated inhomogeneous size-dependent Timoshenko nanobeams. Advances in Nano Research 4 (3):197-228
[28] Ebrahimi, F., & Barati, M. R (2018) Vibration analysis of piezoelectrically actuated curved nanosize FG beams via a nonlocal strain-electric field gradient theory Mechanics of Advanced Materials and Structures 25(4):350-359.
[29] Zhao, X., Iegaink, F. J. N., Zhu, W. D., & Li, Y. H (2019) Coupled thermo-electro-elastic forced vibrations of piezoelectric laminated beams by means of Green's functions International Journal of Mechanical Sciences.
[30] Shen H-S (2005) Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings. International Journal of Solids and Structures 42 (23):6101-6121
[31] Ke L-L, Yang J, Kitipornchai S, Xiang Y (2009) Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials. Mechanics of Advanced Materials and Structures 16 (6):488-502
[32] Cowper, G. R. (1966) The shear coefficient in Timoshenko’s beam theory. Journal of applied mechanics 33(2):335-340.